Pharmaceutical Process Engineering
Early in my professional life I was introduced to David Ganderton’s excellent
text Unit Processes in Pharmacy, first published in 1968. As my teaching
commitments grew, so did my desire to use this as a source volume. However,
I was surprised and disappointed to find that it was out of print.
Undoubtedly, there have been some classical texts on engineering principles
applied to unit operation, most notably McCabe, Smith, and Harriott
(Unit Operations of Chemical Engineering, McGraw-Hill). However, the uncomplicated
manner in which Ganderton’s book dealt with engineering principles
gave it broad appeal. In 1996, Dr. Ganderton was kind enough to collaborate
with me to reduce the original volume to two chapters for inclusion in
the Encyclopedia of Pharmaceutical Technology. This achieved my major objective
of making this material available to a new generation of pharmaceutical
scientists and technologists. However, by inclusion in an encyclopedia, some
of its earlier convenience was lost.
Imagine my delight to be invited by Marcel Dekker, Inc., to coauthor
a revised and expanded volume on the subject of pharmaceutical process engineering.
My enthusiasm was increased by the knowledge that Dr. Ganderton
would again join me in preparing the material. We have updated the previous
text and are privileged to place this volume back in print—a privilege that,
in my opinion, it should never have been denied.
Pharmaceutical manufacturing entails the combination of a number of
unit processes. The major processes are described in this text. The efficiency,
quality, and economy of manufacturing depend on an understanding of the
individual operations involved in processing. In many cases—unlike in other
types of industrial processing—safety and efficacy of a therapeutic agent may
be affected. This text constitutes a guide or introduction to the practical aspects
of unit operations in pharmacy.
It is my sincere desire that this text should again find a role as a reference
and review book for those new to the field of pharmaceutical manufacturing,
from various scientific and engineering disciplines.
Anthony J. Hickey
Forty years ago it became clear that the contribution that a pharmaceutical
scientist made to the manufacture of medicines would be enhanced by recruiting
the principles used by chemical engineers. However, simple adoption was
unsatisfactory because, in general, their texts were too complex and inadequately
focused. For example, the study of mixing and dose uniformity, drying
and product stability, and many others needed special consideration. For such
reasons, Unit Processes in Pharmacy was written and published in the late
1960s. It enjoyed many years of success before it went out of print.
A generation later, Tony Hickey, who closely shares my enthusiasm for
better understanding of pharmaceutical manufacture, suggested that the text
should be brought up to date. This was a most flattering proposal and, recognizing
the energy he has brought to the revision, I feel most privileged to see
a new text with exactly the same ambitions as those that inspired me so many
This text would not have been possible without the contributions of Mr. Vasu
Sethuraman. His endeavors with respect to the integration of chapters, production
of figures, and copyediting are greatly appreciated. There is no doubt that
his activities have contributed to the clarity and continuity of the book in its
final form. I am grateful to Dr. Paul Pluta for sharing his thoughts on solid
dosage forms and allowing me to use them in the relevant sections of the
The majority of the text of this book is based on a portion of David
Ganderton’s Unit Processes in Pharmacy, a book published in 1968 by Heineman
Medical Books, Ltd., and now out of print. It is appropriate to acknowledge
the contributions to that original volume.
The original text was the commission of Dr. D. M. Moulden. We acknowledge
the considerable help given by his ideas, plans, and drafts. In addition,
we thank Mr. Lan Boyd and Dr. John Hersey, who read and evaluated
The pharmaceutical scientist is probably familiar with the units of centimeter
(length), gram (mass), and second (time) or conventional Syste`me Internationale
(SI) units of meters, kilograms, and seconds. The engineer, on the other
hand, will sometimes express his equations and calculations in units that suit
the quantities he or she is measuring. To reconcile in small part this disparity,
a brief account of units and dimensions follows.
Mass [M], length [L], time [T], and temperature [°] are four of six fundamental
dimensions, the units of which have been fixed arbitrarily and from
which all other units can be derived. The fundamental units chosen for this
book are the kilogram (kg), meter (m), second (s), and kelvins (K). In many
cases, derived units are self-evident. Examples are area (m2) and velocity (m/s).
Others are derived from established physical laws. Thus, a unit of force can be
obtained from the law that relates force, F, to mass, m, and acceleration, a:
where k is a constant. If we choose our unit of force to be unity when the
mass and acceleration are each unity, the units are consistent. On this basis,
the unit of force is the newton (N). This is the force that will accelerate a
kilogram mass at 1 m/s2.
viii Units and Dimensions
Similarly, a consistent expression of pressure (i.e., force per unit area)
is newtons per square meter (N/m2 or pascal, Pa). The expression exemplifies
the use of multiples or fractions of the fundamental units to give derived units
of practical value. A second example is dynamic viscosity [M L1 T1] when
the consistent unit kg ? m1 ? s1, which is enormous, is replaced by kg ? m1 ?
hr1, or even by the poise. Basic calculations using these quantities must then
include conversion factors.
The relationship between weight and mass causes much confusion. A
body falling freely due to its weight accelerates at kg ? m/s2 (g varies with
height and latitude). Substituting 1 in the preceding equation gives W mg,
where W is the weight of the body (in newtons). The weight of a body has
the dimensions of force, and the mass of the body is given by
The weight of a body varies with location; the mass does not. Problems
arise when, as in many texts, the kilogram is used as a unit of mass and the
weight of a kilogram as the unit of force. For example, an equation describing
pressure drop in a pipe is
when written in consistent units—?P as N/m2, ? as kg/m ? s, u as m/s, l as
m, and d as m. If, however, the kilogram force was used (i.e., pressure was
measured in kg/m2), the equation must be
where g 9.8 m/s2. In texts using this convention, the conversion factor g
appears in many equations.
The units of mass, length, and time commonly used in engineering heat
transfer are the kilogram, the meter, and the second, respectively. Temperature,
which forms a fourth fundamental unit, is measured in kelvins (K). The
unit of heat is the joule (J), which is the quantity of heat required to raise the
temperature of 1 g of water by 1 K. The rate of heat flow, Q, often referred
to as the total heat flux, is therefore measured in J/s. The units of thermal conductivity
are J/m2 ? s ? K/m. This may also be written as J/m ? s ? K, although
this form is less expressive of the meaning of the thermal conductivity.
Units and Dimensions vii
1. Fluid Flow 1
2. Heat Transfer 36
3. Mass Transfer 56
4. Powders 66
5. Air Conditioning and Humidification 79
6. Drying 86
7. Solid–Liquid Extraction 110
8. Crystallization 117
9. Evaporation and Distillation 128
10. Filtration 150
11. Size Reduction and Classification 174
12. Mixing 198
13. Solid Dosage Forms 215
14. Sterilization 228
15. Bioprocessing 235
1.1 SOME PROPERTIES OF FLUIDS
Fluids (liquids and gases) are a form of matter that cannot achieve equilibrium
under an applied shear stress but deform continuously, or flow, as long as the
shear stress is applied.
Viscosity. Viscosity is a property that characterizes the flow behavior
of a fluid, reflecting the resistance to the development of velocity gradients
within the fluid. Its quantitative significance may be explained by reference
to Figure 1.1 A fluid is contained between two parallel planes each of area A
m2 and distance h m apart. The upper plane is subjected to a shear force of
F N and acquires a velocity of u m sec1 relative to the lower plane. The shear
stress, t, is F/A N m2. The velocity gradient or rate of shear is given by u/
h or, more generally, by the differential coefficient du/dy, where y is a distance
measured in a direction perpendicular to the direction of shear. Since this term
is described by the units velocity divided by a length, it has the dimension
T1 or, in this example, reciprocal seconds. For gases, simple liquids, true
solutions, and dilute disperse systems, the rate of shear is proportional to the
shear stress. These systems are called Newtonian, and we can write
2 Chapter 1
FIGURE 1.1 Schematic of fluid flow depicting the applied force, velocity in the direction
of motion, and thickness of fluid.
t ? du
The proportionality constant ? is the dynamic viscosity of the fluid: the
higher its value, the lower the rates of shear induced by a given stress. The
dimensions of dynamic viscosity are M L1 T1. For the SI system of units,
viscosity is expressed in N ?s m2. For the centimeter-gram-second (CGS)
system, the unit of viscosity is the poise (P). One N ?s m2 is equivalent to
10 P. The viscosity of water at room temperature is about 0.01 P or 1 centipoise
(cP). Pure glycerin at this temperature has a value of about 14 P. Air has a
viscosity of 180 106 P.
Complex disperse systems fail to show the proportionality described by
equation 1.1, the viscosity increasing or, more commonly, decreasing with
increase in the rate of shear. Viscosity may also depend upon the duration of
shear and even on the previous treatment of the fluids. Such fluids are termed
Equation 1.1 indicates that wherever a velocity gradient is induced
within a fluid, a shear stress will result. When the flow of a fluid parallel to
some boundary is considered, it is assumed that no slip occurs between the
boundary and the fluid, so the fluid molecules adjacent to the surface are at
rest (u 0). As shown in Figure 1.2, the velocity gradient du/dy decreases
from a maximum at the boundary (y 0) to zero at some distance from the
boundary (y y?) when the velocity becomes equal to the undisturbed velocity
of the fluid (u u?). The shear stress must, therefore, increase from zero at
this point to a maximum at the boundary. A shear stress, opposing the motion
of the fluid and sometimes called fluid friction, is therefore developed at the
boundary. The region limited by the dimension y?, in which flow of the fluid
is perturbed by the boundary, is called the boundary layer. The structure of
this layer greatly influences the rate at which heat is transferred from the
Fluid Flow 3
FIGURE 1.2 Distribution of velocities at a boundary.
boundary to the fluid under the influence of a temperature gradient or the rate
at which molecules diffuse from the boundary into the fluid under a concentration
gradient. These topics are discussed in Chapters 2 and 3.
Compressibility. Deformation is not only a shear-induced phenomenon.
If the stress is applied normally and uniformly over all boundaries, then
fluids, like solids, decrease in volume. This decrease in volume yields a proportionate
increase in density. Liquids can be regarded as incompressible, and
changes of density with pressure can be ignored, with consequent simplification
of any analysis. This is not possible in the study of gases if significant
changes in pressure occur.
Surface Tension. Surface tension, a property confined to a free surface
and, therefore, not applicable to gases, is derived from unbalanced intermolecular
forces near the surface of a liquid. This may be expressed as the work
necessary to increase the surface by unit area. Although not normally important,
it can become so if the free surface is present in a passage of smalldiameter
orifice of tube. Capillary forces, determined by the surface tension
and the curvature of the surface, may then be comparable in magnitude to
other forces acting in the fluid. An example is found in the movement of liquid
through the interstices of a bed of porous solids during drying.
1.2 FLUIDS AT REST—HYDROSTATICS
The study of fluids at rest is based on two principles:
1. Pressure intensity at a point, expressed as force per unit area, is the
same in all directions.
4 Chapter 1
2. Pressure is the same at all points in a given horizontal line in a
The pressure, P, varies with depth, z, in a manner expressed by the hydrostatic
dP ?g dz (1.2)
where ? is the density of the fluid and g is the gravitational constant. Since
water and most other liquids can be regarded as incompressible, the density
is independent of the pressure, and integration between the limits P1 and P2,
z1 and z2, gives
P1 P2 ?g(z1 z2) (1.3)
1.3 THE MEASUREMENT OF PRESSURE
Application of equation 1.3 to the column of liquid shown in Figure 1.3(a)
PA P1 ?gh
P1 PA ?gh
FIGURE 1.3 Pressure measurement apparatus.
Fluid Flow 5
The density term should be the difference between the density of the
liquid in the column and the density of the surrounding air. The latter is relatively
small and this discrepancy can be ignored. P1 is the absolute pressure
at the point indicated, and PA is the atmospheric pressure. It is often convenient
to refer to the pressure measured relative to atmospheric pressure, i.e., P1
PA. This is called the gauge pressure and is equal to ?gh. Pressure measured
in SI units has units of N m2. Alternatively, the gauge pressure can be expressed
as the height or head of a static liquid that would produce this pressure.
Figure 1.3(a) represents the simplest form of manometer, a device
widely used for the measurement of pressure. It consists of a vertical tube
tapped into the container of the fluid under study. In this form, it is confined
to the pressure measurement of liquids. This device is unsuitable for the measurement
of very large heads, due to unwieldy construction, or very small
heads, due to low accuracy. The U-tube manometer, shown in Figure 1.3(b),
may be used for the measurement of higher pressures with both liquids and
gases. The density of the immiscible liquid in the U-tube, ?1 is greater than
the density of the fluid in the container, ?2. The gauge pressure is given by
P h1?1g h2?2g
The disadvantage of reading two levels may be overcome by the modi-
fication in Figure 1.3(c). The cross-sectional area of one limb is many times
larger than that of the other, and the vertical movement of the heavier liquid
in the wider arm can be neglected and its level is assumed to be constant.
Sloping the reading arm of the manometer can increase the accuracy of
the pressure determination, for small heads, with any of the manometers just
described. The head is now derived from the distance moved along the tube
and the angle of slope.
The Bourdon gauge, a compact instrument widely used for the measurement
of pressure, differs in principle from the manometer. The fluid is admitted
to a sealed tube of oval cross section, the shape of which is shown in
Figure 1.3(d). The straightening of the tube under internal pressure is opposed
by its elasticity. The movement to an equilibrium position actuates a recording
mechanism. The gauge is calibrated by an absolute method of pressure measurement.
The principles of pressure measurement also apply to fluids in motion.
However, the presence of the meter should minimize perturbation in flow. A
calming section, in which a flow regime becomes stable, is present upstream
from the pressure tapping, and the edge of the latter should be flush with the
inside of the container to prevent flow disturbance.
6 Chapter 1
1.4 FLUIDS IN MOTION
Streamlines are hypothetical entities without width that are drawn parallel at
all points to the motion of the fluid. Figure 1.4 illustrates their use in depicting
the flow of a fluid past a cylinder. If the flow at any position does not vary
with time, it is steady and the streamlines retain their shape. In steady flow,
a change in the spacing of the streamlines indicates a change in velocity because,
by definition, no fluid can cross a streamline. In the regions on the
upstream side of the cylinder, the velocity of the fluid is increasing. On the
downstream side, the reverse occurs. The maximum velocity occurs in the
fluid adjacent to regions B and D. At points A and C, the fluid is at rest. As
the velocity increases, the pressure decreases. The pressure field around the
cylinder is therefore the reverse of the velocity field. This statement may appear
to contradict common experience. However, it follows from the principle
of conservation of energy and finds expression in Bernoulli’s theorem.
1.5 BERNOULLI’S THEOREM
At any point in flowing fluid, the total mechanical energy can be expressed
in terms of the following components: potential energy, pressure energy, and
kinetic energy. The potential energy of a body is its capacity to do work by
reason of its position relative to some center of attraction. For a unit mass of
fluid at a height z above some reference level,
Potential energy zg
where g is the acceleration due to gravity.
FIGURE 1.4 Flow of a fluid past a cylinder.
Fluid Flow 7
The pressure energy or flow energy is an energy form peculiar to the
flow of fluids. Figure 1.5 describes the flow of a volume of fluid, abdc, across
the section XX1. The work done and the energy acquired in transferring the
fluid are the product of the pressure, P, and the volume. The volume of unit
mass of the fluid is the reciprocal of the density, ?. For an incompressible
fluid, the density is not dependent on the pressure, so that for a unit mass of
The kinetic energy is a form of energy possessed by a body by reason
of its movement. If the mass of the body is m and its velocity is u, the kinetic
energy is 1/2 mu2, and for a unit mass of fluid,
The total mechanical energy of a unit mass of fluid is, therefore,
The mechanical energy at two points, A and B, will be the same if no
energy is lost or gained by the system. Therefore, we can write
FIGURE 1.5 Pressure energy of a fluid.
8 Chapter 1
This relationship neglects the frictional degradation of mechanical energy that
occurs in real systems. A fraction of the total energy is dissipated in overcoming
the shear stresses induced by velocity gradients in the fluid. If the energy
lost during flow between A and B is E, then equation 1.5 becomes
zBg E (1.6)
This is a form of Bernoulli’s theorem, restricted in application to the flow of
incompressible fluids. Each term is expressed in absolute units, such as N m
kg1. The dimensions are L2 T2. In practice, each term is divided by g(L T2)
to give the dimension of length. The terms are then referred to as velocity
head, pressure head, potential head, and friction head, the sum giving the total
head of the fluid:
The evaluation of the kinetic energy term requires consideration of the
variation in velocity found in a direction normal to flow. The mean velocity,
calculated by dividing the volumetric flow rate by the cross-sectional area of
the pipe, lies between 0.5 and 0.82 times the maximum velocity found at the
pipe axis. The value depends on whether flow is laminar or turbulent, terms
which are described later. The mean kinetic energy, given by u2
from the true kinetic energy found by summation across the flow direction.
The former can be retained, however, if a correction factor, a, is introduced.
where a has a value of 0.5 in laminar flow and approaches unity when flow
is fully turbulent.
A second modification may be made to equation 1.5 if mechanical energy
is added to the system at some point by means of a pump. If the work
done, in absolute units, on a unit mass of fluid is W, then
Fluid Flow 9
The power required through a system at a certain rate may be calculated using
equation 1.8 to drive a liquid. The changes in velocity, pressure, height, and
the mechanical losses due to friction are each expressed as a head of liquid.
The sum of heads, ?H, is the total head against which the pump must work.
If the work performed and energy acquired by unit mass of fluid is ?Hg, then
the power required to transfer mass m in time t is
Since the volume flowing in unit time, Q, is m/?t, then
Power Q?Hg? (1.9)
1.6 FLOW MEASUREMENT
The Bernoulli theorem can also be applied to the measurement of flow rate.
Consider the passage of an incompressible fluid through the constriction
shown in Figure 1.6. The increase in kinetic energy as the velocity increases
from u1 to u2 is derived from the pressure energy of the fluid, the pressure of
which drops from P1 to P2, the latter being recorded by manometers. There
is no change in height, and equation 1.5 can be rearranged to give
FIGURE 1.6 Flow through a constriction.
10 Chapter 1
The volumetric flow rate Q u1a1 u2a2. Therefore, by rearrangement,
Substituting for u1 gives
u2 v 2(P1 P2)
Q a2 v 2(P1 P2)
The derivation neglects the correction of kinetic energy due to nonuniformity
of flow in both cross sections and the frictional degradation of energy during
passage through the constriction. This is corrected by the introduction of a
numerical coefficient, CD, known as the coefficient of discharge. Therefore,
Q CDa2 v 2(P1 P2)
The value of CD depends upon conditions of flow and the shape of the constriction.
For a well-shaped constriction, such as that shown in Figure 1.6, it would
vary between 0.95 and 0.99 for turbulent flow. The value is much lower in
laminar flow because the kinetic energy correction is larger. The return of the
fluid to the original velocity by means of a diverging section forms a flowmeasuring
device known as the Venturi meter.
Fluid Flow 11
FIGURE 1.7 Flow meters.
The Venturi meter is shown in Figure 1.7(a). The converging cone leads
to the narrowest cross section, known as the throat. The change in pressure
is measured across this part of the meter, and the volumetric flow rate found
by substitution into equation 1.11. Values of the coefficient of discharge are
given in the preceding paragraph. The diverging section, or diffuser, is designed
to induce a gradual return to the original velocity. This minimizes eddy
formation in the diffuser and permits the recovery of a large proportion of the
increased kinetic energy as pressure energy. The permanent loss of head due
to friction in both converging and diverging sections is small. The meter is
When the minimization of energy degradation is less important, the
gradual, economical return to the original velocity may be abandoned, compensation
for loss of efficiency being found in a device that is simpler, cheaper,
and more adaptable than the Venturi meter. The orifice meter, to which this
statement applies, consists simply of a plate with an orifice. A representation
12 Chapter 1
of flow through the meter is shown in Figure 1.7(b), indicating convergence
of the fluid stream after passage through the orifice to give a cross section of
minimum area called the vena contracta. The downstream pressure tapping
is made at this cross section. The volumetric flow rate is given by equation
1.11, for which a2 is the jet area at the vena contracta. The measurement of
a2 is inconvenient. It is therefore related to the area of the orifice, a0, which
can be accurately measured, by the coefficient of contraction, Cc, defined by
The coefficient of contraction, frictional losses between the tapping
points, and kinetic energy corrections are absorbed in the coefficient of discharge.
The volumetric flow rate is then
Q a0v 2(P1 P2)
The term 1 a20
1 approaches unity if the orifice is small compared to the
pipe cross section. Since P2 P1 ?h?g, where ?h is the difference in head
developed by the orifice, equation 1.12 reduces to
Q a0CD v2?hg (1.13)
The value of CD for the orifice meter is about 0.6, varying with construction,
the ratio a0/a1, and flow conditions within the meter. Due to its complexity,
it cannot be calculated. After passage through the orifice, flow disturbance
during retardation causes the dissipation of most of the excess kinetic energy
as heat. The permanent loss of head is therefore high, increasing as the ratio
a0/a1 falls and ultimately reaching the differential head produced within the
meter. When constructional requirements and methods of installation are followed,
the correcting coefficients can be derived from charts. Alternatively,
the meters can be calibrated.
The Bernoulli theorem may be used to determine the change in pressure
caused by retardation of fluid at the upstream side of a body immersed in a
fluid stream. This principle is applied in the use of the Pitot tube, shown in
Figure 1.7(c). The fluid velocity is reduced from ua, the velocity of the fluid
filament in alignment with the tube, to zero at B, a position known as the
stagnation point. The pressure, Pb, is measured at this point by the method
shown in Figure 1.7(c). The undisturbed pressure, Pa, is measured in this examFluid
ple with a tapping point in the wall connected to a manometer. Since the
velocity at B is zero, equation 1.10 reduces to
and ua can be calculated. Since only a local velocity is measured, variation
of velocity in a section can be studied by altering the position of the tube.
This procedure must be used if the flow rate in a pipe is to be measured. The
mean velocity is derived from velocities measured at different distances from
the wall. This derivation and the low-pressure differential developed render
the Pitot tube less accurate than either the Venturi tube or the orifice meter
for flow measurement. However, the tube is small in comparison with the pipe
diameter and therefore produces no appreciable loss of head.
The rotameter (a variable-area meter), shown in Figure 1.7(d), is commonly
used, giving a direct reading of flow rate by the position of a small
float in a vertical, calibrated glass tube through which the fluid is flowing.
The tube is internally tapered toward the lower end so that the annulus between
float and wall varies with the position of the float. Acceleration of the fluid
through the annulus produces a pressure differential across the position of the
float and an upward force upon it. At the equilibrium position, which may be
stabilized by a slow rotation of the float, the weight force acting on the float
balances this upward force. If increasing the rate of flow disturbs equilibrium,
the balance of weight force and pressure differential is produced by movement
of the float upward to a position at which the area of the annulus is bigger.
For accurate measurement, the rotameter is calibrated with the fluid to be
metered. Its use is then restricted to that fluid. A theoretical derivation of flow
rate is also available.
1.7 LAMINAR AND TURBULENT FLOWS
The translation of the energy of flow from one form to another has been described
with little reference to the actual nature of flow. Flow of fluids can
be laminar (and may be depicted by streamlines) or turbulent, terms that are
best introduced by describing a series of simple experiments performed in
1883 by Osborne Reynolds. The apparatus, shown in Figure 1.8, consisted of
a straight glass tube through which the fluid was allowed to flow. The nature
of flow was examined by introducing a dye into the axis of the tube. At low
speeds, the dye formed a coherent thread that grew very little in thickness
14 Chapter 1
FIGURE 1.8 The Reynolds experiment (diagrammatic).
with distance down the tube. However, with progressive increase in speed,
the line of dye first began to waver and then to break up. Secondary motions,
crossing and recrossing the general flow direction, were clearly revealed. Finally,
at very high speeds, no filament of dye could be detected, and mixing
to a dilute color was almost instantaneous. In this experiment, flow changed
from laminar to turbulent, the change occurring at a critical speed. In the
former, flow was ordered, always moving parallel to the walls of the tube.
Generalizing, in laminar flow the instantaneous velocity at a point is always
the same as the mean velocity in both magnitude and direction. In turbulent
flow, order is lost and irregular motions are imposed upon the main steady
motion of the fluid. At any instant of time, the fluid velocity at a point varies
in magnitude and direction, having components perpendicular, as well as parallel,
to the direction of net flow. Over time, these fluctuations even out to
give the net velocity in the direction of flow.
In turbulent flow, rapidly fluctuating velocities produce high-velocity
gradients within the fluid. Proportionately large shear stresses are developed,
and to overcome them mechanical energy is degraded and dissipated in the
form of heat. The degradation of energy in laminar flow is much smaller.
The random motions of turbulent flow provide a mechanism of momentum
transfer not present in laminar flow. If a variation in velocity occurs across
Fluid Flow 15
a fluid stream, as in a pipe, a quantity of fast-moving fluid can move across
the flow direction to a slower-moving region, increasing the momentum of
the latter. A corresponding movement must take place in the reverse direction
elsewhere, and a complementary set of rotational movements, called an eddy,
is imposed on the main flow. This is a powerful mechanism for equalizing
momentum. By the same mechanism, any variation in the concentration of a
component is quickly eliminated. Admitting dye to the fluid stream in Reynolds’
original experiment showed this. Similarly, the gross mixing of turbulent
flow quickly erases variations in temperature.
The turbulent mechanism that carries motion, heat, or matter from one
part of the fluid to another is absent in laminar flow. The shear stress arises
from the variations in velocity; i.e., the viscosity brings about momentum
transfer. Similarly, heat and matter can only be transferred across streamlines
on a molecular scale, heat by conduction and matter by diffusion. These mechanisms,
which are present but less important in turbulent flow, are comparatively
slow. Velocity, temperature, and concentration gradients are, therefore,
much greater than in turbulent flow.
1.8 LIQUIDS FLOW IN PIPES
The many pharmaceutical processes that involve the transfer of a liquid from
one place to another confer great importance on the study of flow in pipes.
This study permits the evaluation of pressure loss due to friction in a simple
pipe and assesses the additional effects of pipe roughness, changes in diameter,
bends, exits, and entrances. When the total pressure drop due to friction is
known for the system, the equivalent head can be derived and the power requirement
for driving a liquid through the system can be calculated from equation
1.8.1 Streamline Flow in a Tube
The mathematical analysis of streamline flow in a simple tube is complete
and results in the expression known as Poiseuille’s law, one form of which
where Q is the volumetric flow rate or discharge, ?P is the pressure drop
16 Chapter 1
FIGURE 1.9 Streamline flow: velocity distribution in a pipe.
across the tube, d and l are the diameter and length of the tube, respectively,
and ? is the fluid viscosity.
Whether flow in the tube is streamline or turbulent, an infinitesimally
thin stationary layer is found at the wall. The velocity increases from zero at
this point to a maximum at the axis of the tube. For streamline flow, the velocity
profile is presented in Figure 1.9(a). The velocity gradient, du/dr, varies
from a maximum at the wall to zero at the axis. In flow through a tube, the
rate of shear is equal to the velocity gradient, so that equation 1.1 dictates the
same variation of shear stress.
To derive Poiseuille’s law, the form of the velocity profile must first be
established. Consider the fluid contained within a radius r flowing in a tube
of radius R. This is shown in Figure 1.9(b). If the pressure drop across length
l is ?P, the force attributed to the applied pressure driving this section is
?P?r 2. If flow is steady, this force can only be balanced by opposing viscous
forces acting on the ‘‘wall’’ of the section. This force, the product of the shear
stress ? and the area over which it acts, is 2t?l. The expression given by
equating these forces is
Fluid Flow 17
Substituting from equation 1.1 gives
The velocity gradient is negative because u decreases as r increases. When r
R, u 0. Integrating gives
2?l R2 r 2
This relation shows that the velocity distribution across the tube is parabolic.
For such a distribution, the maximum velocity is twice the mean velocity. The
volumetric flow rate across the annular section between r and r dr, shown
in Figure 1.9(c), is
Q 2?r ? dr ? u
Substituting for u from equation 1.15 gives
(R2 r r 3) dr
The total volumetric flow rate is the integral between the limits r R and r
(R2 r r 3) dr
2?l R2 r 2
18 Chapter 1
where d is the diameter of the tube. Since Q umean?d2/4, substitution and
1.8.2 Dimensional Analysis and Flow through
a Tube: A General Approach
The utility of equation 1.16 for evaluating the loss of pressure due to friction
in a tube is limited because streamline conditions are rare in practice. The
theoretical analysis of turbulent flow, however, is incomplete, and experiments
with fluids are necessary for the development of satisfactory relations between
the controlling variables. In such experiments, it is often not possible to study
the relation of two variables, one in terms of the other, while other variables
are temporarily held constant. Dimensional analysis is a procedure in which
the interaction of variables is presented in such a way that the effect of each
variable can be assessed.
The method is based on the requirement that the dimensions of all terms
of a physically meaningful equation are the same; i.e., an equation must be
dimensionally homogeneous. This principle may be usefully illustrated by reference
to equation 1.14 written in the form
Rewriting in basic units of mass, length, and time, and using the symbol [ ]
to represent dimensions of, [Q] [L3 T1], [?P] [M L1 T2], [dn] [Ln],
and [?] [M L1 T1]. Equating gives
[L3 T2] M L1 T2 ? Ln
M L1 T1 ? L [Ln1 T1]
[M] and [T] are correct, as they must be. Equating for [L] gives [L3] [Ln1],
from which n 4.
If no previous knowledge of the combined form of the variables that
determine Q is available, dimensional analysis can be applied in the following
way. The dependence of Q on ?P, l, d, and ? can be written as
Q f(?P, l, d, ?)
Fluid Flow 19
The function f can be expressed as a series, each term of which is the product
of the independent variables raised to suitable powers. Taking the first term
of the series gives
Q N ? ?Pw ? l x ? dy ? ?z
where N is a numerical factor (dimensionless). Rewriting terms as [Q] [L3
T1], [?Pw] [Mw Lw T2w], [l x] [Lx], [dy] [Ly], and [?z] [Mz Lz Tz],
the equation [Q] [?Pw ? l x ? dy ? ?z] becomes [L3 T1] [Mw Lw T2w ? Lx
? Ly ? Mz Lz Tz].
Equating powers of M, L, and T gives the system
M: 0 w z
L: 3 w x y z
T: 1 2w z
Since four unknowns are present in three simultaneous equations, three may
be determined in terms of the fourth. Solving gives w 1, z 1, and x
y 3. Expressing y as 3 x; one gets
Q N ?P
d3x l x
The first part of the example demonstrates the use of dimensions as a
partial check on the derivation or completeness of a solution. In the second
part, a solution, although incomplete, gives considerable information about
discharge of a fluid in streamline flow and its relation to pressure drop, viscosity,
and the geometry of the pipe without any theoretical or experimental analysis.
For example, if two tubes had the same ratio l/d, the values of Q?/d3?P
would also be the same.
Since the exponent x in equation 1.17 is indeterminate, the term in brackets
must be dimensionless. Unlike the lengths from which it is derived, it is
a pure number and needs no system of units for meaningful expression. Its
value is, therefore, independent of the units chosen for its measurement, providing,
of course, that the systems of measurement are not mixed. The equation
may therefore be presented as the relation between two dimensionless groups:
20 Chapter 1
or, since a series of power terms will, in general, form the original unknown
function, each of which has different values of N and x,
The study of frictional losses at the wall of a pipe is facilitated by dimensional
analysis. The shear stress—that is, the force opposing motion of the
fluid acting on each unit of area of the pipe, R—is determined, for a given
pipe surface, by the velocity of the fluid, u, the diameter of the pipe, d, the
viscosity of the fluid, ?, and the fluid density, ?. The equation of dimensions
[R] [u0 ? dq ? ?r ? ?s]
M L1 T2 Lp Tp ? Lq ? Mr Lr Tr ? Ms L3s
Equating M, L, and T, one gets
M: 1 r s
L: 1 p q r 3s
T: 2 p r
Solving for p, r, and s in terms of q gives r q, s 1 q, and p 2
R N ? u2q ? dq ? ?q ? ?1q N ?u2ud?
where N is a numerical factor. Generalizing, R/?u2, which is the friction factor,
is a function of a dimensionless combination of u, d, ?, and ?. This combination
gives a parameter known as the Reynolds number, Re. Therefore,
The form of this relation must largely be determined by experiment. If
the friction factor, R/?u2, is plotted against Re, all data lie on a single curve
which, although restricted to a particular pipe surface, will apply to all fluids,
all pipe diameters, and all velocities.
Fluid Flow 21
In turbulent flow, the shear stress at the wall depends upon the surface,
the value being higher for a rough pipe than for a smooth pipe when flow
conditions are otherwise the same. Equation 1.19 therefore yields a family of
curves when pipes of differing surface condition are used. This is rationalized
by the introduction of another dimensionless group, e/d, in which e is a linear
dimension expressing roughness. Values of e are known for many materials.
The complete dimensionless correlation, plotted on logarithmic coordinates
so that widely varying conditions are covered, is given in Figure 1.10.
The curve can be divided into four regions. When Re 2000, flow is streamline
and the equation of the line in this region is R/?u2 8/Re. This is simply
another form of Poiseuille’s law. The friction factor is independent of the
roughness of the pipe and all data fall on a single line.
When Re lies between 2000 and 3000, flow normally becomes turbulent.
The exact value of the transition depends upon the idiosyncrasies of the system.
For example, in a smooth pipe, streamline conditions will persist at higher
Reynolds number than in a pipe in which disturbances are created by surface
At higher values of Re, flow becomes increasingly turbulent to give a
region in which the friction factor is a function of Re and surface roughness.
Ultimately, this merges with a region in which the friction factor is indepen-
FIGURE 1.10 Pipe friction chart.
22 Chapter 1
dent of Re. Flow is fully turbulent and, for a given surface, the shear stress
at the pipe wall is proportional to the square of the fluid velocity. The onset
of the fourth region occurs at a lower Re in rough pipes.
The essential difference between laminar flow and turbulent flow has
already been described. In a pipe, the enhanced momentum transfer of the
latter modifies the velocity distribution. In laminar flow, this distribution is
parabolic. In turbulent flow, a much greater equalization of velocity occurs,
the velocity profile becomes flatter, and high-velocity gradients are confined
to a region quite close to the wall. In both cases, the boundary layer, the region
in which flow is perturbed by the presence of the boundary, extends to the
pipe axis and completely fills the tube. In laminar conditions, the structure of
the layer is quite simple, layers of fluid sliding one over another in an orderly
fashion. In turbulent flow, however, division can be made into three regimes:
(1) The core of fluid is turbulent. (2) In a thin layer at the wall a fraction of
a millimeter thick, laminar conditions persist. This is called the laminar
sublayer and it is separated from the turbulent core by (3) a buffer layer in
which transition from turbulent flow to laminar flow occurs.
This description of the turbulent boundary layer applies generally to the
flow of fluids over surfaces. The properties of this layer are central in many
aspects of the flow of fluids. In addition, these properties determine the rate
at which heat or mass is transferred to or from the boundary. These subjects
are described in Chapters 2 and 3.
1.9 THE SIGNIFICANCE OF REYNOLDS’
In Reynolds’ experiment, described previously, progressive increase in velocity
caused a change from laminar flow to turbulent flow. This change would
also have occurred if the diameter of the tube was increased while maintaining
the velocity, or if the fluid was replaced by one of higher density. On the other
hand, an increase in viscosity could promote a change in the opposite direction.
Obviously, all these factors are simultaneously determining the nature of flow.
These factors, which alone determine the character of flow, combine to give
some value of Re. This indicates that the forces acting on some fluid element
have a particular pattern. If some other geometrically similar system has the
same Re, the fluid will be subject to the same force pattern.
More specifically, the Reynolds number describes the ratio of the inertia
and viscous or frictional forces. The higher the Reynolds number, the greater
will be the relative contribution of inertial effects. At very low Re, viscous
Fluid Flow 23
FIGURE 1.11 Flow of a fluid past a cylinder.
effects predominate and the contribution of inertial forces can be ignored. A
clear example of the changing contributions of viscous and inertia or momentum
effects and the resulting changes in the flow pattern is given in Figure
1.11. A Reynolds number can also characterize flow in this quite different
1.10 CALCULATION OF THE PRESSURE
DROP IN A PIPE DUE TO FRICTION
If the volumetric flow rate of a liquid of density ? and viscosity ? through a
pipe of diameter d is Q, the derivation of the mean velocity, u, from the flow
rate and pipe area completes the data required for calculating Re. If the pipe
roughness factor is known, the equivalent value of R/?u2 can be determined
from Figure 1.10, and the shear stress at the pipe wall can be calculated. The
total frictional force opposing motion is the product of R and the surface area
of the pipe, ?dl, where l is the pipe length. If the unknown pressure drop
across the pipe is ?P, the force driving the fluid through the pipe is ?P
(?d2/4). Equating pressure force and frictional force gives
Division by ?g gives the pressure loss as a friction head. This form is
used in equations 1.7 and 1.8.
24 Chapter 1
1.11 FLOW IN TUBES OF NONCIRCULAR
Discussion of flow in pipes has been restricted to pipes of circular cross section.
The previous exposition may be applied to turbulent flow in noncircular
ducts by introducing a dimension equivalent to the diameter of a circular pipe.
This is known as the mean hydraulic diameter, dm, which is defined as four
times the cross-sectional area divided by the wetted perimeter. The following
examples are given:
For a square channel of side b:
For an annulus of outer radius r1 and inner radius r2:
This simple modification does not apply to laminar flow in noncircular ducts.
1.12 FRICTIONAL LOSSES AT PIPE FITTINGS
Losses occur at the various fittings and valves used in practical systems in
addition to the friction losses at the wall of a straight pipe. In general, these
losses are derived from sudden changes in the magnitude or direction of flow
induced by changes in geometry. They can be classified as loss due to a sudden
contraction or enlargement, losses at entrance or exit, and loss due to pipe
curvature. Losses can be conveniently expressed as a length of straight pipe
offering the same resistance. This is usually in the form of a number of pipe
diameters. For example, the loss at a right-angled elbow is equivalent to a
length of straight pipe equal to 40 diameters. The sum of the equivalent lengths
of all fittings and valves is then added to the actual pipe length and the total
frictional loss is estimated by equation 1.20.
1.13 MOTION OF BODIES IN A FLUID
When a body moves relative to a fluid in which it is immersed, resistance to
motion is encountered and a force must be exerted in the direction of relative
body movement. The opposing drag force is made up from two components:
Fluid Flow 25
viscous drag and form drag. This may be explained by reference to Figure
1.11, which describes the flow past a body, in this case a cylinder with axis
normal to the page, by means of streamlines. As mentioned, streamlines are
hypothetical lines drawn tangential at all points to the motion of the fluid.
Flow past the cylinder immobilizes the fluid layer in contact with the surface,
and the induced velocity gradients result in a shear stress or viscous drag on
the surface. The crowding of streamlines on the upstream face of the cylinder
to points B and D indicates an increase in velocity and, therefore, a decrease
in pressure. If there is to be no inertial force acting on the cylinder, the flow
pattern and momentum changes on the downstream surface must be exactly
reversed. This is shown in Figure 1.11(a), and the entire force opposing relative
motion of the cylinder and fluid is viscous drag. However, conditions of
increasing pressure and decreasing velocity that exist on the downstream surface
may cause the boundary layer to separate. The region between the breakaway
streamlines—the wake—is occupied by eddies and vortices, and the
flow pattern shown in Figure 1.11(b) is established. The kinetic energy of the
accelerated fluid is dissipated and not recovered as pressure energy on the
downstream surface. Under these conditions, there is a second component to
the force opposing relative motion. This is known as form drag. Its contribution
to the total drag increases as the velocity increases.
Once again, viscous and inertial forces are operating to determine the
flow pattern and drag force on a body moving relative to a fluid. Reynolds
number, which expresses their ratio, is used as a parameter to predict flow
behavior. The relation between the drag force and its controlling variables is
presented in a manner similar to that employed for flow in a pipe. If we consider
a sphere moving relative to a fluid, the projected area normal to flow is
where d is the diameter of the sphere. The drag force acting on unit projected
area, R?, is determined by the fluid’s velocity, u, viscosity, ?, and density, ?,
and by d. Dimensional analysis yields the relation
f(Re?) f ud?
This form of Reynolds number, Re?, employs the sphere diameter as the linear
dimension. With the exception of an analysis at very low Reynolds numbers,
the form of this function is established by experiment. Results are presented
on logarithmic coordinates in Figure 1.12. When Re? 0.2, viscous forces
are solely responsible for drag on the sphere and equation 1.21 is
26 Chapter 1
FIGURE 1.12 R?/?u2 vs. Re? for a smooth sphere.
Total drag force R? ?d2
This is the normal form of Stokes’ law.
At larger values of Re?, the experimental curve progressively diverges
from this relation, ultimately becoming independent of Re? and giving R?/?u2
0.22. As Re? increases, the form drag increases, ultimately becoming solely
responsible for the force opposing motion.
For nonspherical particles the analysis employs the diameter of a sphere
of equivalent volume. A correction factor, which depends upon the shape of
the body and its orientation in the fluid, must then be applied.
An important application of this analysis is the estimation of the speed
at which particles settle in a fluid. Under the action of gravity, the particle
accelerates until the weight force, mg, is exactly balanced by the opposing
drag. The body then falls at a constant terminal velocity u. Equating weight
and drag forces gives
d3 (?s ?)g R? ?d2
where ?s is the density of the particle.
Fluid Flow 27
For a sphere falling under streamline conditions (Re? 0.2), R? ?u2
(12/Re?). Substituting in equation 1.23, we obtain
This expression follows more simply from the equation mg 3 ??du.
1.14 FLOW OF FLUIDS THROUGH PACKED
Fluids flow analysis through a permeable bed of solids is widely applied in
filtration, leaching, and several other processes. A first approach may be made
by assuming that the interstices of the bed correspond to a large number of
discrete, parallel capillaries. If flow is streamline, the volumetric flow rate, Q,
is given for a single capillary by equation 1.14:
where l is the capillary length, d is capillary diameter, ?P is the pressure drop
across the capillary, and ? is the fluid viscosity. The capillary length will
exceed the depth of the bed by an amount that depends upon its tortuosity.
The bed depth L is, however, proportional to l, so
where k is a constant for a particular bed. If the area of the bed is A and
contains n capillaries per unit area, the total flow rate is given by
Although n and d are not normally known, they have certain values for a given
bed so that
where K d4n/k is a permeability coefficient and 1/K is the specific resistance.
Its value characterizes a particular bed.
The postulate of discrete capillaries precludes valid comment on the
28 Chapter 1
factors that determine the permeability coefficient. Channels are not discrete
but are interconnected in a random manner. Nevertheless, the resistance to the
passage of fluid must depend on the number and dimensions of the channels.
These quantities can be expressed in terms of the fraction of the bed that is
void—that is, the porosity—and the manner in which the void fraction is
distributed. With reference to a specific example, water flows more easily
through a bed with a porosity of 40% than through a bed of the same material
with a porosity of 25%. It also flows more quickly through a bed of coarse
particles than through a bed of fine particles packed to the void fraction or
porosity. The latter effect can be expressed in terms of the surface area offered
to the fluid by the bed. This property is inversely proportional to the size of
the particles forming the bed. Permeability increases as the porosity increases
and the total surface of the bed decreases, and these factors may be combined
to give the hydraulic diameter, d?, of an equivalent channel, defined by
Volume of voids
Total surface of material forming bed
The volume of voids is the porosity, and the volume of solids is 1 ?. If the
specific surface area, that is, the surface area of unit volume of solids, is S0,
the total surface presented by unit volume of the bed is S0(1 ?). Therefore;
Under laminar flow conditions, the rate at which a fluid flows through
this equivalent channel is given by Poiseuille’s equation, 1.14:
The velocity, u?, in the channel is derived by dividing the volumetric flow
rate by the area of the channel, k?d?2. Combining the constants produces
This velocity, when averaged over the entire area of the bed, solids, and voids,
gives the lower value u. These velocities are related by the equation u u??.
Fluid Flow 29
Substituting for d? by means of equation 1.26 gives
(1 ?)2 S20
In this equation, known after its originator as Kozeny’s equation, the constant
k? has a value of 5 0.5. Since Q uA, where A is the area of the bed,
equation 1.27 can be transformed to
This analysis shows that permeability is a complex function of porosity
and surface area, the latter being determined by the size distribution and shape
of the particles. The appearance of a specific surface in equation 1.28 offers
a method for its measurement and provides the basis of fluid permeation methods
of size analysis. The equation is also applied in the studies of filtration.
Equations 1.8 and 1.9 examined the power requirement for driving a liquid
through a system against an opposing head. This energy is normally added
with a pump. In different processes, the quantities to be delivered, the opposing
head, and the nature of the fluid vary widely and many pumps are made to
meet these different requirements. Basically, however, pumps can be divided
into two main categories: positive displacement pumps, which may be reciprocating
or rotary, and impeller pumps. Positive displacement pumps displace
a fixed volume of fluid with each stroke or revolution. Impeller pumps, on
the other hand, impart high kinetic energy to the fluid that is subsequently
converted to pressure energy. The volume discharged depends on the opposing
Equipment for pumping gases and liquids is essentially similar. Machines
delivering gases are commonly called compressors or blowers. Compressors
discharge at relatively high pressures and blowers at relatively low
pressures. The lower density and viscosity of gases lead to the use of higher
30 Chapter 1
operating speeds and, to minimize leakage, smaller clearance between moving
1.15.1 Positive Displacement Pumps
Positive displacement pumps are most commonly used for the discharge of
relatively small quantities of fluid against relatively large heads. The small
clearance between moving parts precludes the pumping of abrasive slurries.
The single-acting piston pump in Figure 1.13(a) exemplifies the reciprocating
pump. The fluid is drawn into a cylinder through an inlet valve by
movement of the piston to the right. The stroke in the opposite direction drives
fluid through the outlet valve. Leakage past the piston may be prevented by
rings or packing. Cessation of pumping on the return stroke is overcome in
the double-acting piston pump by utilizing the volume on both sides of the
piston. Fluid is drawn in on one side by a stroke that delivers the fluid on the
other [Figure 1.13(b)]. In both pumps, delivery fluctuates. Operation, however,
is simple and both are efficient under widely varying conditions. The principle
is widely used in gas compressors. In pumping liquids, no priming is necessary
FIGURE 1.13 Positive displacement pumps.
Fluid Flow 31
because the pump will effectively discharge air present in the pump or feed
A modification, known as the diaphragm pump, is constructed so that
reciprocating parts do not contact the pumped liquid [Figure 1.13(c)]. A flexible
disk, fixed at the periphery, expands and contracts the pumping chamber,
drawing in and discharging liquid through valves.
Rotary positive displacement pumps operate by presenting an expanding
chamber to the fluid that is then sealed and conveyed to the outlet. Both liquids
and gases are discharged so that priming is not necessary. The principle is
illustrated in Figure 1.14, which describes a gear pump, a lobe pump, and a
vane pump. In the gear pump, the liquid is conveyed in the spaces formed
between a case and the consecutive teeth of two gears that intermesh at the
center of the pump to prevent return of the liquid to the inlet. The lobe pump,
widely used as a liquid pump and as a blower, operates in a similar manner.
Each impeller carries two or three lobes that interact with very small clearance
to convey fluid from inlet to outlet.
Sliding vanes, mounted in the surface of an off-center rotor but main-
FIGURE 1.14 Gear, vane, and lobe pumps.
32 Chapter 1
tained in contact with the case by centrifugal force or spring loading, provide
the pumping action of the vane pump. Fluid is drawn into the chamber created
by two vanes at the inlet. The fluid is rotated and expelled by contraction at
the outlet. Besides liquid pumping, the principle of the vane pump is used in
blowers and, by evacuating at the inlet and discharging to atmosphere at the
outlet, in vacuum pumps.
The Mono pump consists of a stator in the form of a double internal
helix and a single helical rotor. The latter maintains a constant seal across the
stator and this seal travels continuously through the pump. The pump is suitable
for viscous and nonviscous liquids. The stator is commonly made of a
rubber or similar material, so slurries are effectively delivered. Discharge is
nonpulsating and can be made against very high pressures. The pump is commonly
used to drive clarifying and cake filters.
1.15.2 Centrifugal Impeller Pumps
The centrifugal impeller pump is the type most widely used in the chemical
industry. The impeller consists of a number of vanes, usually curved backward
from the direction of rotation. The vanes may be open or, more commonly,
closed between one or two supporting plates. This reduces swirl and increases
efficiency. The impeller is rotated at high speeds, imparting radial and tangential
momenta to a liquid that is fed axially to the center and which spirals
through the impeller. In the simple volute pump [Figure 1.15(a)] the liquid is
received into a volute chamber. The cross section increases toward the tangential
outlet. The liquid therefore decelerates, allowing a conversion of kinetic
energy to pressure energy. In the diffuser pump, correctly aligned blades of
FIGURE 1.15 Volute pump and diffuser pump.
Fluid Flow 33
a diffusing ring over which the fluid velocity decreases smoothly receive the
liquid from the impeller and the pressure rises. Flow through a diffuser pump
is described in Figure 1.15(b).
Due to the less precise control of the direction of the liquid leaving the
impeller, the volute pump is less efficient than the diffuser pump. However,
it is more easily fabricated in corrosion-resistant materials and is more commonly
used. The pump, which is compact and without valves, may be used
to pump slurries and corrosive liquid, steadily delivering large volumes against
moderately large heads. For large heads, pumps are used in series. Unlike
positive displacement pumps, impeller pumps continue to operate if the delivery
line is closed, the kinetic energy of the liquid being degraded to heat.
A disadvantage of the centrifugal pump is that the conditions under
which a pump of given size will operate with high efficiency are limited. The
relation between the quantity discharged and the opposing head for a volute
pump operating at a given speed is shown in Figure 1.16. As the head increases,
the quantity discharged decreases. The mechanical efficiency of the
pump is the ratio of the power acquired by the liquid, given by equation 1.9,
to the power input. A maximum value is shown in Figure 1.16, indicating
optimal operating conditions. The effect on the efficiency when the pump
operates at other conditions can be seen from the figure, and to achieve reasonable
operating efficiency for a given discharge and opposing head a pump of
suitable size and operating speed must be used.
FIGURE 1.16 Performance curve of a volute pump running at a fixed speed.
34 Chapter 1
A second disadvantage of the centrifugal pump lies in priming. If the
pump contains air alone, the low kinetic energy imparted by the impeller creates
a very small pressure increase across the pump and liquid is neither drawn
into the pump nor discharged. To begin pumping, the impeller must be primed
with the liquid to be pumped. Where possible, the pump is placed below the
level of the supply. Alternatively, a nonreturn valve could be placed on the
suction side of the pump to prevent draining when rotation ceases.
The same principle is employed in centrifugal fans and blowers used to
displace large quantities of air and other gases. The gas enters the impeller
axially and is moved outward into a scroll. The opposing static head is usually
small, and energy appears mainly as the kinetic energy of the moving gas
1.15.3 Other Impeller Pumps
The propeller pump, exemplified by a domestic fan, is used to deliver large
quantities of fluids against low heads. These conditions are common in recirculation
systems. The principle is also employed in fans used for ventilation,
the supply of air for drying, and other similar operations.
Example 1. In the figure what is the energy loss due to pressure?
Using Bernoulli’s equation, we obtain
Calculate the velocity head and potential head at points A and B.
Velocity head at A:
Velocity head at B:
Fluid Flow 35
Potential head at A 0 m
Potential head at B 10 m
Friction head 0 m
? PB PA
Example 2. Calculation of pressure drop in a pipe due to friction.
For a smooth 0.08 m pipe, 130 m long, find the friction head. The density of
water is 1000 kg/m3, the viscosity of water is 9.28 105 kg-m/s, the mean
velocity of flow is 1.8 m/s.
Calculate the Reynolds number.
(1.8 m/s)(0.0254 m)(1000 kg/m3)
R (2.5 103)(1000 kg/m3)(1.8 m/s)2 8.1 N/m2
(4)(8.1 N/m2)(130 m)
1.7 105 N/m2
1.7 105 N/m2
(1000 kg/m3)(9.8 m/s2)
Heat transfer is a major unit operation in pharmacy. Heat energy can only be
transferred from a region of higher temperature to a region of lower temperature.
Understanding heat transfer requires the study of the mechanism and rate
of this process. Heat is transferred by three mechanisms: conduction, convection,
and radiation. It is unusual for the transfer to take place by one mechanism
Conduction is the most widely studied mechanism of heat transfer and
the most significant in solids. The flow of heat depends on the transfer of
vibrational energy from one molecule to another and, in the case of metals,
the movement of free electrons such that no appreciable displacement of matter
occurs. Radiation is rare in solids, but examples are found among glasses
and plastics. Convection, by definition, is not possible in these conditions.
Conduction in the bulk of fluids is normally overshadowed by convection, but
it assumes great importance at fluid boundaries.
The motion of fluids transfers heat between the fluids by convection. In
natural convection the movement is caused by buoyancy forces induced by
variations in the density of the fluid, caused by differences in temperature. In
Heat Transfer 37
forced convection the movement is created by an external energy source, such
as a pump.
All bodies with a temperature above absolute zero radiate heat in the
form of electromagnetic waves. Radiation may be transmitted, reflected, or
absorbed by matter, the fraction absorbed being transformed into heat. Radiation
is important at extremes of temperature and in circumstances in which
the other modes of heat transmission are suppressed. Although heat losses
can, in some cases, equal the losses by natural convection, the mechanism is,
from the standpoint of pharmaceutical processing, least important and needs
only brief consideration.
Heat transfer in many systems occurs as a steady-state process and the
temperature at any point in the system will not vary with time. In other important
processes, temperatures in the system do vary with time. The latter, which
is common among the small-scale, batch-operated processes of the pharmaceutical
and fine chemicals industry, is known as unsteady heat transfer, and,
since warming or cooling occurs, the thermal capacity (i.e., the size and specific
heat) of the system becomes important. Unsteady heat transfer is a complex
phenomenon that is difficult to analyze from first principles at a fundamental
2.1 HEAT TRANSFER BETWEEN FLUIDS
The transfer of heat from one fluid to another across a solid boundary is of
great importance in pharmaceutical processing. The system, which frequently
varies in nature from one process to another, can be divided into constituent
parts and each part characterized in its resistance to the transfer of heat. The
whole system may be considered in terms of the equation
Rate at which heat is transferred
Total temperature difference
Total thermal resistance
A hot liquid passing through a heavily lagged metal pipe may be considered
as an example. The transfer of heat from the liquid to the pipe, conduction
through the pipe wall and across the insulation, and heat loss to the surroundings
by natural convection can each be assigned a thermal resistance. A system
in which steam is admitted to the outside of a vertical pipe containing a boiling
liquid may serve as a second example. This arrangement is common in evaporators,
and the evaluation of heat transfer rates demands a study of condensa38
tion, conduction across the wall of the tube and any deposited scale, and the
mechanism of boiling.
2.2 HEAT TRANSFER THROUGH A WALL
Heat transfer by conduction through walls follows the basic relation given by
Fourier’s equation where the rate of heat flow, Q, is proportional to the temperature
gradient, dT/dx, and to the area normal to the heat flow, A:
As the distance, x, increases, the temperature, T, decreases. Hence, measuring
in the x direction, dT/dx is algebraically negative. The proportionality constant
k is the thermal conductivity. Its numerical value depends on the material of
which the body is made and on its temperature. Values of k for various materials
are given in Table 2.1. Metals have high conductivity, although values
vary widely. The nonmetallic solids normally have lower conductivities than
metals. For the porous materials of this group, the overall conductivity lies
between that of the homogeneous solid and the air that permeates the structure.
Low resultant values lead to their wide use as heat insulators. Carbon is an
exception among nonmetals. Its relatively high conductivity and chemical inertness
permit its wide use in heat exchangers.
Steady nondirectional heat transfer through a plane wall of thickness x
and area A is represented in Figure 2.1(a). If the thermal conductivity does
not change with temperature, the temperature gradient is linear and equal to
(T1 T2)/x, where T1 is the temperature of the hot face and T2 is the temperature
of the cool face. Equation 2.1 then becomes
which may be rearranged to
where x/k is the thermal resistance. Thus, for a given heat flow, a large temperature
drop must be created if the wall or layer has a high thermal resistance.
An increase in thermal resistance will reduce the heat flow promoted by a
given temperature difference. This is the principle of insulation by lagging,
Heat Transfer 39
40 Chapter 2
FIGURE 2.1 Conduction of heat through a wall.
and it is illustrated by a composite wall in Figure 2.1(b). The rate of heat
transfer is the same for both materials if steady-state heat transfer exists.
The major temperature drop occurs across the distance x2 since this material
provides the major thermal resistance. (In the case of heavily lagged, thin
metal walls, the temperature drop and thermal resistance of the metal are so
small that they can be ignored.) Rearranging this equation and eliminating the
junction temperature give
Equations of this form can be applied to any number of layers.
2.3 HEAT TRANSFER IN PIPES AND TUBES
Pipes and tubes are common barriers over which heat exchange takes place.
Conduction is complicated in this case by the changing area over which heat
is transferred. If equation 2.2 is to be retained, some value of A must be derived
Heat Transfer 41
from the length of the pipe, l, and the internal and external radii, r1 and r2,
respectively. When the pipe is thin-walled and r2/r1 1.5, the heat transfer
area can be based on an arithmetic mean of the two radii. Equation 2.2 then
Q k2?r2 r1
This equation is inaccurate for thick-walled pipes. Heat transfer area must
then be calculated from the logarithmic mean radius, rm. The equation for heat
transfer is then
2.4 HEAT EXCHANGE BETWEEN A FLUID
AND A SOLID BOUNDARY
Conduction and convection contribute to the transfer of heat from a fluid to
a boundary. The distribution of temperatures at a plane barrier separating two
fluids is shown in Figure 2.2. If the fluids are in turbulent motion, temperature
FIGURE 2.2 Heat transfer between fluids.
42 Chapter 2
gradients are confined to a relatively narrow region adjacent to the wall. Outside
this region, turbulent mixing, the mechanism of which is explained in
Chapter 1, is very effective in the transfer of heat. Temperature gradients are
quickly destroyed, and equalization of values T1 and T2 occurs. Within the
region, there exists a laminar sublayer across which heat is transferred by
conduction only. Reference to Table 2.1 shows that the thermal conductivity
of most fluids is small. The temperature gradients produced by a given heat
flow are correspondingly high. Outside the laminar layer, eddies contribute to
the transfer of heat by moving fluid from the turbulent bulk to the edge of
the sublayer, where heat can be lost or gained, and by corresponding movements
in the opposite direction. The temperature gradients in this region,
where both convection and conduction contribute to heat transfer, are smaller
than in the sublayer.
The major resistance to heat flow resides in the laminar sublayer. Its
thickness, therefore, is of critical importance in determining the rate of heat
transfer from the fluid to the boundary. The thickness depends on the physical
properties of the fluid, the flow conditions, and the nature of the surface. Increase
in flow velocity, for example, decreases the thickness of the layer and,
therefore, its resistance to heat flow. The interaction of these variables is exceedingly
A film, transmitting heat only by conduction, may be postulated in order
to evaluate the rate of heat transfer at a boundary. This fictitious film presents
the same resistance to heat transfer as the complex turbulent and laminar regions
near the wall. If, on the hot side of the wall, the fictitious layer had a
thickness x1, the equation of heat transfer to the wall would be
where k is the thermal conductivity of the fluid. A similar equation applies to
heat transfer at the cold side of the wall. The layer thickness is determined
by the same factors that control the extent of the laminar sublayer. In general
it is not known, and the previous equation may be rewritten
Q h1A(T1 T1wall) (2.7)
where h1 is the heat transfer coefficient for the film under discussion. It corresponds
to the ratio k/x1 and has units J/m2-s K. This is a convenient, numerical
expression of the flow of heat by conduction and convection at a boundary.
Typical values of heat transfer or film coefficients are given in Table 2.2. The
approximate evaluation of these coefficients is discussed in the next section.
Heat Transfer 43
TABLE 2.2 Film Coefficient h for
Various Fluids (J/m2-s-K)
Organic solvents 340–2840
The ratio of the temperature difference and the total thermal resistance
determines the rate of heat transfer across the three layers of Figure 2.2. Using
the film coefficient h2 to characterize heat transfer from the barrier to the colder
fluid, one obtains
where kw is the thermal conductivity of the wall.
Adding and rearranging these equations give
1/h1 xw/kw 1/h2
(T1 T2) (2.8)
1/h1 xw/kw 1/h2
is called the overall heat transfer coefficient, U. A general expression of the
rate of heat transfer then becomes
Q UA?T (2.9)
44 Chapter 2
2.5 APPLICATION OF DIMENSIONAL
ANALYSIS TO CONVECTIVE HEAT
Dimensional analysis offers a rational approach to the estimation of the complex
phenomena of convective heat transfer rates.
Free convection describes heat transfer by the bulk movement of fluids
induced by buoyancy forces. These arise from the variation of fluid density
with temperature. If the surface in contact with the fluid is hotter, the fluid
will absorb heat, a local decrease in density will occur, and some of the fluid
will rise. If the surface is colder, the reverse takes place. For these conditions,
the following factors will influence the heat transferred per unit area per unit
time, q. The dimensional form of these factors is given, using the additional
fundamental dimensions of temperature, [?], and heat [H]. The latter is justi-
fied if interchange of heat energy and mechanical energy is precluded. This
is approximately true in the subject under discussion, the heat produced by
frictional effects, for example, being negligible.
The viscosity of the fluid, ?. [M L1 T1]
The thermal conductivity of the fluid, k. [H T1 L1 ?1]
The temperature difference between the surface and [?]
the bulk of the fluid, ?T.
The density, ?. [M L3]
The specific heat, Cp. [H M1 ?1]
The buoyancy forces. They depend on the product [?1 L T2]
of the coefficient of thermal expansion a, and the
acceleration due to gravity, g.
Normally only one dimension, that of the physical dimensions of the surface,
is important. For example, the height of a plane vertical surface has greater
significance than the width that only determined the total area involved. The
important characteristic dimension is designated l [L]. The equation of dimensions
[q] [l x?Tykz?pCqp
[H L2 T1] [Lx?yHzTzLz?zMpLpTpHqMq?q?rLrT2rMsL3s]
Equating indices gives
H 1 q z
L 2 x p r 3s z
Heat Transfer 45
T 1 p 2r z
? 0 y q r z
M 0 p q s
Solving for x, y, z, p, and s in terms of q and r gives
z 1 q
y r 1
p q 2r
x 3r 1
[q] [l 3r1 ?T r1Cqp
Collecting into three groups the variables to the power of 1, the power q, and
the power r, we can write
q Constant ?Tk
l l 3?Tag?2
?2 r Cp ?
Constant l 3?Tag?2
Heat transfer by free convection can thus be presented as a relation between
three dimensionless groups. The quantity Cp?/k is known as the Prandtl number,
the combination l 3?Tag?2/?2 is known as the Grashof number, and ql/
?Tk is the Nusselt number. Since the film coefficient, h, is given by q/?T,
the Nusselt number may also be written hl/k.
The specific relation in which these groups stand is established for a
particular system by experiment. Then, for the same geometric arrangement, in
which heat is transferred by free convection, the correlation allows the Nusselt
46 Chapter 2
number, Nu, to be determined with reasonable accuracy from known values
of the variables which constitute the Grashof number, Gr, and the Prandtl
number, Pr. From Nu, the heat transferred per unit area per unit time, q, and
the film coefficient, h, can be determined.
The fluid properties Cp, k, ?, and ? are themselves temperature dependent.
In establishing a correlation, the temperature at which these properties
are to be measured must be chosen. This temperature is usually that of the main
body of the fluid or the mean of this temperature and the surface temperature.
Experimental correlations for many surface configurations are available.
The exponents r and q are usually equal to 0.25 in streamline flow and 0.33
in turbulent flow. The constant varies with the physical configuration. As an
example, the heat transfer to gases and liquids from a large horizontal pipe
by free convection is described by the relation
The linear dimension in this correlation is the pipe diameter d. The fluid
properties are to be measured at the mean of the wall and bulk fluid temperatures.
In forced convection the fluid is moved over the surface by a pump or
blower. The effects of natural convection are usually neglected. The study of
forced convection is of great practical importance, and a vast amount of data
has been documented for streamline and turbulent flows in pipes, across and
parallel to tubes, across plane surfaces, and in other important configurations
such as jackets and coils. Such data is again correlated by means of dimensionless
In forced convection the heat transferred per unit area per unit time, q,
is determined by a linear dimension which characterizes the surface, l, the
temperature difference between the surface and the fluid, ?T, the viscosity,
?, density, ?, and velocity, u, of the fluid, its conductivity, k, and its specific
heat, Cp. Dimensional analysis yields the relation
where ql/k?T is the Nusselt number, Nu, Cp?/k is the Prandtl number, Pr, and
ul?/? is Reynolds number, Re, a parameter discussed in Chapter 1. The values
of the indices x and y and of the constant are established for a particular system
Heat Transfer 47
by experiment. For turbulent flow in pipes, the correlation for fluids of low
Nu 0.023 Prx Re0.8 (2.13)
where x 0.4 for heating and 0.3 for cooling. The linear dimension used to
calculate Re or Nu is the pipe diameter, and the physical properties of the
fluid are to be measured at the bulk fluid temperature. This relation shows
that in a given system, the film coefficient varies as the fluid velocity0.8. If the
flow velocity is doubled, the film coefficient increases by a factor of 1.7.
Although the correlations given may appear complex, their use in practice
is often simple. A large quantity of tabulated data is available, and numerical
values of the variables and their dimensionless combinations are readily
accessible. The graphical presentation of these variables or groups in many
cases permits an easy solution. In other cases the correlation can be greatly
simplified if it is restricted to a particular system. Free convection to air is an
2.6 HEAT TRANSFER TO BOILING LIQUIDS
Heat transfer to boiling liquids occurs in several operations, such as distillation
and evaporation. Heat is transferred by conduction and convection in a process
further complicated by the change of phase which occurs at the heating boundary.
When boiling is induced by a heater in contact with a pool of liquid, the
process is known as pool boiling. Liquid movement is derived only from heating
effects. In other systems, the boiling liquid may be driven through or over
heaters, a process referred to as boiling with forced circulation.
2.7 POOL BOILING
If a horizontal heating surface is in contact with a boiling liquid, a sequence
of events occurs as the temperature difference between the surface and the
liquid increases. Figure 2.3 relates heat flux per unit area at the surface, q, to
the temperature difference between the surface and boiling water, ?T. The
derived value of the heat transfer coefficient, h q/?T, is also plotted.
When ?T is small, the degree of superheating of the liquid layers adjacent
to the surface is low, and bubble formation, growth, and disengagement,
if present, are slow. Liquid disturbance is small, and heat transfer can be estimated
from expressions for natural convection given, for example, in equation
48 Chapter 2
FIGURE 2.3 Variation in heat transfer coefficient and heat flux per unit area.
2.11. This regime corresponds to section AB of Figure 2.3, over which both
q and h increase.
In section BC, vapor formation becomes more vigorous, and bubble
chains rise from points which progressively increase in number and finally
merge. This movement increases liquid circulation and q and h rise rapidly.
This phase is called nucleate boiling and is the practically important regime.
For water, approximate values of q and h may be read from Figure 2.3. At
point C a peak flux occurs and a maximum heat transfer coefficient is obtained.
At this point ?T is known as the critical temperature drop. For water, the value
lies between 25 and 32 K. The critical temperature drop for organic liquids
is somewhat higher. Beyond C, vapor formation is so rapid that escape is
inadequate and a progressively larger fraction of the heating surface becomes
covered with a vapor film, the low conductivity of which leads to a decrease
in q and h. This represents a transition from nucleate boiling to film boiling.
When this transition is complete (D), the vapor entirely covers the surface,
film boiling is fully established, and the heat flux again rises.
The low heat transfer coefficient renders film boiling undesirable, and
equipment is designed for and operated at temperature differences that are
less than the critical temperature drop. If a constant temperature heat source,
Heat Transfer 49
such as steam or hot liquid, is employed, exceeding the critical temperature
drop results simply in a drop in heat flux and process efficiency. If, however,
a constant heat input source is used, as in electrical heating, decreasing heat
flux as the transition region is entered causes a sudden and possibly damaging
increase in the temperature of the heating element. Damage is known as boiling
burnout. Under these circumstances, the region CD of Figure 2.3 is not
Boiling heat transfer coefficients depend on the physical character of the
liquid and the nature of the heating surface. Through the agencies of wetting,
roughness, and contamination, the latter greatly influences the formation,
growth, and disengagement of bubbles in the nucleate boiling regime. At present
there is no reliable method of estimating the boiling coefficients of heat
transfer from the physical properties of the system. Coefficients, as shown for
water in Figure 2.3, are large, and higher resistances elsewhere often limit the
rate at which heat can be transferred through a system as a whole.
2.8 BOILING INSIDE A VERTICAL TUBE
Heat transfer to liquids boiling in vertical tubes is common in evaporators. If
a long tube of suitable diameter, in which liquid lies at a low level, is heated,
the pattern of boiling shown in Figure 2.4 is established (McCabe et al, 1993).
At low levels, boiling may be suppressed by the imposed head [Figure 2.4(a)].
Higher in the tube, bubbles are produced which rise and coalesce [Figure
2.4(b)]. Slug formation due to bubble coagulation occurs [Figure 2.4(c), (d)].
The slugs finally break down [Figure 2.4(e)]. Escape is hindered and both
liquid and vapor move upward at increasing speed. Draining leads to separation
of the phases, giving an annular film of liquid dragged upward by a core
of high-velocity vapor [Figure 2.4(f)]. In long tubes the main heat transfer
takes place in this region by forced convection or nucleate boiling. At low
temperature differences between wall and film, heat transfer occurs quietly as
in forced convection. This is the normal regime in a climbing film evaporator,
and heat flux can be calculated from correlations of the type given in equation
2.12. At higher temperature differences, nucleate boiling takes place in the film
and the vigorous movement leads to an increase in heat transfer coefficient.
2.9 BOILING WITH FORCED CIRCULATION
In many systems, movements other than those caused by boiling are imposed.
For example, boiling in agitated vessels is common in many batch processes.
50 Chapter 2
FIGURE 2.4 Boiling in narrow vertical tube.
The boiling heat transfer coefficients depend on the properties of the liquid,
the nature of the surface, and the agitation used. Coefficients obtained are
slightly higher than those of pool boiling. Inside tubes the pattern of forced
circulation boiling is similar to that described in the previous section. Coeffi-
cients, however, are higher because the velocities attained are higher.
2.10 HEAT TRANSFER FROM CONDENSING
When a saturated vapor is brought into contact with a cool surface, heat is
transferred to the surface and a liquid condenses. The vapor may consist of
a single substance or a mixture, some components of which may be noncondensable.
The process is described by the following sequence: The vapor diffuses
to the boundary where actual condensation takes place. In most cases,
Heat Transfer 51
the condensate forms a continuous layer over the cooling surface, draining
under the influence of gravity. This process is known as film condensation.
The latent heat liberated is transferred through the film to the surface by conduction.
Although this film offers considerable resistance to heat flow, film
coefficients are usually high.
2.11 DROPWISE CONDENSATION
Under some surface conditions the condensate does not form a continuous
film. Droplets are formed which grow, coalesce, and then run from the surface.
Since a fraction of the surface is always directly exposed to the vapor, film
resistance is absent and heat transfer coefficients that may be 10 times those
of film condensation are obtained. This process is known as dropwise condensation.
Although highly desirable, its occurrence, which depends on the wettability
of the surface, is not predictable and cannot be used as a basis for design.
2.12 CONDENSATION OF A PURE VAPOR
For film condensation a theoretical analysis of the laminar flow of a liquid
film down an inclined surface and the progressive increase in thickness due
to condensation yields the following expression for the mean heat transfer
hm Constant ?2k3?g
where ? is the latent heat of vaporization, and ?, k, and ? are the liquid’s
density, thermal conductivity, and viscosity, respectively; ?T is the difference
in temperature between the surface and the vapor. Experimentally determined
coefficients confirm the validity of equation 2.14. In practice, however, coef-
ficients are somewhat higher due to disturbance of the film arising from a
number of factors. As the condensation rate rises, the thickness of the condensate
layer increases and the film coefficient falls. However, a point may be
reached in long vertical tubes at which flow in the layer becomes turbulent.
Under these conditions the coefficient again rises, and equation 2.14 is not
valid. Coefficients may also be increased if high vapor velocities induce ripples
in the film.
52 Chapter 2
2.13 CONDENSATION OF MIXED VAPORS
If a mixture of condensable and noncondensable gases is cooled below its
dew point at a surface, the former condenses leaving the adjacent layers richer
in the latter, thus creating an added thermal resistance. The condensable fraction
must diffuse through this layer to reach the film of condensate, and heat
transfer coefficients are normally very much lower than the corresponding
value for the pure vapor. For example, the presence of 0.5% of air has been
found to reduce the heat transfer by condensation of steam by as much as 50%.
2.14 HEAT TRANSFER BY RADIATION
There is continuous interchange of energy between bodies by the emission
and absorption of radiation. If two adjacent surfaces are at different temperatures,
the hotter surface radiates more energy than it receives and its temperature
falls. The cooler surface receives more energy than it emits and its temperature
rises. Ultimately thermal equilibrium is reached. Interchange of energy
continues but gains and losses are equal.
Of the radiation which falls on a body, a fraction, a, is absorbed, a
fraction, r, is reflected, and a fraction, t, is transmitted. These fractions are
called the absorptivity, the reflectivity, and the transmissivity, respectively.
Most industrial solids are opaque, so the transmissivity is zero and
a r 1 (2.15)
Reflectivity and, therefore, absorptivity depend greatly on the nature of
the surface. The limiting case—that of a body which absorbs all and reflects
none of the incident radiation—is called a blackbody.
2.15 EXCHANGE OF RADIATION
The exchange of radiation is based on two laws. The first, known as Kirchhoff’s
law, states that the ratio of the emissive power to the absorptivity is
the same for all bodies in thermal equilibrium. The emissive power of a body,
E, is the radiant energy emitted from unit area in unit time (J/m2-s). A body
of area A1 and emissivity E1 therefore emits energy at a rate E1A1. If the radiation
falling on unit area of the body is Eb, the rate of energy absorption is
Eba1A1, where a1 is the absorptivity. At thermal equilibrium, Eba1A1 E1A1.
For another body in the same environment, Eba2A2 E2A2. Therefore,
Heat Transfer 53
For a blackbody, a 1. The emissive power is therefore Eb. The blackbody
is a perfect radiator and is used as the comparative standard for other
surfaces. The emissivity of a surface is defined as the ratio of the emissive
power, E, of the surface to the emissive power of a blackbody at the same
The emissivity is numerically equal to the absorptivity. Since the emissive
power varies with wavelength, the ratio should be quoted at a particular
wavelength. For many materials, however, the emissive power is a constant
fraction of the blackbody radiation; i.e., the emissivity is constant. These materials
are known as graybodies.
The second fundamental law of radiation, known as the Stefan-Boltzmann
law, states that the rate of energy emission from a blackbody is proportional
to the fourth power of the absolute temperature, T:
E ?T4 (2.18)
where E is the total emissive power and ? is the Stefan-Boltzmann constant, the
numerical value of which is 5.676 108 J/m2-s-K4. It is sufficiently accurate to
say that the heat emitted in unit time, Q, from a blackbody of area A is
and for a body which is not perfectly black by
Q ?eAT 4 (2.19)
where e is the emissivity.
The net energy gained or lost by a body can be estimated with these
laws. The simplest case is that of a graybody in black surroundings. These
conditions, in which none of the energy emitted by the body is reflected back,
are approximately those of a body radiating to atmosphere. If the absolute
temperature of the body is T1, the rate of heat loss is ?eAT 41
where A is the area of the body and e is its emissivity. Surroundings at a
temperature T2 will emit radiation proportional to ?T 42
and a fraction, determined
by area and absorptivity, a, will be absorbed by the body. This heat
will be ?aAT 42
, and since absorptivity and emissivity are equal
54 Chapter 2
Net heat transfer rate ?eA(T 41
If part of the energy emitted by a surface is reflected back by another
surface, the calculation of radiation exchange is more complex. Equations for
various surface configurations are available. These take the general form
Q F1F2?A(T 4
A T 4
where F1 and F2 are factors determined by the configuration and emissivity
of surfaces at temperatures TA and TB.
Example 1. A stainless steel pipe has an internal radius of 0.019 m
and an external radius of 0.024 m. The thermal conductivity of stainless steel
is 34.606 J/m-s-K. Steam at 422 K surrounds the pipe, which is lagged with
0.051 m of insulation with a conductivity of 0.069 J/m-s-K. The temperature
of the outer surface of the insulation is 311 K. What is the heat loss per meter
For the wall of the pipe,
Therefore, the arithmetic mean best defines the radius:
0.019 m 0.024 m
For the insulation,
Therefore, the logarithmic mean best defines the radius:
For the pipe,
Q (34.606 J/m-s-K)(2 ?)(0.022 m)(1 m) T1 T2
0.024 m 0.019 m
Heat Transfer 55
For the insulation,
Q (0.069 J/m-s-K)(2 ?)(0.036 m)(1 m) T2 T3
0.051 m 0.024 m
Rearranging these equations gives
T1 T3 111 K
Example 2. A 0.051-m uninsulated horizontal pipe is carrying steam
at 389 K to the surroundings at 294 K. The emissivity, e, of the pipe is 0.8.
Absolute zero is 273 K. Find the heat loss by radiation.
(5.676 108 J/m2-s-K4)(0.058 m)(?)(0.8)[(116 K)4 (21 K)4]
This chapter briefly reviews mass transfer to complete the overview of the
fundamental unit processes in pharmacy. Mass transfer is conceptually and
mathematically analogous to heat transfer, as will be seen in the following
exposition. Many processes are adopted so that a mixture of materials can be
separated into component parts. In some, purely mechanical means are used.
Solids may be separated from liquids by the arrest of the former in a bed
permeable to the fluid. This process is known as filtration. In other examples,
a difference in density of two phases permits separation. This is found in
sedimentation and centrifugation. Many other processes, however, operate by
a change in the composition of a phase due to the diffusion of one component
in another. Such processes are known as diffusional or mass transfer processes.
Distillation, dissolution, drying, and crystallization are examples of mass
transfer processes. In all cases, diffusion is the result of a difference in the
concentration of the diffusing substance. This component moves from a region
of high concentration to a region of low concentration under the influence of
the concentration gradient.
In mass transfer operations, two immiscible phases are normally present,
one or both of which are fluid. In general, these phases are in relative motion
Mass Transfer 57
and the rate at which a component is transferred from one phase to the other
is greatly influenced by the bulk movement of the fluids. In most drying processes,
for example, water vapor diffuses from a saturated layer in contact
with the drying surface into a turbulent airstream. The boundary layer, as
described in Chapter 1, consists of a sublayer in which flow is laminar and
an outer region in which flow is turbulent. The mechanism of diffusion differs
in these regimes. In the laminar layer, movement of water vapor molecules
across streamlines can only occur by molecular diffusion. In the turbulent
region the movement of relatively large units of gas, called eddies, from one
region to another causes mixing of the gas components. This mixing is called
eddy diffusion. Eddy diffusion is a more rapid process, and although molecular
diffusion is still present, its contribution to the overall movement of material
is small. In still air, eddy diffusion is virtually absent and evaporation occurs
only by molecular diffusion.
3.1 MOLECULAR DIFFUSION IN GASES
Transport of material in stagnant fluids or across the streamlines of a fluid
in laminar flow occurs by molecular diffusion. In Figure 3.1, two adjacent
compartments, separated by a partition, are drawn. Each compartment contains
a pure gas, A or B. Random movement of all molecules occurs so that after
a period of time, molecules are found quite remote from their original positions.
If the partition is removed, some molecules of A will move toward the
FIGURE 3.1 Molecular diffusion of gases A and B.
58 Chapter 3
region occupied by B, their number depending on the number of molecules
at the point considered. Concurrently, molecules of B diffuse toward regions
formerly occupied by pure A. Ultimately, complete mixing occurs. Before this
point in time, a gradual variation in the concentration of A exists along an axis,
designated x, which joins the original compartments. This variation, expressed
mathematically, is dCA/dx, where CA is the concentration of A. The negative
sign arises because the concentration of A decreases as the distance x increases.
Similarly, the variation in the concentration of gas B is dCB/dx.
These expressions, which describe the change in the number of molecules of
A or B over some small distance in the direction indicated, are concentration
gradients. The rate of diffusion of A, NA, depends on the concentration gradient
and on the average velocity with which the molecules of A move in the
x direction. Fick’s law expresses this relationship:
where D is the diffusivity of A in B. It is a property proportional to the average
molecular velocity and, therefore, dependent on the temperature and pressure
of the gases. The quantity NA is usually expressed as the number of moles
diffusing across unit area in unit time. In the S.I. unit system, which is used
frequently for mass transfer, NA is expressed as moles per square meter per
second. The units of diffusivity then become m2 s1. As with the basic equations
of heat transfer, equation 3.1 indicates that the rate of a process is directly
proportional to a driving force, which, in this context, is a concentration gradient.
This basic equation can be applied to a number of situations. If discussion
is restricted exclusively to steady-state conditions, in which neither dCA/
dx or dCB/dx change with time, then equimolecular counterdiffusion is considered
3.2 EQUIMOLECULAR COUNTERDIFFUSION
If no bulk flow occurs in the element of length dx, shown in Figure 3.1, the
rates of diffusion of the two gases, A and B, must be equal and opposite:
The partial pressure of A changes by dPA over the distance dx. Similarly,
the partial pressure of B changes by dPB. Since there is no difference in total
Mass Transfer 59
pressure across the element (no bulk flow), dPA/dx must equal dPB/dx. For
an ideal gas, the partial pressure is related to the molar concentration by the
where nA is the number of moles of gas A in a volume V. Since the molar
concentration, CA, is equal to nA/V,
Therefore for gas A, equation 3.1 can be written
where DAB is the diffusivity of A in B. Similarly,
It therefore follows that DAB DBA D. If the partial pressure of A at x1 is
PA1 and at x2 is PA2, integration of equation 3.2 gives
A similar equation may be derived for the counterdiffusion of gas B.
3.3 DIFFUSION THROUGH A STATIONARY,
An important practical case arises when a gas A diffuses through a gas B,
there being no overall transport of gas B. It arises, for example, when a vapor
formed at a drying surface diffuses into a surrounding gas. At the liquid surface,
the partial pressure of A is dictated by the temperature. For water, it
would be 12.8 mmHg at 298 K. Some distance away the partial pressure is
lower and the concentration gradient causes diffusion of A away from the
surface. Similarly, a concentration gradient for B must exist, the concentration
being lowest at the surface. Diffusion of this component takes place toward
the surface. There is, however, no overall transport of B, so diffusional movement
must be balanced by bulk flow away from the surface. The total flow
60 Chapter 3
of A is, therefore, the diffusional flow of A plus the transfer of A associated
with this bulk movement.
3.4 MOLECULAR DIFFUSION IN LIQUIDS
Equations describing molecular diffusion in liquids are similar to those applied
to gases. The rate of diffusion of material A in a liquid is given by equation
Fick’s law for steady-state, equimolal counterdiffusion is then
where CA2 and CA1 are the molar concentrations at points x2 and x1, respectively.
Equations for diffusion through a layer of stagnant liquid can also be
developed. The use of these equations is, however, limited because diffusivity
in a liquid varies with concentration. In addition, unless the solutions are very
dilute, the total molar concentration varies from point to point. These complications
do not arise with diffusion in gases.
Diffusivities in liquids are very much less than diffusivities in gases,
commonly by a factor of 104.
3.5 MASS TRANSFER IN TURBULENT AND
As already explained, movement of molecules across the streamlines of a fluid
in laminar flow can only occur by molecular diffusion. If the concentration
of a component, A, varies in a direction normal to the streamlines, the molar
rate of diffusion is given by equation 3.1.
When a fluid flows over a surface, the surface retards the adjacent fluid
region, forming a boundary layer. If flow throughout the fluid is laminar, the
equation for molecular diffusion may be used to evaluate the mass transferred
across the boundary layer. In most important cases, however, flow in the bulk
of the fluid is turbulent. The boundary layer is then considered to consist of
Mass Transfer 61
three distinct flow regimes. In the region of the boundary layer most distant
from the surface, flow is turbulent and mass transfer is the result of the interchange
of large portions of the fluid. Mass interchange is rapid and concentration
gradients are low. As the surface is approached, a transition from turbulent
flow to laminar flow occurs in the transition or buffer region. In this region,
mass transfer by eddy diffusion and molecular diffusion is of comparable magnitude.
In a fluid layer at the surface, a fraction of a millimeter thick, laminar
flow conditions persist. This laminar sublayer, in which transfer occurs by
molecular diffusion only, offers the main resistance to mass transfer, as shown
in Figure 3.2. As flow becomes more turbulent, the thickness of the laminar
sublayer and its resistance to mass transfer decrease.
One approach to the evaluation of the rate of mass transfer under these
conditions lies in the postulation of a film, the thickness of which offers the
same resistance to mass transfer as the combined laminar, transition, and turbulent
regions. The analogy with heat transfer by conduction and convection
is exact, and quantitative relations between heat and mass transfer can be developed
for some situations. This, however, is not attempted in this text. The
postulate of an effective film is explained by reference to Figure 3.2.
FIGURE 3.2 Mass transfer at a boundary.
62 Chapter 3
As gas flows over a surface and equimolecular counterdiffusion of components
A and B occurs, component A moves away from the surface and
component B moves toward the surface. The variation in partial pressure of
A with distance from the surface is shown in Figure 3.2. At the surface the
value is PAi. A linear fall to PAb occurs over the laminar sublayer. Beyond this
the partial pressure falls less steeply to the value PA at the edge of the boundary
layer. A value slightly higher than this, PAg, is the average partial pressure of
A in the entire system. In general, the gas content of the laminar layer is so
small that PA and PAg are virtually equal. If molecular diffusion were solely
responsible for diffusion, PAg would be reached at some fictitious distance, x?,
from the surface, over which the concentration gradient (PAi PAg)/x? exists.
The molar rate of mass transfer would then be
However, x? is not known and this equation may be written
(PAi PAg) (3.5)
where kg is a mass transfer coefficient, the units of which are m s1. Since CA
PA/RT, we can also write
NA kg(CAi CAg)
where CAi and CAg are the gas concentrations at either side of the film. Similar
equations describe the diffusion of B in the opposite direction.
Diffusion across a liquid film is described by
NA kl(CAi CAl) (3.6)
where CAi is the concentration of component A at the interface and CAl is its
concentration in the bulk of the phase.
In all cases the mass transfer coefficient depends on the diffusivity of
the transferred material and the thickness of the effective film. The latter is
largely determined by the Reynolds number of the moving fluid—that is, its
average velocity, its density, its viscosity, and some linear dimension of the
system. Dimensional analysis gives the relation
constant (Re)q ?
Mass Transfer 63
where Re is the Reynolds number, k is the mass transfer coefficient, D is the
diffusivity, and d is a dimension characterizing the geometry of the system.
This relation is analogous to the expression for heat transfer by forced
convection given in Chapter 2. The dimensionless group kd/D corresponds to
the Nusselt group in heat transfer. The parameter ?/?D is known as the
Schmidt number, Sc, and is the mass transfer counterpart of the Prandtl number.
For example, the evaporation of a thin liquid film at the wall of a pipe
into a turbulent gas is described by the equation
0.023 Re0.8 Sc0.33
Although the equation expresses experimental data, comparison with equation
2.13 from the heat transfer section again demonstrates the fundamental relation
of heat and mass transfer.
Similar relations have been developed empirically for other situations.
The flow of gases normal to and parallel to liquid surfaces can be applied to
drying processes, and the agitation of solids in liquids can provide information
for crystallization or dissolution. The final correlation allows estimation of the
mass transfer coefficient with reasonable accuracy.
3.6 INTERFACIAL MASS TRANSFER
So far, only diffusion in the boundary layers of a single phase has been discussed.
In practice, however, two phases are normally present, and mass transfer
across the interface must occur. On a macroscopic scale the interface can
be regarded as a discrete boundary. On the molecular scale, however, the
change from one phase to another takes place over several molecular diameters.
Due to the movement of molecules, this region is in a state of violent
change, the entire surface layer changing many times a second. Transfer of
molecules at the actual interface is, therefore, virtually instantaneous, and the
two phases are at this point in equilibrium.
Since the interface offers no resistance, mass transfer between phases
can be regarded as the transfer of a component from one bulk phase to another
through two films in contact, each characterized by a mass transfer coefficient.
This is the two-film theory and is the simplest of the theories of interfacial
mass transfer. For the transfer of a component from a gas to a liquid, the theory
is described in Figure 3.3. Across the gas film, the concentration, expressed as
partial pressure, falls from a bulk concentration PAg to an interfacial concentra64
FIGURE 3.3 Interfacial mass transfer.
tion PAi. In the liquid the concentration falls from an interfacial value CAi to
a bulk value CAl.
At the interface equilibrium conditions exist. The break in the curve is
due to the different affinity of component A for the two phases and the different
units expressing concentration. The bulk phases are not, of course, at equilibrium,
and it is the degree of displacement from equilibrium conditions that
provides the driving force for mass transfer. If these conditions are known,
an overall mass transfer coefficient can be calculated and used to estimate the
rate of mass transfer.
Transfer of a component from one mixed phase to another, as described
previously, occurs in several processes. Liquid-liquid extraction, leaching, gas
adsorption, and distillation are examples. In other processes, such as drying,
crystallization, and dissolution, one phase may consist of only one component.
Concentration gradients are set up in one phase only with the concentration
at the interface given by the relevant equilibrium conditions. In drying, for
example, a layer of air in equilibrium, (i.e., saturated with the liquid) is postulated
at the liquid surface, and mass transfer to a turbulent airstream is deMass
scribed by equation 3.5. The interfacial partial pressure is the vapor pressure
of the liquid at the temperature of the surface. Similarly, dissolution is described
by equation 3.6, the interfacial concentration being the saturation concentration.
The rate of solution is determined by the difference between this
concentration, the concentration in the bulk solution, and the mass transfer
Powders are employed in many pharmaceutical processes. They are more dif-
ficult to handle and process than liquids and gases primarily because their
flow properties are fundamentally different. Unlike fluids, a particulate mass
will resist stresses less than a limiting value without continuous deformation,
and many common powders will not flow because the stresses imposed, for
example, by gravity are insufficiently high. Often additional processes that
improve flow, such as granulation and fluidization, are adopted to facilitate
powder transport and powder feeding.
Another important property of powders is the manner in which the particles
of a powder pack together to form a bed and its influence on bulk density.
The latter is the ratio of the mass of the powder to its total volume, including
voids. Unlike fluids, it varies greatly with the particle size, distribution, and
shape of the particles because they affect the closeness of packing and the
fraction of the bed that is void. Vibration and tapping, which cause rearrangement
of the particles and a decrease in the void fraction, increase the
bulk density. In several processes, these factors are important because the
powder is subdivided and measured by volume. Variation of bulk density then
causes variation in weight and dose. The variation in the weight of compressed
tablets is an excellent example of this effect. The manner of packing also
influences the behavior of a bed when it is compressed.
Finally, in a static condition, there is no leveling at the free surface of
a bed of powder, nor is pressure transmitted downward through the bed. Instead,
the walls of the containing vessel carry the weight of the bed.
4.1 PARTICLE PROPERTIES
In order to understand particle properties it is important to consider their origins.
Particles may be produced by different processes that can be regarded
as constructive or destructive (Hickey, 1993). Constructive methods include
crystallization, precipitation, and condensation. Destructive methods include
milling and spray-drying.
The most common methods of bulk manufacture are crystallization or
precipitation from saturated solutions. These solutions are saturated by exceeding
the solubility limit in one of several ways (Martin, 1993). Adding
excess solid in the form of nucleating crystals results in crystallization from
saturated solution. This can be controlled by reducing the temperature of the
solution, thereby reducing the solubility. For products that can be melted at
relatively low temperatures, heating and cooling can be used to invoke a controlled
crystallization. The addition of a cosolvent with different capacity to
dissolve the solute may also be used to reduce the solubility and result in
precipitation. In the extreme a chemical reaction or complexation occurs to
produce a precipitate (e.g., amine-phosphate/sulfate interactions; Fung, 1990)
crystallization. Condensation from vapors is a technical possibility and has
been employed for aerosol products (Pillai et al., 1993) but has little potential
as a bulk manufacturing process.
Milling (Carstensen, 1993) and spray-drying (Masters, 1991) may be
described as destructive methods since they take bulk solid or liquid and increase
the surface area by significant input of energy, thereby producing small
discrete particles or droplets. The droplets produced by spraying may then
be dried to produce particles of pure solute. A variety of mills are available
distinguished by their capacity to introduce energy into the powder. Spray
dryers are available which may be utilized to produce powders from aqueous
or nonaqueous solutions (Sacchetti and Van Oort, 1996).
68 Chapter 4
The structure of particles may be characterized in terms of crystal system and
crystal habit. The crystal system can be defined by the lattice group spacing
and bond angles in three dimensions. Consequently, in the simplest form a
crystal may be described by the distance between planes of atoms or molecules
in three dimensions (a, b, and c) and by the angles between these planes (?,
?, and ?), where each angle is opposite the equivalent dimension (e.g., ? opposite
a). These angles and distances are determined by X-ray diffraction utilizing
Bragg’s law (Mullin, 1993). Crystals may be considered as polygons
wherein the numbers of faces, edges, and vertices are defined by Euler’s law.
There are more than 200 possible permutations of crystal system based on
this definition. In practice, each of these geometries can be classified into seven
specific categories of crystal system: cubic, monoclinic, triclinic, hexagonal,
trigonal, orthorhombic, and tetragonal.
Once the molecular structure of crystals has been established, the manner
in which crystal growth occurs from solution is dictated by inhibition in
any of the three dimensions. Inhibition of growth occurs because of differences
in surface free energy or surface energy density. These differences may be
brought about by regions of different polarity at the surface, charge density
at the surface, the orientation of charged side groups on the molecules, the
location of solvent at the interface, or the adsorption of other solute molecules
(e.g., surfactant). Crystal growth gives rise to particles of different crystal
habit. It is important to recognize that different crystal habits, or superficial
appearance, do not imply different lattice group spacing, as defined by the
crystal system. Also it is possible that products may be produced by any of
the methods described that have no regular structure or specific orientation of
molecules, which are, by definition, amorphous.
Properties dictated by the method of manufacture include particle size and
distribution, shape, specific surface area, true density, tensile strength, melting
point, and polymorphic form. Arising from these fundamental physicochemical
properties are other properties such as solubility and dissolution rate.
Polymorphism, or the ability of crystals to exhibit different crystal lattice
spacings under different conditions (usually of temperature or moisture content),
can be evaluated by thermal techniques. Differential scanning calorimetry
may be used to determine the energy requirements for rearranging molecules
in the lattice as they convert from one form to another. This difference
between polymorphic forms of the same substance can also be detected by
assessing their solubility characteristics.
4.2 PARTICLE INTERACTIONS
The attraction between particles or between particles and a containing boundary
influences the flow and packing of powders. If two particles are placed
together, the cohesive bond is normally very much weaker than the mechanical
strength of the particles themselves. This may be due to the distortion of the
crystal lattice, which prevents correct alignment of the atoms, or the adsorption
of surface films. These prevent contact of the surfaces and usually, but not
always, decrease cohesion. Low cohesion is also the result of small area of
contact between the surfaces. On a molecular scale, surfaces are very rough,
and the real area of contact is very much smaller than the apparent area. Finally,
the structure of the surface may differ from the interior structure of the
particle. Nevertheless, the cohesion and adhesion that occur with all particles
are appreciable. They are normally ascribed to nonspecific van der Waals
forces, although in moist materials a moisture layer can confer cohesiveness
by the action of surface tension at the points of contact. For this reason, an
increase in humidity can produce a sudden increase in cohesiveness and the
complete loss of mobility in a powder that ceases to flow and pour. The acquisition
of an electric charge by frictional movement between particles is another
mechanism by which particles cohere together or adhere to containers.
These effects depend on the chemical and physical form of the powder.
They normally oppose the gravitational and momentum forces acting on a
particle during flow and therefore become more effective as the weight or size
of the particle decreases. Cohesion and adhesion increase as the size decreases
because the number of points in contact in a given area of apparent contact
increases. The effects of cohesion often predominate at sizes less than 100
micrometers and powders will not pass through quite large orifices, and vertical
walls of a limited height appear in a free surface. The magnitude of cohesion
also increases as the bulk density of the powder increases.
Cohesion also depends on the time for which contact is made. This is
not fully understood but may be due to the gradual squeezing of air and adsorbed
gases from between the approaching surfaces. The result, however, is
that a system which flows under certain conditions may cease to flow when
these conditions are restored after interruption. This is of great importance in
the storage and intermittent delivery of powders. Fluctuating humidity can
also destroy flow properties if a water-soluble component is present in the
70 Chapter 4
powder. The alternating processes of dissolution and crystallization can produce
very strong bonds between particles which cement the mass together.
4.2.1 Measurement of the Effects of Cohesion
Measuring the cohesion between two particles or the adhesion of a particle
to a boundary is difficult, although several methods can be used. More commonly,
these effects are assessed by studying an assembly of particles in the
form of a bed or a heap. Flow and other properties of the powder are then
predicted from these studies.
The most commonly observed and measured property of a heap is the
maximum angle at which a free powder surface can be inclined to the horizontal.
This is the angle of repose and it can be measured in a number of ways,
four of which are shown in Figure 4.1. The angle depends to some extent on
the method chosen and the size of the heap. Minimum angles are about 25°,
and powders with repose angles of less than 40° flow well. If the angle is over
50°, the powder flows with difficulty or not at all.
FIGURE 4.1 Measurement of the angle of repose, ?.
The angle, which is related to the tensile strength of a powder bed, increases
as the particle shape departs from sphericity and as the bulk density
increases. Above 100 microns, it is independent of particle size, but below
this value it increases sharply. The effect of humidity on cohesion and flow
is reflected in the repose angle. Moist powders form an irregular heap with
repose angles of up to 90°.
A more fundamental measure is the tensile stress necessary to divide a
powder bed. The powder may be dredged onto a split plate or, in a more
refined apparatus, contained within a split cylinder and carefully consolidated.
The stress is found from the force required to break the bed and the area of
the divided surface. The principles of this method are shown in Figure 4.2(a),
and stresses of up to 100 N/m2 are necessary to divide a bed of fine powders.
Values increase as the bulk density increases. Changes in cohesiveness with
time and the severe changes in the flow properties of some powders that occur
when the relative humidity exceeds 80% can be assessed with this apparatus.
Apparatus for shearing a bed of powder is shown diagrammatically in
Figure 4.2(b). The shear stress at failure is measured while the bed is constrained
under a normal stress. The latter can be varied. The relation between
these stresses, a subject fully explored in the science of soil mechanics, is
used in the design of bins and hoppers for storage and delivery of powders.
The adhesion of particles to surfaces can be studied in a number of ways.
Measuring the size of the particles retained on an upturned plate is a useful
qualitative test. A common method measures the angle of inclination at which
a powder bed slides on a surface, the bed itself remaining coherent.
FIGURE 4.2 Measuring the (a) tensile and (b) shear strength of a powder bed.
72 Chapter 4
4.3 POWDER FLOW
The physics of powder flow has been studied thoroughly (Crowder and
Hickey, 2000). However, it is only recently that this body of knowledge has
been fully applied to pharmaceutical systems. Pharmaceutical applications exist
for specific unit operations. The gravity flow of powders in chutes and
hoppers and the movement of powders through a constriction occur in tabletting,
encapsulation, and many processes in which a powder is subdivided
for packing into final containers. In many cases, the accuracy of weight and
dose depends on the regularity of flow. The flow of powders is extremely
complex and is influenced by many factors. A profile in two dimensions of
the flow of granular solids through an aperture is shown in Figure 4.3. Particles
slide over A while A slides over B; B moves slowly over the stationary region
E. Material is fed into zone C and moves downward and inward to a tongue
D. Here, packing is less dense, particles move more quickly, and bridges and
arches formed in the powder collapse. Unless the structure is completely emptied,
powder in region E never flows through the aperture. If, in use, a container
is partially emptied and partially filled, this material may spoil. If the container
is narrow, region E is absent and the whole mass moves downward, the central
part of region C occupying the entire tube.
For granular solids, the relation between mass flow rate, G, and the
diameter of a circular orifice, DO, is expressed by the equation
G Constant ? Da
FIGURE 4.3 Profile of granules flow through an orifice.
where H is the height of the bed and a and b are constants. For a wide variety
of powders, the constant a lies between 2.5 and 3.0. If the height of the bed
is several times that of the orifice, H lies between 0 and 0.05. The absence
of a pressure-depth relation, already observed in a static bed, seems, therefore,
to persist in dynamic conditions.
The relation between mass flow rate and particle size is more complex.
With an orifice of given size and shape, the flow increases as the particle size
decreases until a maximum rate is reached. With further decrease in size and
increase in cohesiveness,flowdecreases andbecomesirregular. Archesand bridges
form above the aperture and flow stops. Determining the minimum aperture
through which a powder will flow without assistance is a useful laboratory exercise.
The distribution of particle sizes also affects the flow in a given system.
Often, the removal of the finest fraction greatly improvesflow.Onthe other hand,
the addition of very small quantities of fine powder can, in some circumstances,
improve flow. This is probably due to adsorption of these particles onto the
original material, preventing close approach and the development of strong cohesional
bonds. Magnesia and talc, for example, promote the flow of many cohesive
powders. These materials, which can be called glidants, are useful additives
when good flow properties of a powder are required.
Vibration and tapping may maintain or improve the flow of cohesive
powders by preventing or destroying the bridges and arches responsible for
irregular movement or blockage. Vibration and tapping to initiate flow are
less satisfactory because the associated increase in bulk density due to closer
packing renders the powder more cohesive.
4.4 PACKING OF POWDERS
Bulk density, already defined, and porosity are terms used to describe the
degree of consolidation in a powder. The porosity, ?, is the fraction of the
total volume which is void, often expressed as a percentage. It is related to
the bulk density, ?b, by the equation
where ? is the true density of the powder.
When spheres of equal size are packed in a regular manner, the porosity
can vary from a maximum of 46% for a cubical arrangement to a minimum
of 26% for a rhombohedral array. These extremes are shown in Figure 4.4.
74 Chapter 4
FIGURE 4.4 Systematic packing of spheres.
For ideal systems of this type, the porosity is independent of particle size. In
practice, of course, packing is not regular. Cubic packing, obtained when the
next layer is placed directly on top of the four spheres above, is the most open
packing, as shown in Figure 4.4(a). Rhombohedral packing, obtained when
the next layer is built around the sphere shown in a broken line in Figure
4.4(b), is the closest packing.
Nevertheless, for coarse, isodiametric particles with a narrow range of
sizes, the porosity is remarkably constant at between 37% and 40%. Lead
shot, for example, packs with the same porosity as a closely graded sand. With
wider size distributions, the porosity decreases because some packing of fine
particles in the interstices between the coarsest particles becomes possible.
These effects are absent in fine powders. Due to their more cohesive nature,
the porosity increases as the particles become finer and variation in the size
distribution has little effect.
In any irregular array, the porosity increases as particle shape departs
from sphericity because open packing and bridging become more common.
A flaky material, such as crushed mica, packs with a porosity of about 90%.
Roughness of the particles’ surface increases porosity.
In operations in which powders are poured, chance packing occurs and
porosity is subject to the operation’s speed and degree of agitation. If the
powder is poured slowly, each particle can find a stable position in the developing
surface. Interstitial volumes are small, the number of contacts with
neighboring particles is high, and the porosity is low. If pouring is quick,
there is insufficient time for stable packing, bridges are created as particles
fall together, and a bed of higher porosity is formed. Vibration opposes open
packing and the formation of bridges. It is often deliberately applied when
closely packed powder beds are required.
Packing at a boundary differs from packing in the bulk of a powder.
The boundary normally creates a region of more open packing, several particle
layers in extent. This is important when particles are packed into small volumes.
If the particles are relatively large, the region of expanded packing and
low bulk density will be extensive and, for these conditions, the weight of
material that fills the volume will decrease as particle size increases. With
finer powders the opposite is true, and cohesiveness causes the weight of powder
which fills a volume to decrease as particle size decreases. There is, therefore,
some size of particle for which the capacity of a small volume is a maximum.
This depends on the dimensions of the space into which the particles
Granulation is a term for several processes used to produce materials in the
form of coarse particles. In pharmacy, it is closely associated with the preparation
of compressed tablets. Discussion is here limited to a general account of
Ideally, granulation yields coarse isodiametric particles with a very narrow
size distribution. The several advantages of this form can be inferred from
the foregoing discussion. Granules flow well. They feed evenly from chutes
and hoppers and pack into small volumes without great variation of weight.
Segregation in a mixture of powders is prevented if the mixture is granulated.
Each granule contains the correct proportions of the components so that segregation
of granules cannot cause inhomogeneity in the mixture. The hazards
of dust are eliminated and granules are less susceptible to lumping and caking.
Finally, granular materials fluidize well, and a material may be granulated to
gain the advantages of this process.
The starting materials for granulation vary from fine powders to solutions.
Methods can be classified as wet or dry granulation. In the latter, a very
coarse material is comminuted and classified. If the basic material is a fine
powder, it is first aggregated by pressure with punches and dies, to give tablets
or briquettes, or by passage through rollers, to give a sheet that is then broken.
In wet methods a liquid binder is added to a fine powder. If the proportion
added converts the powder to a crumbly adhesive mass, it can be granulated
by forcing it through a screen with an impeller. The wet granules are
76 Chapter 4
then dried and classified. If a wetter mass is made, it can be granulated by
extrusion. Alternatively, the powder can be rotated in a pan and granulating
fluid added until agglomeration occurs. Granule growth depends critically on
the amount of fluid added and other variables, such as the particle’s size and
pan speed and the surface tension of the granulating fluid, must be closely
Granular materials are also prepared by spray-drying and by crystallization.
The movement of fluids through a fixed bed was described in Chapter 1. If
the fluid velocity is low, the same situation is found when fluid is driven
upward through a loose particulate bed. At higher velocities, however, frictional
drag causes the particles to move into a more expanded packing which
offers less resistance to flow. At some critical velocity, the particles are just
touching and the pressure drop across the bed just balances its weight. This
is the point of incipient fluidization; beyond it true fluidization occurs, the bed
acquiring the properties of surface leveling and flow.
If the fluid is a liquid, increase in velocity causes the quiescent bed to
rock and break, allowing individual particles to move randomly in all directions.
Increase in velocity causes progressive thinning of this system. In fluidization
by gases, the behavior of the bed is quite different. Although much of
the gas passes between individual particles in the manner already described,
the remainder passes in the form of bubbles so that the bed looks like a boiling
liquid. Bubbles rise through the bed, producing an extensive wake from which
material is continually lost and gained, and breaking at the surface distributes
powder widely. This mixing mechanism is effective, and any nonhomogeneity
in the bed is quickly destroyed. Rates of heat and mass transfer in the bed are
Bubble size and movement vary in different systems. In general, both
decrease as particle size decreases. As the size decreases and the powder becomes
more cohesive, fluidization becomes more difficult. Eventually, bubbles
do not form and very fine powders cannot be fluidized in this way.
The final stage of fluidization occurs at very high velocities when, in
liquid and gaseous systems, the particles become entrained in the fluid and
are carried along with it. These conditions are used to convey particulate solids
from one place to another.
4.7 MIXING AND BLENDING
Mixing and blending may be achieved by rotating or shearing the powder bed.
Mixing two or more components that may differ in composition, particle size,
or some other physicochemical property is brought about through a sequence
of events. Most powders at rest occupy a small volume such that it would be
difficult to force two static powder beds to mix. The first step in a mixing
process, therefore, is to dilate the powder bed. This second step, which may
be concurrent with the first, is to shear the powder bed. Ideally, shearing occurs
at the level of planes of individual particles. The introduction of large interparticulate
spaces is achieved by rotating the bed. A V blender or a barrel roller
are classical examples of systems which, by rotating through 360°, dilate the
powder bed while, through the influence of gravity, shearing planes of particles.
A planetary mixer uses blades to mechanically dilate and shear the powder.
Each of these systems is a batch process. A ribbon blender uses a screwing
action to rotate and shear the bed from one location to another in a continuous
Since the shearing of particles in a bed to achieve a uniform mix or blend
is a statistical process, it must be monitored for efficiency. Sample thieves are
employed to probe the powder bed, with minimal disturbance, and draw samples
for analysis. These samples are then analyzed for the relevant dimension
for mixing, e.g., particle sizes, drug, or excipient content. Statistical mixing
parameters have been derived based on the mean and standard deviation of
samples taken from various locations in a blend at various times during the
processing (Carstensen, 1993). In large-scale mixers random number tables
may be employed to dictate sample sites. There is a considerable science of
sampling that can be brought to bear on this problem (Thompson, 1992). The
sample size for pharmaceutical products is ideally of the scale of the unit dose.
This is relevant as it relates to the likely variability in the dose that in turn
relates to the therapeutic effect. In the case of small unit doses the goal should
be to sample at a size within the resolution of the sample thief.
The origins, structure, and properties of particles within a powder dictate their
dynamic performance. Gathering information on the physicochemical properties
of powders is a prerequisite for interpreting and manipulating their flow
and mixing properties. Flow properties are important to many unit processes
78 Chapter 4
in pharmacy, including transport and movement through hoppers, along conveyor
belts, in granulators, and in mixers. Ultimately, the packing and flow
properties can be directly correlated with the performance of the unit dose.
Filling of capsules, blisters, or tablet dies, compression of tablets, and dispersion
of powder aerosols all relate to powder properties.
Air Conditioning and
Air conditioning for comfort means the provision of warm, filtered air. High
moisture content or humidity is oppressive, but a low humidity may cause
irritation by excessive loss of moisture from the skin. In some climates steps
may be taken to add or remove water vapor from the air. The air is cleaned,
usually by passage through a fabric filter which may be dry or moistened with
a viscous liquid, and heated electrically or by banks of finned tubes supplied
with steam or hot water over which the air is blown. Electrostatic precipitation
provides an alternative method of air cleaning. The fine particles entrained in
the air are charged by the absorption of electrons as they pass between two
electrodes. The charged particle then migrates in the electrical field and is
finally arrested on one electrode.
The same general principles apply to the supply of air in some pharmaceutical
processes. However, the control of its quality may be more stringent. In
areas in which sterile materials are made and handled, for example, the air cleaning
must remove bacteria. In other processes, it may be necessary to remove
water vapor. The flow of powders is a sensitive function of moisture content.
The equilibrium moisture content of a material is determined by the humidity.
Some tableting processes break down if the humidity is too high. In such pro-
80 Chapter 5
cesses, the scale of the air conditioning varies. It may be necessary to supply a
whole room with air of a certain quality. Alternatively, conditioning may be
restricted to a small area surrounding a particular piece of equipment.
5.1 VAPOR AND GAS MIXTURES
The humidity of a vapor-gas mixture is defined as the mass of vapor associated
with unit mass of the gas. This principle is generally applicable to any vapor
present in any noncondensable gas. In this section, however, only water vapor
in air is considered. The percent humidity is the ratio of ambient humidity to
the humidity of the saturated gas at the same temperature, expressed as a
percentage. These terms should be carefully distinguished from the relative
humidity with which they are distantly related. The relative humidity is the
ratio of the partial pressure of the vapor in the gas to the partial pressure when
the gas is saturated. This is also usually expressed as a percentage. The relative
humidity of a given vapor-gas mixture changes with temperature, but the humidity
The study of the properties of the air-water vapor mixture is called psychrometry,
and data is presented in the form of psychrometric charts. These
take various forms and present various data (Perry and Chilton, 1973). In
FIGURE 5.1 A psychrometric chart that can be used to determine the humidity, dew
point, and wet and dry bulb temperatures.
Air Conditioning and Humidification 81
Figure 5.1, humidity is plotted as the ordinate and temperature as the abscissa.
Percent relative humidity is then plotted as a series of curves running across
the chart. The use of this simplified chart is demonstrated later in this chapter
and the next.
5.2 HYGROMETRY, THE MEASUREMENT OF
The accurate determination of the air’s humidity is carried out gravimetrically.
The water vapor present in a known volume of air is chemically absorbed
with a suitable reagent and weighed. In other less laborious methods, the humidity
is derived from the dew point or the wet bulb depression of a water
The dew point is the temperature at which a vapor-gas mixture becomes
saturated when cooled at constant pressure. If air of the condition denoted by
point A in Figure 5.1 is cooled, the relative humidity increases until the mixture
is fully saturated. This condition is given by point B where the temperature
coordinate is the dew point. This can be measured rapidly by evaporating ether
in a silvered bulb. The temperature at which dew deposits from the surrounding
air is noted, and the humidity is read directly from a psychrometric
Humidity derivation from the wet bulb depression requires a preliminary
study of the transfer of mass and heat at a boundary between air and water.
Since this process is also important in the study of drying, a detailed explanation
is set out. If a small quantity of water evaporates into a large volume of
air, conditions which make the change in humidity negligible, the latent heat
of evaporation is supplied from the sensible heat of the water. The latter cools
and the temperature gradient between water and air promotes the flow of heat
from the surrounding air to the surface. As the temperature falls, the rate of
heat flow increases until it equals the rate at which heat is required for evaporation.
The temperature at the surface then remains constant at what is known
as the wet bulb temperature. The difference between the air temperature and
the wet bulb temperature is the wet bulb depression. If these temperatures are
denoted by Ta and Twb, the rate of heat transfer, Q, is
Q hA(Ta Twb) (5.1)
where A is the area over which heat is transferred and h is the heat transfer
coefficient. Mass transfer of water vapor from the water surface to the air is
82 Chapter 5
described by the equation
(Pwi Pwa) (5.2)
where Pwi is the partial pressure of water vapor at the surface, Pwa is the partial
pressure of water vapor in the air, kg is a mass transfer coefficient, and N is
the number of moles transferred from unit area in unit time. Rewriting this
equation in terms of the mass, W, transferred at the whole surface in unit time,
where Mw is the molecular weight of water vapor, we get
kg(Pwi Pwa) (5.3)
where A is the area of the surface. If the partial pressure of water vapor in a
system has the value Pw, then, from the general gas equation, the mass of
vapor in unit volume is (Pw/RT) Mw. Similarly, if the total pressure is P, the
mass of air in unit volume is [(P Pw)/RT ]/Ma, where Ma is the ‘‘molecular
weight’’ of the air. The humidity, H, is the ratio of these two quantities:
If P Pw, H (Pw/P)(Mw/Ma). Rearranging and substituting humidity
for partial pressure in equation 5.3 give
kgA(Hi Ha) (5.5)
where Ha is the humidity of the air and Hi is the humidity at the surface. The
latter is known from the vapor pressure of water at the wet bulb temperature.
Since PMa/RT ?, equation 5.5 can be written
W ?kgA(Hi Ha) (5.6)
where ? is the density of the air. If the latent heat of evaporation is ?, the
heat transfer rate necessary to promote this evaporation is
Q ?kgA(Hi Ha) (5.7)
Equating expressions 2.7 and 5.7 then gives
(Ta Twb) (5.8)
Air Conditioning and Humidification 83
Both the heat and mass transfer coefficients are functions of air velocity.
However, at air speeds greater than about 4.5 m s1, the ratio h/kg is approximately
constant. The wet bulb depression is directly proportional to the difference
between the humidity at the surface and the humidity in the bulk of the
In the wet and dry bulb hygrometers, the wet bulb depression is measured
by two thermometers, one of which is fitted with a fabric sleeve wetted
with water. These are mounted side by side and shielded from radiation, an
effect neglected in the preceding derivation. Air is then drawn over the thermometers
by a small fan. The derivation of the humidity from the wet bulb
depression and a psychrometric chart will be discussed later.
Many wet and dry bulb hygrometers operate without any form of induced
air velocity at the wet bulb. This may be explained by examining another
air-water system. If a limited quantity of air and water is allowed to
equilibrate in conditions in which heat is neither gained nor lost by the system,
the air becomes saturated and the latent heat required for evaporation is drawn
from both fluids, which will cool to the same temperature. This temperature
is the adiabatic saturation temperature, Ts. It is a peculiarity of the air-water
system that the adiabatic saturation temperature and the wet bulb temperature
are the same. If water at this temperature is recycled in a system through which
air is passing, the incoming air is cooled until it reaches the adiabatic saturation
temperature, at which point it is saturated. The temperature of the water, on the
other hand, remains constant, and all the latent heat required for evaporation is
drawn from the sensible heat of the air. Equilibrium is then expressed by the
(Ta T?)S (H? Ha)? (5.9)
where Ta is the temperature of the incoming air, S is its specific heat, Ha and
H? are the humidities of the incoming air and the saturated air, and ? is the
latent heat of evaporation for water.
The process of adiabatic saturation in which the humidity progressively
rises and the temperature progressively falls is described on a humidity chart
by adiabatic cooling lines which run diagonally to the saturation curve. Charts
are specially constructed so that these lines become parallel.
If a wet and dry bulb hygrometer is exposed to still air, the region adjacent
to the wet bulb closely resembles the system described. After a considerable
period, equilibrium is attained and the wet bulb records the adiabatic
When both wet and dry bulb temperatures have been found, the humidity
is read from the psychrometric chart in the following way. The point on the
84 Chapter 5
saturation curve corresponding to the wet bulb temperature is first found. An
adiabatic cooling line is then interpolated and followed until the coordinate
corresponding to the dry bulb temperature is reached. The humidity is read
from the other axis.
The change in the physical properties of a hair or fiber with change in
humidity is utilized in many instruments. After calibration, they are suitable
for use over a limited range of humidity.
5.3 HUMIDIFICATION AND
Most commonly, air is humidified by passage through a spray of water. Three
methods are illustrated by the humidity diagrams in Figure 5.2. In the first,
air at temperature T1 is heated to T2. The latter temperature is chosen so that
adiabatic cooling and saturation followed by heating to T4 will give a humidity
rise from H1 to H2. The humidification stage is performed by passing the air
FIGURE 5.2 Humidification and dehumidification of air.
Air Conditioning and Humidification 85
through water sprays at the adiabatic saturation temperature, T3. Alternatively,
the incoming air could be heated to T5, air of the correct humidity emerging
when it is adiabatically cooled to T4 with water. In neither of these methods
is control of the water temperature necessary. In the third method, air of humidity
H1 and temperature T1 is passed through and saturated by a water spray
maintained at T3. On leaving the chamber, it is heated to T4.
For small quantities of air, dehumidification is most easily accomplished
by adsorbing water vapor with alumina or silica gel arranged in columns.
These columns are mounted in pairs so that one can be regenerated while the
other is in use. Alternatively, the air can be cooled below the dew point. Excess
water vapor condenses and the cold saturated air is then reheated. For wellmixed
gases, the process is described in Figure 5.2.
Drying may be defined as the vaporization and removal of water or other
liquid from a solution, suspension, or other solid-liquid mixture to form a dry
solid. The change of phase from liquid to vapor distinguishes drying from
mechanical methods of separating solids from liquids, such as filtration. The
latter often precede drying since, where applicable, they offer a cost-effective
method for removing a large part of the liquid.
Drying might still be confused with evaporation. Greater precision is
not possible because the division of the two operations is to some extent
arbitrary. Drying is normally associated with the removal of relatively small
quantities of liquid to give a dry product. Evaporation is more often applied
to the concentration of solutions. However exceptions to these generalizations
Adjustment and control of moisture levels by drying are important in
the manufacture and development of pharmaceutical products. Apart from the
obvious requirement of dry solids for many operations, drying may be carried
1. Improve handling characteristics, as in bulk powder filling and other
operations involving powder flow
2. Stabilize moisture-sensitive materials, such as aspirin and ascorbic
A wide range of drying equipment is available to meet these ends, but
in practice the choice is limited by the scale of the operation and may be
determined partly or completely by the thermal stability of the material and
the physical form in which it is required. In the pharmaceutical industry, batch
sizes are frequently small and of high value and the same dryer may be used
to dry different materials. These factors limit the application of continuous
dryers and promote the use of batch dryers that give low product retention
and are easily cleaned. Recovery of solvents, where economically justified,
may be another factor affecting choice of equipment.
6.1 THEORY OF DRYING
Theories of drying are limited in application in that drying times are normally
experimentally determined. Nevertheless, an appreciation of the scope and
limitations of the different drying methods is given. The following terms are
employed in discussing drying: humidity, humidity of saturated air, relative
humidity, wet bulb temperature, and adiabatic cooling line (see Chapter 5).
Other terms may be defined as follows:
Moisture content. This is usually expressed as a weight per unit weight
of dry solids.
Equilibrium moisture content. If a material is exposed to air at a given
temperature and humidity, it will gain or lose moisture until equilibrium
is reached. The moisture present at this point is defined as the
equilibrium moisture content for the given exposure conditions. At a
given temperature it varies with the partial pressure of the water vapor
in the surrounding atmosphere. This is shown for a hypothetical hygroscopic
material in Figure 6.1 in which the equilibrium moisture
content is plotted against the relative humidity. Any moisture present
in excess of the equilibrium moisture content is called free water.
Equilibrium moisture content curves vary greatly with the type of material
examined. Insoluble, nonporous materials, such as talc or zinc oxide, give
equilibrium moisture contents of almost zero over a wide humidity range. A
moisture content of between 10% and 15% may be expected for cotton fabrics
under normal atmospheric conditions. Drying below the equilibrium moisture
content for room conditions may be deliberately undertaken, particularly if
88 Chapter 6
FIGURE 6.1 Relation between equilibrium moisture content and relative humidity
for a hygroscopic solid.
the material is unstable in the presence of moisture. Subsequent storage conditions
then become important for product stability.
The equilibrium moisture content at 100% relative humidity represents
the minimum amount of water associated with the solid that still exerts a vapor
pressure equal to a separate water surface. If the humidity is reduced, only
part of the water evaporates before a new equilibrium is established. The water
retained at less than 100% relative humidity must, therefore, exert a vapor
pressure below that of a dissociated water surface. Such water is called bound
water. Unlike the equilibrium moisture content, bound water is a function of
the solid only and not of the surroundings. Such water is usually held in small
pores bound with highly curved menisci, is present as a solution, or is adsorbed
on the surface of the solid.
The value of equilibrium moisture content curves is illustrated in Figure
6.2. The equilibrium moisture content of the antacid granules, composed of
magnesium trisilicate granulated with syrup, is a sensitive function of relative
humidity. If it is to be dried to a moisture content of 3%, air at a relative
humidity of less than 35% must be used. With knowledge of the humidity of
the circulating air, psychrometric charts may be used to determine the minimum
air temperature that will dry the material to the required standard. (In
fact, the temperature has an effect on the equilibrium moisture content that is
independent of the humidity, but this can be neglected to a first approximation.)
The lactose granulation, on the other hand, has a low sensitivity to relaDrying
FIGURE 6.2 Equilibrium moisture content curves for two tablet granulations.
tive humidity. Drying at low relative humidities derived from high air temperatures
causes only a marginal decrease in the final moisture content, and the
stability of the active ingredients associated with the lactose filler could be
impaired. This argument may only be applied to the final moisture content.
It is not related to the rate of drying, which would, of course, be greater at
higher temperatures and lower humidities.
The effects of storage after drying may also be assessed from the equilibrium
moisture content curves. Storage conditions are not critical for lactose
granulation. If the antacid formulation was stored at a relative humidity of
only 65% it would, given sufficient time, absorb moisture until the content was
9%. This could be associated with poor flow characteristics and its attendant
difficulties during compression.
Dynamic vapor sorption techniques now exist which allow thorough
studies of moisture association with solids under a wide range of relative humidity
conditions based on microbalance technology.
6.2 EVAPORATION OF WATER INTO AN
The evaporation of moisture into a warm airstream, the latter providing the
latent heat of evaporation, is a common drying mechanism although it is not
90 Chapter 6
easily adapted to the recovery of the liquid. We will first consider evaporation
from a liquid surface which, with the passage of air, falls to the wet bulb
temperature corresponding to the temperature and humidity of the air, as described
in Chapter 5. The rate at which water vapor is transferred from the
saturated layer at the surface to the drying stream is described by equation
(Pwi Pwa) (3.5)
where Pwi is the partial pressure of the water vapor at the surface, Pwa is the
partial pressure of water vapor in the air, kg is a mass transfer coefficient, and
N is the number of moles of vapor transferred from unit area in unit time.
Rewriting this in terms of the total mass, W, transferred in unit time from the
entire drying surface of area A; we obtain
kg(Pwi Pwa) (6.1)
where Mw is the molecular weight of water vapor, R is the gas constant, and
T is the absolute temperature.
The mass transfer coefficient, kg, is a function of the temperature and
the air’s velocity and angle of incidence. A high velocity or angle of incidence
diminishes the thickness of the stationary air layer in contact with the liquid
surface and, therefore, lowers the diffusional resistance.
The rate of evaporation may also be expressed in terms of the heat transferred
across the laminar film from the drying gases to the surface. This is
described by equation 2.7:
Q hA(Ta Ts) (2.7)
where Q is the rate of heat transfer, A is the area of the surface, Ta and Ts are
the temperatures of the drying air and the surface, respectively, and h is the
heat transfer coefficient. The latter is also a function of air velocity and angle
of impingement. If the latent heat of evaporation is ?, this affords a mass
transfer rate, W, given by
(Ta Ts) (6.2)
Equilibrium drying conditions are represented by the equality of relations
6.1 and 6.2. When these conditions pertain to drying, the surface temperature,
Ts, which is the wet bulb temperature, is normally much lower than the
temperature of the drying gases. This is of great importance in the drying of
If solids are present in the surface, the rate of evaporation is modified,
the overall effect depending on the structure of the solids and the moisture
6.3 STATIC BEDS OF NONPOROUS SOLIDS
Drying wet granular beds, the particles of which are not porous and are insoluble
in the wetting liquid, has been extensively studied. The operation is presented
as the relation of moisture content and drying time [Figure 6.3(a)].
Note that the equilibrium moisture content is approached slowly. A protracted
period may be required for the removal of water just above the equilibrium
value. This time is not justified if a small amount of water can be tolerated in
further processing, and such a process indicates the importance of establishing
realistic drying requirements. The stability of the solids, maintained, as shown
later, at a temperature close to that of the drying air, may allow unnecessary
The data has been converted to a curve relating the rate of drying to
moisture content [Figure 6.3(b)]. The initial heating-up period during which
equilibrium is established is short and has been omitted from both figures.
FIGURE 6.3 (a) Moisture content vs. time of drying; (b) rate of drying vs. moisture
92 Chapter 6
Assuming that sufficient moisture is initially present, the drying rate
curve exhibits three distinct sections limited by points A, B, C, and D. In
section A-B, called the constant rate period, it is considered that moisture is
evaporating from a saturated surface at a rate governed by diffusion from the
surface through the stationary air film in contact with it. An analogy with
evaporation from a plain water surface can therefore be drawn. The drying
rate during this period depends on the air temperature, humidity, and speed,
which, in turn, determine the temperature of the saturated surface. Assuming
that these are constant, all variables in the drying equations are fixed, and a
constant rate of drying is established which is largely independent of the material
being dried. The drying rate is somewhat lower than for a free-water surface
and depends to some extent on the particle size of the solids. During the
constant rate period, liquid must be transported to the surface at a rate suffi-
cient to maintain saturation. The mechanism of transport is discussed later.
At the end of the constant rate period, B, a break in the drying curve
occurs. This point is called the critical moisture content, and a linear fall in
the drying rate occurs with further drying. This section, B-C, is called the first
falling rate period. At and below the critical moisture content, the movement
of moisture from the interior is no longer sufficient to saturate the surface. As
drying proceeds, moisture reaches the surface at a decreasing rate, and the
mechanism that controls its transfer will influence the rate of drying. Since the
surface is no longer saturated, it tends to rise above the wet bulb temperature.
For any material, the critical moisture content decreases as the particle
size decreases. Eventually, moisture does not reach the surface that becomes
dry. The plane of evaporation recedes into the solid, the vapor reaching the
surface by diffusion through the pores of the bed. This section is called the
second falling rate period and is controlled by vapor diffusion, a factor largely
independent of the conditions outside the bed but markedly affected by the
particle size due to the latter’s influence on the dimensions of pores and channels.
During this period, the surface temperature approaches the temperature
of the drying air.
Considerable migration of liquid occurs during the constant rate and first
falling rate periods. Associated with the liquid are any soluble constituents
that will form a concentrating solution in the surface layers as drying proceeds.
Deposition of these materials takes place when the surface dries. Considerable
segregation of soluble elements in the cake can occur, therefore, during drying.
If the soluble matter forms a skin or gel on drying rather than a crystalline
deposit, a different drying curve (Figure 6.4) is obtained. The constant
rate period is followed by a continuous fall in the drying rate in which no
differentiation of first and second falling rate periods can be made. During this
FIGURE 6.4 Driving curve for a skin-forming material.
period, drying is controlled by diffusion through the skin that is continually
increasing in thickness. Soap and gelatin are solutes that behave in this way.
6.4 THE INTERNAL MECHANISM OF DRYING
Extensive studies have been made to determine the nature of the forces that
initially convey moisture to the surface at a rate sufficient to maintain saturation
and their subsequent failure. Liquid movement may occur by diffusion
under the concentration gradient created by water depletion at the surface by
evaporation, as the result of capillary forces, through a cycle of vaporization
and condensation, or by osmotic effects. Of these, capillary forces offer a
coherent explanation for the drying periods of many materials.
If a tapered capillary is filled with water and exposed to a current of
air, the meniscus at the smaller end remains stationary while the tube empties
from the wider end. A similar situation exists in a wet particulate bed, and
the phenomenon is explained by the concept of suction potential. A negative
pressure exists below the meniscus of a curved liquid surface which is proportional
to the surface tension, ?, and inversely proportional to the radius of
curvature, r. (The meniscus is assumed to be part of a hemisphere.) This negative
pressure or suction potential may be expressed as the height of liquid, h,
it will support:
94 Chapter 6
where ? is the density of the liquid. The suction potential, hx, acting at a depth
x below the meniscus is then
hx h x (6.4)
The particles of the bed enclose spaces or pores connected by passages,
the narrowest part of which is called the waist. The waist dimensions are
determined by the size of the surrounding particles and the manner in which
they are packed. In a randomly packed bed, pores and waists of varying sizes
are found. Thus, the radius of a capillary running through the bed varies continuously.
The depletion of water in this network is controlled by the waists
because the radii of curvature are smaller and the suction potentials greater
than for the pores. Depletion occurs in the following way. As evaporation
proceeds, the water surface recedes into the waists of the top layer of particles
and a suction potential develops. The maximum suction potential a waist can
develop is called its ‘‘entry’’ suction potential and this potential is exceeded
for larger waists by the suction potential developed by the smaller waists and
transmitted through the continuous, connecting thread of liquid. The menisci
in the larger waists then collapse and the pores they protect are emptied. A
surface waist developing a suction potential, hs, assuming an interconnecting
thread of liquid, causes the collapse of an interior waist developing a suction
potential, hi, at a distance, x, below the surface if hs hi x. The liquid in
the exposed pores is then lost at the surface by evaporation. This effect continues
until a waist provides an opposing suction potential equal to or greater
than the suction potential provided at that depth by the fine surface waist
meniscus. The latter then collapses and the pore it protects is emptied.
By this mechanism, a meniscus in a fine surface waist holds its position
and depletes the interior of moisture. If sufficient full surface waists are present,
the constant rate period is maintained since the stationary air film in contact
with the bed can be saturated. The first falling rate period indicates that
insufficient full surface waists are present. Eventually, the collapse of all surface
waists takes place, giving a breakdown of the capillary network supplying
moisture to the surface, and the second falling rate period ensues.
6.5 STATIC BEDS OF POROUS SOLIDS
The drying curve obtained when the particles that compose the bed are themselves
porous is shown in Figure 6.5. It differs from the curve obtained with
nonporous materials in that the constant rate period is shorter. The rate of
drying may be higher and is almost independent of particle size. The critical
FIGURE 6.5 Drying curves for a tablet granulation dried in a tray dryer.
moisture content is a function of the pore and particle sizes. During the first
falling rate period, the rate of drying falls steeply due, it is thought, to the
drying of the surface granules. The second falling rate period is influenced by
the diffusion of moisture from within the particles.
6.6 THROUGH CIRCULATION DRYING
If the particles are in a suitable granular form, it is often possible to pass the
airstream downward through the bed of solids. Drying will then follow the
pattern described in previous sections except that each particle or agglomerate
behaves as a drying bed. The surface area exposed to the drying gases is
greatly increased, and drying rates 10 to 20 times greater than those encountered
when air is passed over a free surface are obtained.
6.7 METHODS INVOLVING MOVEMENT OF
As an extension of drying by passing the airstream through a static bed of
solids, it is possible to project air upward through the bed at a velocity high
enough to fluidize the particles. Alternatively, the material may be mechanically
subdivided and then introduced into the drying stream. Both methods
give high drying rates due to high interfacial contact between the drying sur96
faces and the airstream. Fluidized bed dryers and spray dryers, respectively,
use these principles.
6.8 OTHER METHODS OF DRYING
Apart from specialized dryers using infrared or dielectric heating, the chief
method of passing heat into a drying solid, other than from a hot airstream,
is by conduction from a heated surface. When a wet solid is placed in contact
with a hot surface, subsequent events depend on the surface temperature relative
to the liquid’s boiling point, the nature of the solid, and the method of
heating the surface. It is assumed here that the surface temperature is not hot
enough for convective boiling to take place.
Consider first a cake of finely divided solids saturated with water. A
temperature gradient will be established through the cake and evaporation
from the free surface will take place at a rate governed entirely by the rate of
heat input. During this period, the rate of evaporation and the temperature of
a particular layer of cake are approximately constant. This continues until
capillary forces are unable to transfer liquid to the free surface at the required
rate. The temperature gradients during this period are given in Figures 6.6(a)
and 6.6(b) for conditions in which the shelf temperature is below and above
the boiling point of the liquid, respectively.
With a comparatively low heat flux, such that the partially dried cake
can conduct heat away from the hot surface at the required rate, the free surface
will dry and a fictitious drying line recedes slowly into the cake. The vapor
diffuses through the dry cake to the free surface. The temperature gradient
during this falling rate period is shown in Figure 6.6(c). If the heat flux is
high, the point at which mobile water can no longer reach the surface is marked
by the onset of drying in a layer adjacent to the hot surface, and vapor is
forced through the wet cake above. As the solid dries, its temperature increases
and a temperature gradient is established through the dry solids to the upwardreceding
drying line [Figure 6.6(d)]. The free surface of the solid appears wet
and is at a constant temperature. These conditions are destroyed when the
drying line reaches the surface.
In either case, a low and falling rate of drying will persist as the absorbed
water is removed. In this form of drying, the heat treatment received by the
solid is not uniform but depends on its position in the cake.
A hot surface may also be used to dry solutions, such as milk or plant
extracts, which do not readily give porous, crystalline solids on concentration.
FIGURE 6.6 Drying by conduction of heat from a heated surface
Apart from an initial constant rate period, when heat transfer is mainly convective,
drying periods are ill-defined. As concentration proceeds, the liquor becomes
more viscous and heat transfer is mainly by conduction. Large volume
changes occur between initial and final stages. It is possible to dry thin films
of solution to a solid film, but if deeper layers are taken a skin is frequently
formed at the free surface that is almost impervious to the vapor. Frothing
and drying to a porous, friable structure then occur. They may also occur if,
during the upward recession of the drying line, the material above is too viscous
to allow vapor to escape.
98 Chapter 6
FIGURE 6.7 (a) Tray dryer. (b) Temperature-humidity sequence of drying air.
6.9 SOLIDS MOVING OVER A HOT SURFACE
Conditions in which the solids move over a heated surface are employed in
tumbling and agitated dryers. Drying rates are higher than those obtained in
static beds because fresh solids are continually exposed to the hot surface.
The heat treatment received by the solid will be more uniform.
6.10 BATCH DRYERS
6.10.1 Hot Air Ovens
Ovens operating by passing hot air over the surface of a wet solid that is
spread over trays arranged in racks provide the simplest and cheapest dryer.
On small installations, the air is passed over electrically heated elements and
once through the oven. Larger units may employ steam-heated, finned tubes,
and thermal efficiency is improved by recirculating the air. This is controlled
by manually set dampers, and a common operating position gives 90% recirculation
and 10% bleed-off. The heater bank is placed so that the solids do not
receive radiant heat, and incoming air may be filtered. A typical hot air oven
is illustrated schematically in cross section in Figure 6.7(a).
The temperature-humidity sequence of the circulating drying air is presented
in Figure 6.7(b). The incoming air, at a temperature and humidity given
by point A, is heated at constant humidity to point B and passed over the wet
solid. The humidity rises and the temperature falls as the adiabatic cooling line
is followed until the air leaves the tray in condition C. It is then recirculated to
the heater; in Figure 6.7(b), two further cycles are shown.
We have assumed that all heat is drawn from the air and transmitted
across the stationary air layer in contact with the drying surface, as described
earlier. Surface temperatures are, in fact, modified by heat absorbed and conducted
from unwetted surfaces, such as the underside of the tray, and by radiation.
The chief advantage of the hot air oven, apart from its low initial cost,
is its versatility. With the exception of dusty solids, materials of almost any
other physical form may be dried. Thermostatically controlled air temperatures
between 40° and 120°C permit heat-sensitive materials to be dried. For small
batches a hot air oven is, therefore, often the plant of choice. However, the
following inherent limitations have led to the development of other small
a. A large floor space is required for the oven and tray loading facilities.
b. Labor costs for loading and unloading the oven are high.
c. Long drying times, usually about 24 hr, are necessary.
d. Solvents can be recovered from the air only with difficulty.
e. Unless carefully designed, nonuniform distribution of air over the
trays gives variation in temperature and drying times within the
oven. Variations of 7°C in temperature have been found from location
to location during the drying of tablet granules. Poor air circulation
may permit local saturation and the cessation of drying.
If the material is of suitable granular form, drying times may be reduced
to an hour or less by passing the air downward through the material laid on
mesh trays. The oven in this form is called a batch-through-circulation dryer.
6.10.2 Vacuum Tray Dryers
Vacuum tray dryers [Figure 6.8(a)], differing only in size from the familiar
laboratory vacuum oven, offer an alternative method for drying small quantities
of material. When scaled up, construction becomes massive to withstand
the applied vacuum and cost is further increased by the associated vacuum
equipment. Vacuum tray dryers are, therefore, only used when a definite advantage
over the hot air oven is secured, such as low-temperature drying of
thermolabile materials or the recovery of solvents from the bed. The exclusion
of oxygen may also be advantageous or necessary in some operations.
Heat is usually supplied by passing steam or hot water through hollow
shelves. Drying temperatures can be carefully controlled and, for the major
part of the drying cycle, the material remains at the boiling point of the wetting
100 Chapter 6
FIGURE 6.8 (a) Rotary vacuum dryer and (b) fluidized bed dryer.
liquid under the operating vacuum. Radiation from the shelf above may cause
a significant increase in temperature at the surface of the material if high drying
temperatures are used. Drying times are long, usually about 12 to 48 hr.
6.10.3 Tumbling Dryers
The limitations of ovens, particularly with respect to the long drying times,
has, where possible, promoted the design and application of other batch dryers.
The simplest of these is the tumble dryer, for which the most common shape is
the double cone in Figure 6.8(a). Operating under vacuum, this dryer provides
controlled low-temperature drying, the possibility of solvent recovery, and
increased rates of drying. Heat is supplied to the tumbling charge by contact
with the heated shell and by heat transfer through the vapor. Optimum conditions
are established experimentally by varying the vacuum, temperature, and,
if the material passes through a sticky stage, rotation speed. With correct operation
a uniform powder should be obtained, as distinct from the cakes produced
when static beds are dried. Some materials, such as waxy solids, cannot
be dried by this method because the tumbling action causes the material to
aggregate into balls.
A normal charge would be about 60% of the total volume, and, for dryers
0.7 to 2 m in diameter, drying times of 2 to 12 hr may be expected. When
applied to drying tablet granules, periods of 2 to 4 hr replace the 18 to 24 hr
obtained with hot air ovens. The mixing and granulating capacity of the tumDrying
bling action has suggested that these operations could precede drying in the
6.10.4 Fluidized Bed Dryers
The term fluidization is applied to processes in which a loose, porous bed of
solids is converted to a fluid system, having the properties of surface leveling,
flow and pressure-depth relationships, by passing the fluid up through the bed.
Fluidized bed techniques, employing air as the fluidizing medium, have
been successfully applied to drying when the solid is of suitable physical form.
The high interfacial contact between drying air and solids gives drying rates
10 to 20 times greater than are obtained during tray drying. A drying curve
for this method is shown in Figure 6.9.
The dryer, illustrated in Figure 6.8(b), consists of a basket of plastic or
stainless steel with a perforated bottom mounted in the body of the drier and
into which the material to be dried is placed. Heated air may be blown or
sucked through the bed. The air leaving the basket passes through an air filter
and may be recirculated. Particle properties, such as shape and size distribution,
affect fluidization, and a unit must have a variable airflow, adjusted so
that the material is fluidized but is not carried into the filters. For this reason,
the material must have a fairly close size range or elutriation of fine particles
into the filters will take place.
FIGURE 6.9 Drying curves.
102 Chapter 6
Fluidized bed dryers are particularly suitable for granulated materials
and are increasingly being used for tablet granulations when product changeover
is not too frequent. It may be advantageous to preform other materials,
such as a dewatered filter cake, into granules solely in order to employ fluidized
bed drying. If fluidizing conditions are ideal, the granulation will not
require further grinding. Tray dryers, on the other hand, produce a caked product
that may require mild comminution. Variation in temperature, which may
be quite marked in tray dryers, is virtually eliminated in fluidized bed dryers
by the intense mixing action. The floor space for a given capacity is small
compared with a tray dryer. Machines vary in size, handling up to 250 kg.
Drying times, maximum, minimum, and optimum air velocities, air temperature,
and the tendency to cake and channel are established experimentally since
they cannot be predicted accurately at present.
Considerable erosion and the production of large amounts of fines might
be expected from the intense turbulent movement. Experience shows that the
opposite is true. The particles are to some extent ‘‘padded’’ by the surrounding
fluid so that either the amount of contact between particles is low or the impact
energy is small.
6.10.5 Agitated Batch Dryers
Agitated batch dryers consist of a jacketed cylindrical vessel with agitator
blades designed to scrape the bottom and the walls. The body may be run at
atmospheric pressure or under vacuum. Pasty materials, which could not be
handled in tumbling or fluidized bed dryers, may be successfully dried at rates
higher than can be achieved in an oven.
Freeze-drying is an extreme form of vacuum drying in which the solid is
frozen and drying takes place by subliming the solid phase (Pikal et al., 1984;
Nail, 1980; Jennings, 1988; Dushman and Lafferty, 1962). Low temperatures
and pressures are used. Establishing and maintaining these conditions, together
with the low drying rates obtained, create a most expensive method of drying
which is only used on a large scale when other methods are inadequate.
Freeze-drying is extensively used in two principal fields: (1) when high
rates of decomposition occur during normal drying; (2) with substances that
can be dried at higher temperatures but are thereby changed in some way.
Fruit juices, for example, are reputed to lose subtle elements of flavor and
odor, and proteinaceous materials are partly denatured by the concentration
and higher temperatures associated with conventional drying. Drying blood
plasma and some antibiotics are important large-scale applications of freezedrying.
On a smaller scale, it is extensively used for the dehydration of bacteria,
vaccines, blood fractions, and tissues.
Freeze-drying is theoretically a simple technique. Pure ice exhibits an
equilibrium vapor pressure of 4.6 mmHg at 0°C and 0.1 mmHg at 40°C.
The vapor pressure of ice containing dissolved substances will, of course,
be lower. If, however, the pressure above the frozen solution is less than its
equilibrium vapor pressure, the ice will sublime, eventually leaving the solute
as a sponge-like residue equal in apparent volume to the original solid and,
therefore, of low bulk density. The latter is readily dissolved when water is
added, and freeze-drying has been called lyophilic drying or lyophilization for
this reason. No concentration, in the normal sense of the word, occurs, and
structural changes in, for example, protein solutions are minimized.
In practice, many difficulties are encountered. Under conditions of high
vacuum, water vapor must be trapped or eliminated. To maintain drying, heat
must be supplied to the frozen solid to balance the latent heat of sublimation
without melting the solid. Difficulties become acute if, like blood plasma, the
product is dried in the final container under aseptic conditions.
In the first stage of the process, the material is cooled and frozen. If the
temperature of a dilute solution of a salt is slowly reduced, leveling occurs
in the time-temperature curve just below 0°C, due to the liberation of the latent
heat of fusion of ice, and pure ice separates. With further cooling, the solution
becomes concentrated until the eutectic mixture is formed. This freezes to
give a plateau in the cooling curve. It is a clear indication of complete freezing.
If the concentration of the liquid eutectic mixture is small, the material may
appear to be completely frozen at higher temperatures. Under these conditions,
some drying from a liquid phase will occur, possibly with damaging results.
This can be detected by measuring the electrical resistance of the ice, which
becomes infinitely great when the eutectic mixture freezes. Conversely, thawing
gives a marked decrease in resistance, an effect that can be used to automatically
control the state of the drying solid. Protein solutions do not give
clearly defined eutectic points and are usually frozen to below 25°C before
drying. Freezing is carried out quickly to prevent concentration of the solution
and to produce fine ice crystals. Some degree of supercooling may be induced
followed by a very quick freeze. Freezing may or may not be carried out
in the drying chamber. If drying in final containers is necessary, small-scale
operations may employ immersion in a coolant such as liquid air or isopentane.
Larger-scale installations may cool with a blast of very cold air. Alternatively,
104 Chapter 6
evaporative freezing, in which the liquid is cooled to near its freezing point
and the system rapidly evacuated, is employed. The evaporating liquid cools
and freezes rapidly. Frothing caused by the evolution of dissolved gases may
complicate this technique. For bulk drying the liquid is placed in shallow trays
on refrigerated shelves in the drying cabinet.
A suitable ratio of surface area to depth of solid must be provided to
facilitate drying. Thin layers of frozen liquid are used in bulk drying. The
surface area of bottle-dried plasma may be increased by spinning in a vertical
axis during freezing to give a frozen shell about 2 cm thick around the inside
periphery of the bottle. Spinning also prevents frothing during evaporative
freezing by inhibiting the formation of bubbles.
In plasma processing, freezing, and drying, handling must be carried
out aseptically. This is maintained by a filter at the neck of the bottle that
allows the passage of water vapor but prevents the ingress of bacteria. Similar
precautions are taken during the drying of antibiotics.
Effective drying vacuum of from 0.05 to 0.2 mmHg may be provided
by directly pumping water vapor and permanent gases, originally present or
derived from the drying material and from leaks, out of the system. Normal
practice, however, favors interposing a refrigerated condenser between the
drying surface and the pump. This arrangement allows a smaller pump, handling
mainly permanent gases, to be used but demands a low condenser temperature,
such as 50°C, to remove water vapor at the low operating pressure.
A system for bulk drying in trays is represented in Figure 6.10(a).
During drying, heat must be supplied to the drying surface. When drying
a material, such as plasma, in a final container, a temperature gradient is established
across the container wall and through the ice to the drying surface by
FIGURE 6.10 (a) Equipment for freeze-drying bulk liquids in trays and (b) variations
in temperature and pressure during the freeze-drying cycle for blood plasma.
means of a heater suitably mounted in relation to the container. The power
dissipated by the heater must be carefully controlled so that melting does not
occur at the ice-container junction, the point nearest the heat source and at
highest temperature. At any time, the prevailing conditions are such that the
evaporation rate is approximately constant and temperatures and pressure adjust
so that there are temperature and pressure gradients from the drying surface
to the condenser. As evaporation proceeds, a drying line recedes into the
solid. With the thinning of the ice layer, the temperature gradient through the
ice will be modified by the decreasing resistance to heat flow. An increase in
the rate of drying due to increase in temperature and vapor pressure of the
drying surface might, therefore, be expected. In practice, this increase is modi-
fied by the layer of dried plasma, which offers considerable resistance to the
flow of vapor. The bacterial filter also causes a large, constant pressure drop.
Evaporation of pure ice without the filter and plasma layer would be 300 times
faster. When the plasma is nearly dry, its temperature is allowed to rise to
about 30°C to facilitate final drying. The total drying time is about 48 hr. The
temperatures and pressure in the system during this period are shown, as a
function of time, in Figure 6.10(b).
If the product is not being dried in its final container, radiant heat may
be used to provide the latent heat of sublimation. If the dried solid could be
removed continuously, high drying rates are possible. Not only is heat provided
directly to the drying surface but also there is little danger of melting
the ice at the container wall.
6.11 CONTINUOUS DRYERS
Although many types of continuous dryers are available, the scale of the operation
for which they are designed is rarely appropriate to pharmaceutical manufacture.
As with most continuous plant items, the cost is disproportionately
high for small units. Spray and drum dryers provide an exception to this comment
because residence times in the dryers are short and thermal degradation
is minimized. Under some conditions, freeze-drying may be the only practical
6.11.1 Spray Dryers
As the name implies, the solution or suspension to be dried is sprayed into a
hot airstream and circulated through a chamber. The dried product may be
106 Chapter 6
FIGURE 6.11 Spray dryer.
carried out to a cyclone or bag separator or may fall to the bottom of the
drying chamber and be expelled through a valve. The chambers are normally
cylindrical with a conical bottom, although proportions vary widely. A typical
spray dryer is illustrated in Figure 6.11.
The process can be divided into four sections: fluid atomization, mixing
the droplets, drying, and removing and collecting the dry particles. Atomization
may be achieved by means of single fluid or two fluid nozzles or by
spinning disk atomizers. The single fluid nozzle [Figure 6.12(a)] operates by
forcing the solution under pressure through a fine hole into the airstream. An
intense swirl is conferred on the liquid before it emerges from the orifice. This
causes the jet to break up. In the two fluid nozzles [Figure 6.12(b)] a jet of
air simultaneously emerges from an annular aperture concentric with the liquid
orifice. Both types are subject to clogging and severe erosion, so neither is
well suited to spraying suspensions. The spinning disks [Figure 6.12(c)] are
most versatile and consist, in their simplest form, of a mushroom-shaped disk
spinning at 5000 to 30,000 rpm. Other designs include the slotted disk [Figure
6.12(d)] which will spray thick suspensions and, if special feeding arrangements
are used, pastes. The main factors that determine droplets size are the
liquid’s viscosity and surface tension, the fluid pressure in the nozzles, or, for
FIGURE 6.12 Schematic of atomizers for spray drying.
spinning disks, their size and speed of rotation. A reasonably uniform and
controllable size within the range 10–500 µm is desirable.
In vertical spray dryers, the flow of the drying gas may be concurrent
or countercurrent with respect to the movement of droplets. The movement
of the gas is, however, complex and highly turbulent. Good mixing of droplets
and gas occurs, and the heat and mass transfer rates are high. In conjunction
with the large interfacial area conferred by atomization, these factors give very
high evaporation rates. The residence time of a droplet in the dryer is only a
few seconds (5–30 s). Since the material is at wet bulb temperature for much
of this time, high gas temperatures of 150–200°C may be used even with
thermolabile materials. Although the temperature of the material rises above
108 Chapter 6
the wet bulb temperature at the end of the process, the drying gases will be
cooler and the material will be almost dry, a condition in which many materials
are thermally less sensitive. For these reasons it is possible to dry
complex vegetable extracts, such as coffee or digitalis, milk products,
spore suspensions, and other labile materials without significant loss of
potency or flavor.
Drying is considered to take place by simple evaporation rather than by
boiling, and it has been observed that a droplet reaches a terminal velocity
within about 30 cm of the atomizer. Beyond this, there is no relative velocity
between the droplet and the drying gas unless the former is very large. The
droplets may dry to form a solid, spherical particle. If, however, the emerging
solids form a skin, internal pressure may inflate the particle and the final dry
form will be hollow spheres that may or may not have a blowhole. These
xenospheres may also fragment, so the final product occurs as agglomerates
of finely divided solids. It has been found experimentally that the product’s
bulk density, which is lowest for xenospheres and highest for fragmented solids,
increases as the inlet air temperature is lowered and as the droplet size
increases. A higher feed concentration also increases the bulk density because
drops of the same size give spheres with thicker walls.
These attractive physical characteristics lend further advantage to spraydrying.
The product often has excellent flow and packing properties that
greatly facilitate handling and transport. As an example, spray-dried lactose
is a widely used tablet excipient which will flow, pack, and compact without
prior granulation. Similarly, a slurry of fillers and other excipients could be
granulated by spraying and drying. After adding an active principle, the mix
could be compressed without further processing.
The capital and running costs of spray dryers are high, but if the scale
is sufficiently large it may provide the cheapest method. When thermolabile
materials are dried on a small scale, costs will be 10 to 20 times greater than
for oven drying. Air used to dry fine chemicals or food products is heated
indirectly, thus reducing thermal efficiency and increasing costs. In some other
installations, hot gases from combustion may be used directly.
6.11.2 Drum Dryers
The drum dryer consists of one or two slowly rotating, steam-heated cylinders.
These are coated with solution or slurry by means of a dip feed, illustrated
in Figure 6.13. The lower portion of the drum is immersed in an agitated
trough of feed material or, in the case of some double-drum dryers, by feeding
FIGURE 6.13 Drum dryers.
the liquor into the gap between the cylinders as shown in Figure 6.13. Spray
and splash feeds are also used. When dip feeding is employed, the hot drum
must not boil the liquid in the trough. Drying takes place by simple evaporation
rather than by boiling. The dried material is scraped from the drum at a suitable
point by a knife.
Drying capacity is influenced by drum speed and feed temperature. The
latter may be preheated. With the double-drum dryer, the gap between the
cylinders determines the film thickness.
Drum dryers, like spray dryers, are relatively expensive in small sizes
and their use in the pharmaceutical industry is largely confined to drying thermolabile
materials where the short contact time is advantageous. Drums are
normally fabricated from stainless or chrome-plated steel to reduce contamination.
The heat treatment to which the solid is subjected is greater than in spraydrying
and the physical form of the product is often less attractive. During
drying, the liquid approaches its boiling point and the dry solids approach the
temperature of the drum surface.
Leaching or solid-liquid extraction are terms used to describe the extraction
of soluble constituents from a solid or semisolid by means of suitable solvents.
The process, which is used domestically whenever tea or coffee is made, is
an important stage in the production of many fine chemicals found naturally
in animal and vegetable tissue. Examples are found in the extraction of fixed
oils from seeds, this method offering an alternative to mechanical expression,
in the preparation of alkaloids, such as strychnine from Nux vomica beans or
quinine from Cinchona bark, and in the isolation of enzymes, such as renin,
and hormones, such as insulin, from animal sources. In the past, a wider importance
attended the process because the products of simple extraction procedures,
known as Galenicals, formed the major part of the ingredients used to
fulfill a doctor’s prescription.
7.1 METHODS OF LEACHING
Leaching in the pharmaceutical and allied industries is operated as a batch
process. This is because high-cost materials are processed in relatively small
Solid-Liquid Extraction 111
quantities. Frequent changes of material may be made, creating problems of
cleaning and contamination. For these reasons, continuous extraction, which
is characterized by a large throughput and the mechanical movement of the
solid counter to the flow of solvent, is not applicable to pharmaceutical extraction
and is not described in this text.
Whatever the scale of the extraction, however, leaching is performed in
one of two ways. In the first, the raw material is placed in a vessel, forming
a permeable bed through which the solvent or menstruum percolates. Dissolution
of the wanted constituents occurs and the solution issues from the bottom
of the bed. This liquid is sometimes called the miscella, and the exhausted
solids are called the marc. This process will be called leaching by percolation.
The alternative process is leaching by immersion and consists of immersing
the solid in the solvent and stirring. After a suitable period of time, solid and
liquid are separated.
7.2 LEACHING BY PERCOLATION
Coarse ground material is placed in the body of the extractor. This may be
jacketed to give control of the extraction temperature. The packing must be
even or the solvent will preferentially flow through a limited volume of the bed
and leaching will be inefficient. In large extractors, channeling is prevented or
reduced by horizontal, perforated plates placed at intervals in the bed. These
redistribute the percolating liquid.
Solvent inhibition will swell dried materials and the permeability of the
bed will be reduced. This is most marked with aqueous solvents. If swelling
occurs, it is necessary to moisten the material with water or with the solvent
before it is packed into the extractor.
Once the extractor is packed, leaching may be conducted in a number
of ways. The body of the extractor may be completely filled with the solvent.
Liquid is then withdrawn from the body through the false bottom and more
solvent is added. This is continued until the marc is exhausted. Alternatively,
the solution issuing from the bottom may be returned to the top. After a period
of recirculation, the liquid is completely withdrawn and fresh solvent admitted.
In both processes, a period of steeping or soaking may precede the movement
In beds of high permeability, adequate liquid movement is obtained by
simple gravity operation in an open vessel. If the material forms a dense bed,
however, the liquid must be pumped through if suitable flow rates are to be
secured. A closed extraction vessel must then be used. Closed extraction ves112
sels are also necessary for high-temperature extraction and extraction with
volatile solvents. In alternative methods the liquid is forced upward through
the bed. Possible migration of fine material downward and the formation of
a region of low permeability at the bottom of the bed are prevented in this
way. In other processes, the bed may not be immersed in the menstruum. This
is simply sprinkled onto the upper surface and allowed to trickle through the
bed, the voids of which are mainly filled with air.
Simple extractions of this type, if carried to completion, require large
amounts of solvent and yield dilute extracts. These disadvantages can be overcome
if extraction is followed by evaporation. These operations are often integrated
in extraction plant. The leach liquids leaving the extractor enter an
evaporator heated, for example, by a calandria. Since most materials encountered
are heat sensitive, the evaporator is operated at reduced pressure. The
vapor leaving the evaporator is condensed and returned to the extractor. When
extraction is carried out with water-immiscible solvents, any water derived
from the feed material and present in the condensate is separated and rejected.
The extraction is stopped when the leach liquid is free from wanted constituents.
A concentrated extract remains in the evaporator.
Leaching by percolation provides a simple method of separating leach
liquid and solid during the extraction. When this is complete, the permeable
bed largely drains, permitting extensive solvent recovery. Further recovery
can be gained by mechanical expression.
7.3 LEACHING BY IMMERSION
In pharmaceutical processes, leaching by immersion is carried out in simple
tanks which may be agitated by a turbine or paddle. If the solids are adequately
suspended, intimate contact between the phases promotes efficient extraction.
Incomplete extraction due to channeling is avoided and difficulties due
to swelling do not arise. Problems arise, however, in the subsequent separation
of the phases. The materials to which leaching by immersion is applied
are normally finely divided or coarse and compressible. When agitation
ceases, the solids settle and the leach liquid can be siphoned or pumped off
by lines suitably placed in the tank. The sediment, however, contains a large
volume of the leach liquid which must be recovered by resuspending the
solids in fresh solvent, allowing the solids to sediment, and decanting the
supernatant liquid. Cake filtration provides an alternative method of separation.
The leach liquid remaining in the cake is displaced by passing a
Solid-Liquid Extraction 113
wash liquid. In some cases, a filter press may be used for extraction and
7.4 THE CHOICE OF EXTRACTION METHOD
The choice of extraction method depends primarily on the physical properties
of the basic material and its particle size. If this material is a coarse, rigid
powder, beds of high permeability will form and percolation can be adopted.
The expense of finer grinding is avoided, and the subsequent separation of
solids and liquid is facilitated. The process can be conducted in such a way
that a concentrated product is obtained. Other materials, such as fine powders
or compressible animal tissues, will not form permeable beds, and the alternative
method must be adopted. Some compensation for the difficulties of separation
and the dilution of the extract during washing may be found in a more
rapid and more complete extraction, due to the use of finer powders, the intimate
contact between solids and liquid, and the absence of channeling.
The use of pressure extends the application of percolation to materials
which form beds of low permeability. Alternatively, permeability may be
increased by grinding the solids with a supporting material such as glass
7.5 THE CHOICE OF SOLVENT
The ideal solvent is cheap, nontoxic, and noninflammable. It is highly selective,
dissolving only the wanted constituents of the solid. It should have a low viscosity,
allowing easy movement through a bed of solids, and, if the resulting solution is
to be concentrated by evaporation, a high vapor pressure. These factors greatly
limit thenumber of solvents of commercialvalue.Water and alcohol, and mixtures
of the two, are widely used. Both, however, are nonselective, leaching varying
proportions of gums, mucilages, and other unwanted components. Most of the
tinctures and liquid extracts used in pharmacy are simple, impure extracts made
with waterormixturesof waterandalcohol.Acidifiedor alkalinemixturesof water
and alcohol are used to extract insulin from minced pancreas. A more selective
extraction is given by petroleum solvents and benzene and related solvents. In the
preparation of many pure alkaloids, the powdered material is moistened with an
alkaline solution, packed into a bed, and leached with petroleum. Subsequent puri-
fication by fractional crystallization is facilitated by the absence of gums. Acetone
114 Chapter 7
and chlorinated hydrocarbons also find applications in leaching. In some cases,
specific properties of the wanted constituents may suggest a particular solvent.
Eugenol, for example, can be readily extracted from cloves with a solution of
potassium hydroxide. Care must be given to the selection of solvents, because
they may be subject to regulatory control due to their toxicity or impact on the
7.6 FACTORS AFFECTING THE RATE OF
Whatever method is adopted, leaching consists of a number of consecutive
diffusional or mass transfer processes. The solvent first penetrates the raw
material, and the soluble elements dissolve. These diffuse in the opposite direction
to the surface of the solid matrix and then through the liquid layers
at its surface to reach the bulk solution. These processes proceed under the
influence of an overall concentration gradient, the concentration being least
in the bulk solution. Any of these processes may be responsible for limiting
the rate at which leaching proceeds. In pharmaceutical leaching, however, the
solid matrix is usually cellular, which normally offers the highest diffusional
resistance. The complexity of such structures does not permit a strict analysis
of the mass transfer processes. Nevertheless, the simple diffusional concepts
expressed in Fick’s law suggest that the following factors influence the rate
of leaching: the size distribution of the leached particles, the temperature of
leaching, the physical properties of solvent, and the relative movement imposed
upon the solids and the liquid.
7.7 SIZE AND SIZE DISTRIBUTION OF THE
The particle size of the solids determines the distance which solvent and solute
must diffuse within the solid matrix. Since this offers the major diffusional
resistance, reduction of the distance by comminution greatly increases the
leaching rate, the concentration gradient being effectively increased. In addition,
the inverse relationship between particle size and surface area prescribes
an increase in the area of contact between the matrix and the surrounding
liquid. Solute transfer at this boundary is therefore facilitated. In leaching by
immersion, a further advantage conferred by size reduction is the ease with
Solid-Liquid Extraction 115
which finer particles are suspended. Finally, extensive cell rupture occurs during
grinding, allowing more direct contact between solvent and solute and
more rapid dissolution and diffusion.
Other factors, however, operate against size reduction. Leaching by percolation
demands formation of a permeable bed. Low permeability gives low
flow rates and low rates of extraction. Permeability is a complex function of
particle size and porosity, the former determining how a given void space is
to be disposed within the bed. The disposition of the void space consists of
a few channels of relatively large diameter, i.e., a bed of high permeability,
if the particle size is large. In leaching by immersion, the difficulties of separating
solid and liquid increase as the particle size decreases.
The opposition of the factors suggests an optimum particle size for any
extraction. This is determined to some extent by the physical nature of the
solids. A dense, woody structure would be extracted as a fine powder. An
example is given by the root of Ipecacuanha. A leafy structure, on the other
hand, would be more satisfactorily leached as a coarse powder.
Porosity and permeability are influenced by the particle size distribution.
A high porosity is secured if the distribution is narrow. Small particles may
otherwise fill the interstices created by the contact of larger particles. After
grinding, therefore, it is often necessary to classify the product and remove
undersize material, which is then bulked with the fines from other batches and
separately extracted. A further advantage arising from a narrow size distribution
is even packing and the creation of a regular system of pores and waists.
This promotes even movement of solvent and solution through the bed.
In some cases, size reduction may take a particular form. Seeds and
beans are often rolled or flaked to produce extensive cell rupture. In other
processes, the cell wall, although depressing the rate of extraction, may make
the extraction more selective by preventing the movement of unwanted materials
of high molecular weight. Here, the size reduction must leave most cells
Within the limits imposed by the thermal stability of the wanted constituents, a
high extraction temperature appears desirable. The solubility of most materials
increases as the temperature increases, so higher solute concentrations and
higher concentration gradients are possible. The increased solubility and increased
diffusivity give higher extraction rates. In very many cases, however,
materials are susceptible to heat degradation, and cold extraction must be used.
116 Chapter 7
In addition, the selectivity of a solvent may be impaired at high temperatures.
An example of the use of moderately high temperatures is the extraction of
Rauwolfia alkaloids with boiling methanol.
7.9 PHYSICAL PROPERTIES OF THE
The relevant properties of the solvent are low viscosity and free solution of
wanted constituents. These properties, along with other aspects of the solvent,
have already been discussed.
7.10 RELATIVE MOVEMENT IMPOSED ON
THE SOLIDS AND THE LIQUID
The major and controlling resistance to solute diffusion to the bulk solution
is normally found in the cell matrix. Increased rate of movement of the solution
past the surface will not, therefore, greatly affect the extraction rate, in marked
contrast to the processes of dissolution and crystallization. Nevertheless,
movement is imposed on the menstruum in both general methods described.
In the percolation of a liquid through a bed of solids, mass transfer of the
solute from the surfaces of the solid to the liquid in the interstices of the bed
takes place by molecular diffusion and by natural convection arising from the
density changes created by dissolution. Although these processes are slow, they
are much quicker than mass transfer in the matrix under the same differences in
concentration. Concentration gradients in the liquid outside the particles are,
therefore, very low. At any point in the bed, the introduction of dilute solution
from above and the loss of concentrated solution to below decreases the interstitial
concentration by dilution or displacement. This effect can be considered
simply to decrease the solute concentration at the junction of solid and solution,
thus imposing a favorable concentration gradient within the matrix.
Similarly, the agitation of the slurry in leaching by immersion is not
primarily to decrease the boundary layer thickness at the surface and its diffusional
resistance. Rather, agitation serves only to keep the particles in suspension
and to equalize the solute concentration throughout the liquid. If the particles
settle, the solute must diffuse through the stagnant fluid filling the
interstices of the bed. High diffusional resistance is created and the rate of
extraction is depressed.
As a unit operation, the term crystallization describes the production of a solid,
single-component, crystalline phase from a multicomponent fluid phase. It
may be applied to the production of crystalline solids from vapors, melts, or
solutions. Crystallization from solution is most important. To complete the
preparation of a pure dry solid, it is also necessary to separate the solid from
the fluid phase. This is usually carried out by centrifugation or filtration and
by drying. The importance of crystallization lies primarily in the purification
achieved during the process and in the physical properties of the product. A
crystalline powder is easily handled, is stable, and often possesses good flow
properties and an attractive appearance.
Crystallization from a vapor, which occurs naturally, for example, in
the formation of hoarfrost, is employed in sublimation processes and for the
condensation of water vapor during freeze-drying. Equipment may be regarded
as specialized condensers in which the principal problems are removal
of the latent heat of crystallization and discharge of the solid condensate. Condensers
are commonly mounted in parallel so that one can be shut down and
emptied manually, by conveyor or by melting and draining, without interrupting
sublimation. This process is not further considered.
118 Chapter 8
In the pharmaceutical industry, crystallization is usually performed on
a small scale from solutions, often in jacketed or agitated vessels. The conditions
of crystallization, necessary for suitable purity, yield, and crystal form,
are usually established by experiment. Nevertheless a study of the principal
factors which control crystallization is important. In this study, much information
is derived from the behavior of carefully prepared melts. These reveal
more clearly than solutions the two stages of crystallization: nucleation and
crystal growth. Nucleation describes the formation of small nuclei around
which crystals grow. Without the formation of nuclei, crystal growth cannot
8.1 CRYSTALLIZATION IN MELTS
A melt may be defined as the liquid form of a single material or the homogeneous
liquid form of two or more materials which solidifies on cooling. Crystallization
in such a system is described by the following sequence: imposition
of supercooling, formation of nuclei, and crystal growth.
If a single-component liquid is cooled, some degree, often large, of supercooling
must be established before crystal nuclei are formed and growth
begins. A metastable liquid region exists below the melting point, which can
only be entered by cooling. In this metastable, supercooled region, the absence
of nucleation precludes the formation and growth of crystals. If, however, a
crystal seed is added, growth occurs. The deliberate seeding of a metastable
system is commonly employed in industrial crystallization. With further cooling,
spontaneous nucleation usually takes place and the released heat of crystallization
raises the temperature of the melt to its true melting point. With
some materials, lower temperatures increase the viscosity and prevent nucleation.
The liquid then solidifies into a mass without crystallizing, a process
known as vitrification, the products of which are called glasses. Many organic
materials can be obtained in this form, and, as with glass itself, devitrification
may suddenly occur, particularly after heating.
In certain single-component systems, such as piperidine, nucleation and crystal
growth are independent and can be separately studied. The rate of nucleation
as a function of supercooling is studied by maintaining the melt, for a certain
time, at the given temperature and then quickly raising the temperature to the
FIGURE 8.1 (a) Change in nucleation with degree of supercooling; (b) change in
rate of crystal growth with degree of supercooling.
metastable region where further nucleation is negligible but the already formed
nuclei can grow. Figure 8.1(a) describes the results of such an experiment. At
low degrees of supercooling little or no nucleation takes place. With further
cooling, the rate of nucleation rises to a maximum and then falls. The relation
therefore indicates that excessive cooling may depress the rate of crystallization
by limiting the number of nuclei formed.
Spontaneous nucleation is considered to occur when sufficient molecules
of low kinetic energy come together in such a way that the attraction
between them is sufficient to overcome their momentum. The growth of a
nucleus probably takes place over a very short time in a region of high local
concentration. Once a certain size is reached, the nucleus stabilizes in the
prevailing conditions. As the temperature falls, more low-energy molecules
are present and the nucleation rate rises. The decrease in nucleation rate at
lower temperature is due to increased melt viscosity.
8.3 CRYSTAL GROWTH
If nucleation and crystal growth are independent, the latter can be studied by
seeding a melt with small crystals in conditions of little or no natural nucleation.
The growth rate can then be measured. The relation between growth
rate and temperature [Figure 8.1(b)] also exhibits an optimal degree of supercooling,
although the maximum growth temperature is normally higher than
the temperature of maximum nucleation. The form of the crystal growth curve
120 Chapter 8
is again explained by the molecular kinetics. At temperatures just below the
melting point, molecules have too much energy to remain in the crystal lattice.
As the temperature falls, more molecules are retained and the growth rate
increases. Ultimately, however, diffusion to and orientation at the crystal surface
For crystal growth in a single-component melt, the molecules at the
crystal surface must reach the correct position at the lattice and become suitably
orientated, thereby losing kinetic energy. These energy changes appear
as heat of crystallization, and this heat must be transferred from the surface
to the bulk of the melt. The crystal growth rate is influenced by the heat transfer
rate and the changes taking place at the surface. Agitation of the system increases
heat transfer by reducing the thermal resistance of the liquid layers
adjacent to the crystal until the changes at the crystal face become the controlling
In multicomponent melts and solutions, material deposition at the crystal
face depletes the adjacent liquid layers and a concentration gradient is set up
with saturation at the face and supersaturation in the liquid. Diffusion of molecules
to the crystal face is discussed in the next section.
The foregoing account describes the behavior of certain carefully prepared
melts from which all extraneous matter is rigidly excluded. Dust and
other insoluble matter may increase the nucleation rate by acting as centers
of crystallization. Soluble impurities may increase or decrease the rates of
nucleation and crystal growth. The latter is probably due to adsorption of the
impurity on the crystal face. Impurities may also affect the form in which the
8.4 CRYSTALLIZATION FROM SOLUTIONS
When a material crystallizes from a solution, nucleation and crystal growth
occur simultaneously over a wide intermediate temperature range, so a study
of these processes is more difficult. In general, however, they are thought to
be similar to nucleation and crystal growth in melts. The three basic steps—
induction of supersaturation, formation of nuclei, and crystals growth—are
explained with reference to the solubility curve in Figure 8.2.
A solution with temperature and concentration indicated by point A may
be saturated by cooling to point B or by removing solvent (point C). With
further cooling or concentration, the supersaturated metastable region is entered.
If the degree of supersaturation is small, then spontaneous formation
of crystal nuclei is highly improbable. Crystal growth, however, can occur if
FIGURE 8.2 Solubility-supersolubility diagram.
seeds are added. With greater supersaturation, spontaneous nucleation becomes
more probable, and the metastable region is limited approximately by
the line B?C?. If the solution is cooled to B? or concentrated by solvent removal
to C?, spontaneous nucleation is virtually certain. Crystal growth also occurs in
these conditions. The growth rate, however, is depressed at low temperatures.
During crystal growth, deposition on the crystal faces causes depletion
of molecules in the immediate vicinity. The driving force is provided by the
concentration gradient set up from supersaturation in the solution to lower
concentrations at the crystal face. A large degree of supersaturation therefore
promotes a high growth rate. A reaction at the surface, in which solute molecules
become correctly oriented in the crystal lattice, provides a second resistance
to crystal growth. Simultaneously, the heat of crystallization must be
Agitation modifies the rate of crystal growth for given conditions of
temperature and saturation. Initially, agitation quickly increases the growth
rate by decreasing the boundary layer thickness and the diffusional resistance.
However, as agitation is intensified, a limiting value is reached which is determined
by the kinetics of the surface reaction. In Figure 8.3, the effect of agitation
on the crystal growth rate in solutions of sodium thiosulfate of differing
degrees of supersaturation is described.
As with melts, soluble impurities may increase or retard the rate of nucleation.
Insoluble materials may act as nuclei and promote crystallization.
Impurities may also affect crystal form and, in some cases, are deliberately
added to secure a product with good appearance, absence of caking, or suitable
122 Chapter 8
FIGURE 8.3 Effect of agitation on growth rate of a sodium thiosulfate crystal.
The temperature at which crystallization is performed may be determined
by the crystal form or degree of hydration required of the products.
The solubility curves in Figure 8.4 show that crystallization at 50°C yields
FeSO4?7H2O; at 60°C, FeSO4?4H2O; and at 70°C, FeSO4. The majority of materials,
however, have one or possibly two forms. The degree of supersaturation
of solution 1 is 5 g/L, of solution 2 is 10 g/L, and of solution 3 is 15 g/L.
8.5 PRINCIPLES UNDERLYING THE DESIGN
AND OPERATION OF CRYSTALLIZERS
The purpose of a crystallization plant is to produce, as far as possible, crystals
of the required shape, size distribution, purity, and yield. This purpose is
achieved by maintaining a degree of supersaturation at which nucleation and
crystal growth proceed at appropriate rates. The number of nuclei formed controls
the size of the crystals deposited from a given quantity of solution. Alternatively,
crystal number and size can be controlled by adding the correct
amount of artificial nuclei or seeds to a system in which little or no natural
nucleation is taking place.
In most cases, the mode of operation is determined by the relation between
the solubility of the solute and the temperature, examples of which are
shown in Figure 8.4. This determines how supersaturation is to be achieved.
Other factors of importance are the thermal stability of the solute, the impuriCrystallization
FIGURE 8.4 Solubility curves.
ties which may be present, and the degree of hydration required. If the solubility
of the solute increases greatly with temperature, supersaturation and the
deposition of a large proportion of the solute is brought about by cooling a
hot concentrated solution. Sodium nitrate provides an example. Sodium chloride
and calcium acetate, on the other hand, exemplify materials with a small
or negative temperature coefficient of solubility. Here, supersaturation can best
be achieved by evaporating part of the solvent. In some cases, evaporation
and cooling are employed. The mother liquors following evaporative crystallization
can be cooled to yield a further crop of crystals, provided there is a
suitable change in solubility and impurities present do not prohibit the process.
In other crystallizers, flash cooling is used. A hot solution is passed into a
vacuum chamber in which both evaporation and cooling take place.
Supersaturation can also be induced by the addition of a third substance
which reduces the solubility of a solute in a solvent. These precipitation processes,
which are important in the processing of thermolabile materials, are
controlled by the mixing temperature, the agitation, and the rate at which the
third substance is added. Water-insoluble materials dissolved in water-miscible
organic solvents can be precipitated by adding water. Alternatively, the
aqueous solubility of many materials can be reduced by the change of pH or
by adding a common ion. Proteins can be salted out of solution by adding
124 Chapter 8
ammonium chloride and adjusting the pH. Finally, precipitation of a crystalline
solid may be the result of a chemical reaction.
A crystallizer should produce crystals of uniform particle size, to facilitate
removal of the mother liquor and washing. If large quantities of the liquor
are occluded in the mass of crystals, drying yields an impure product. In addition,
crystals of even size are less likely to cake on storage.
8.6 PRODUCTION OF VERY FINE CRYSTALS
Fine powders are important components in pharmaceutical operations. If a
substance has a steep solubility curve, fine crystals are produced by quickly
cooling the solution through the metastable region to conditions in which the
nucleation rate is high and the crystal growth rate is low. This method is not
always possible, and the precipitation methods described may be adopted.
8.7 PRODUCTION OF LARGE CRYSTALS
Batch production of large, uniform crystals may be carried out in agitated
reaction vessels by slow controlled or natural cooling. Spontaneous nucleation
is improbable until solution A is cooled to X. Crystallization then follows path
XB. Better control is gained if the solution is artificially seeded. Seeding is
shown at X?. Crystallization then follows the broken line X?B, the aim being
to maintain the solution in the metastable region where growth rate is high
and natural nucleation is low. The course of the crystallization is shown in
Figure 8.5. Initially spontaneous nucleation may be allowed by cooling from
FIGURE 8.5 Production of large crystals. The conditions of supersaturation.
A to X. As crystallization takes place, the degree of supersaturation and the
concentration of the solute fall, ultimately reaching saturation at B when
growth ceases. Closer control is secured by artificially seeding the supersaturated
solution in conditions of no natural nucleation. Seeding is indicated by
the point X?. The course of the crystallization is then indicated by the broken
An important principle for the continuous production of large even crystals
is used in Oslo or Krystal crystallizers. A metastable, supersaturated solution
is released into the bottom of a mass of growing crystals on which the
solute is deposited. The crystals are fluidized by the circulation of the solution,
and classification in this zone allows the withdrawal of sufficiently large crystals
from the bottom.
Although other methods may be adopted, crystallizers can be conveniently
classified by the way in which a solution is supersaturated. This leads to the
self-explanatory terms cooling crystallizer and evaporative crystallizer. In vacuum
crystallizers, evaporation and cooling are used.
8.8.1 Cooling Crystallizers
Open or closed tanks, agitated by stirrers, are used for batch crystallization.
The specific heat of the solution and the heat of crystallization are removed
by means of jackets or coils through which cooling water can be circulated.
Agitation destroys temperature gradients in the tanks, opposes sedimentation
and irregular crystal growth at the bottom of the vessel, and, as described,
facilitates growth. Similar equipment is used for crystallization or precipitation
by adding a third substance.
Crystallizers for continuous processes often take the form of a trough
cooled naturally or by a jacket. The solution enters at one end and crystals
and liquid are discharged at the other. In one type of crystallizer, a slowmoving
worm works in the solution and lifts crystals off the cooling surface
to shower them through the solution and slowly convey them through the
trough. The trough of another is agitated by rocking. Baffles are used to increase
the residence time of the solution. Both crystallizers are characterized
by low heat transfer coefficients, and an alternative arrangement consists essentially
of a double-pipe heat exchanger. The crystallizing fluid is carried in
126 Chapter 8
FIGURE 8.6 (a) Cooling crystallizer; (b) evaporative crystallizer; (c) batch vacuum
the central pipe with countercurrent flow of the coolant in the annulus between
the pipes. A shaft rotates in the central tube carrying blades which scrape the
heat transfer surface. High heat transfer coefficients are obtained. An Oslo
crystallizer, in which supersaturation is given by cooling, is described in Figure
8.6(a). The principles underlying this plant have already been described.
8.8.2 Evaporative Crystallizers
On a small scale, simple pans and stirred reaction vessels can be used for
evaporative crystallization. Larger units may employ calandria heating, as
shown in Figure 8.6(b). The downcomer, which must be large enough to accommodate
the flow of the suspension, commonly houses an impeller, forced
circulation increasing the heat transfer to the boiling liquid. These units may
be adapted for batch or continuous processes in which crystal size is not of
great importance. For continuous processes demanding close control of product
size, an Oslo crystallizer which saturates the solution by evaporation may
8.8.3 Vacuum Crystallizers
Vacuum crystallizers produce supersaturated conditions by solvent removal
and cooling [Figure 8.6(c)]. A hot concentrated solution is fed to an agitated
crystallization chamber maintained at low pressure. The solution boils and
cools adiabatically to the boiling point corresponding to the operating pressure.
Crystallization follows concentration, and the product is removed from the
bottom of the vessel. The principles of Oslo crystallizers are also employed
in vacuum crystallization.
Evaporation and Distillation
Evaporation may be defined as the removal of a solvent from a solution by
vaporization, but is usually restricted to the concentration of solutions by boiling.
Crystallization and drying, which may also utilize the vaporization of a
liquid, are considered in subsequent sections. In the pharmaceutical industry
evaporation is primarily associated with removing, by boiling, water and other
solvents in batch processes. However, the principles governing such processes
apply more generally and are derived from studying heat transfer to the boiling
liquid, the relevant physical properties of the liquid, and the thermal stability
of its components.
9.2 HEAT TRANSFER TO BOILING LIQUIDS
IN AN EVAPORATOR
The heat required to boil a liquid in an evaporator is usually transferred from
a heating fluid, such as steam or hot water, across the wall of a jacket or tube
Evaporation and Distillation 129
in or around which the liquid boils. A qualitative discussion of the methods
used to secure high rates of heat flow can be based on equation 2.9:
Q UA?T (2.9)
where Q is the rate of heat flow, U is the overall heat transfer coefficient, A is
the area over which heat is transferred, and ?T is the difference in temperature
between the fluids.
The overall heat transfer coefficient is derived from a series of individual
coefficients that characterize the thermal barriers opposing heat transfer. Thus,
for the heating fluid, the film coefficient for a condensing vapor, such as steam,
is high provided that permanent gases and condensate are removed by venting
and draining. With liquid heating media, the velocity of flow over the heat
transfer surface should be as high as is practicable. If the solid barrier consists
of a thin metal wall, the resistance to heat flow is small. Resistance, however,
is significantly increased by chemical scale which may be deposited on either
side. The accumulation of scale should be prevented. A glass wall may provide
the largest thermal resistance of the system. Neglecting the thermal stability
of the boiling liquid, circulation of the liquid should be rapid and, because of
its influence on viscosity, the temperature of boiling should be as high as
possible. Both factors promote high film coefficients on the product side of
Other factors described by equation 2.9 are the area of the heat transfer
surfaces, which should be as large as possible, and the temperature difference
between the heating surface and the boiling liquid. As long as the critical heat
flux is not exceeded, the latter should also be large.
9.3 PHYSICAL PROPERTIES OF SOLUTION
A number of physical factors, which are interrelated in a complex way, are
relevant to a study of evaporation. For a given heating fluid the temperature
difference across the wall of an evaporator is determined by the boiling temperature,
a variable controlled by the external pressure and the solute concentration
in the solution. The boiling temperature and the solute concentration
influence the viscosity of the solution, a factor which greatly affects the heat
transfer coefficient. The boiling temperature also determines the solubility of
dissolved constituents and the degree of concentration which can be carried
out without separation of solids.
130 Chapter 9
9.3.1 Relation Between Boiling Temperature
and Solute Concentration
When a solute is dissolved in a solvent, the vapor pressure is depressed and the
boiling point rises. Since the boiling point increases as the solute concentration
increases, the temperature difference between the boiling liquid and the heating
surface falls. For dilute solutions the expected rise in boiling point can be
calculated from Raoult’s law. However, this procedure is not applicable to
concentrated solutions or to solutions of uncertain composition. For aqueous
concentrated solutions, Duhring’s rule may be used to obtain the boiling point
rise of a solution at any pressure. This rule states that the boiling point of a
given solution is a linear function of the boiling point of water at the same
pressure. A family of lines is required to cover a range of concentration as
shown in Figure 9.1.
9.3.2 Relation of Boiling Temperature and
The temperature at which a solution of given composition boils is determined
by the external pressure. The vapor pressure of a pure solvent at any temperature
can usually be obtained from published tables. Alternatively, if the vapor
FIGURE 9.1 Duhring chart for sodium chloride.
Evaporation and Distillation 131
pressure at two temperatures is known, the plot of the logarithm of the vapor
pressure against the reciprocal of the absolute temperature yields an approximately
straight line. For intermediate pressures the temperature at which the
solvent boils can be found by interpolation. If dissolved substances are present,
the boiling point must be adjusted by using Duhring’s rule. This value permits
an accurate estimate of the temperature differences in the evaporator.
Reduction in the external pressure lowers the boiling temperature and,
if the associated increase in viscosity is not too great, increases the rate of
evaporation. On large installations a moderate vacuum is widely used to increase
evaporator capacity. The imposition of low pressures and low boiling
temperatures is also necessary when thermolabile materials are processed.
Boiling in tubes is commonly used in evaporators. In these circumstances
the hydrostatic head developed by a column of liquid or the friction
head imposed by its movement can create a local increase in pressure which
suppresses boiling and decreases the evaporating capacity of the system.
9.3.3 Relation of Viscosity to Temperature
and Solute Concentration
The viscosity of a solution is modified by changes in temperature and solute
concentration. Since a low viscosity promotes a high heat transfer coefficient,
the exponential decrease of viscosity with increase in temperature is of great
importance and indicates a high boiling temperature.
In general, adding a nonvolatile solute increases a solution’s viscosity
at any temperature. Consequently, the viscosity increases as evaporation proceeds.
These effects, however, cannot be calculated.
If at the operating temperatures and concentrations the viscosity of a
solution is high, satisfactory heat transfer coefficients may only be obtained
if the liquid is driven over the heating surface. In other systems, movement
of a viscous liquid is assisted by gravity, or the liquid in contact with the
heating surface is disrupted mechanically by scrapers.
9.3.4 Effect of Temperature on Solubility
The solubility of a solution’s components depends on temperature. Most commonly,
solubility increases with increase in temperature, so a greater degree
of concentration is possible at higher temperatures without the separation of
solids. The reverse is true of liquids containing scale-forming solids with in132
verse solubility characteristics, such as calcium or magnesium sulfate, or materials
which decompose and deposit, such as coagulable protein.
9.3.5 Effect of Heat on the Active Constituents
of a Solution
The thermal stability of components of a solution may determine the type of
evaporator to be used and the conditions of its operation. If a simple solution
contains a hydrolyzable material and the rate of its degradation during evaporation
depends on its concentration at any time, an exponential relation between
the remaining fraction, F, and the time, t, characteristic of a first-order
reaction, is obtained:
F ekt (9.1)
The dependence of the reaction velocity constant, k, on the absolute
temperature, T, is expressed by the relation
k AeB/T (9.2)
where A and B are constants characteristic of the reaction. Thus, at temperatures
T1, T2, and T3, where T1 T2 T3, the relation between remaining fraction
and time of heating shown in Figure 9.2 emerges. This indicates the importance
of the temperature and time of heating. If the latter can be shortened,
the evaporation temperature can be greatly increased without increasing the
FIGURE 9.2 Effect of time and temperature on degradation.
Evaporation and Distillation 133
fraction which is degraded. If, therefore, the effect of temperature on evaporation
rate is known, it is possible to define conditions of time and temperature
at which decomposition is a minimum.
In practice, the kinetics of degradation and the relation of evaporation
rate and temperature are usually not known, particularly when the criteria by
which the product is judged are color, taste, or smell. In addition, this analysis
neglects temperature variation in the evaporating liquid and degradation in
boundary films where temperatures are higher. Often, therefore, experiments
are necessary to determine the suitability of an evaporation process.
In batch processes the time of exposure to heat is well defined. This is
also true of continuous processes in which the liquid to be evaporated is passed
only once through the heater. In continuous processes in which the liquid is
recirculated through the heater, the average residence time, a, given by the
ratio (working volume of evaporator)/(volumetric discharge), in which volumetric
discharge is only an indication of the damage which prolonged heating
may cause. If perfect mixing occurs in the evaporator, the fraction, f, which
is in the unit for time, t, or less is given by
f 1 et/a (9.3)
This relation shows, for example, that an evaporator with an average residence
time of 1 hr holds 13.5% of active principles for 2 hr and about 2% for 4 hr.
It is convenient to classify evaporators into the following: natural circulation
evaporators, forced circulation evaporators, and film evaporators.
9.4.1 Natural Circulation Evaporators
Small-scale evaporators consist of a simple pan heated by a jacket, a coil, or
by both. Admission of the heating fluid to the jacket induces a pool boiling
regime in the vessel. Very small evaporators may be open, the vapor escaping
to the atmosphere or into a vented hood. Larger pan evaporators are closed,
the vapor being led away by pipe. Small jacketed pans are efficient, easy to
clean, and may be fitted for the vacuum evaporation of thermolabile materials.
However, because the ratio of heating area to volume decreases as the capacity
increases, their size is limited and larger vessels must employ a heating coil.
This improves evaporating capacity but makes cleaning more difficult.
134 Chapter 9
The large heating area of a tube bundle is utilized widely in largescale
evaporators. Horizontal mounting, with the heating fluid inside the
tube, is limited by poor circulation to the evaporation of nonviscous liquids
in which the bundle is immersed. Normally, the tube bundle is mounted vertically
and is known as a calandria. The boiling of liquids in a vertical tube
and the earlier regimes of this process operate in a calandria. The tube lengths
and the liquid level are such that boiling occurs in the tubes and the mixture
of vapor and liquid rises until the entire calandria is just submerged. A typical
evaporator is shown in Figure 9.3(a). The tubes are from 120 to 180 cm long
and 5.1 to 7.6 cm in diameter. The low density of the boiling liquid and vapor
creates an upward movement in the tubes. Vapor and liquid separate in the
space above the calandria, and the liquid is returned to the pool at the base
of the tubes by a large central downcomer or through an annular space between
the heating element and the evaporator shell. Feed is added and concentrate
is withdrawn from the pool as shown in the figure. As long as the liquid
viscosity is low, good circulation and high heat transfer coefficients are obtained.
In some evaporators, the calandria is inclined and the tubes are lengthened.
FIGURE 9.3 (a) Evaporator with calandria and (b) climbing film evaporator.
Evaporation and Distillation 135
9.4.2 Forced Circulation Evaporators
On the smallest scale, forced circulation evaporators are similar to pan evaporators,
modified only by the inclusion of an agitator. Vigorous agitation increases
the boiling film coefficient, the degree depending on the type and speed
of the agitator. When evaporating viscous materials, one should use an agitator
to prevent material degradation at the heated surfaces.
Some large-scale continuous units are similar to natural circulation evaporators.
The natural circulation induced by boiling in a vertical tube may be
supplemented by an axial impeller mounted in the downcomer of the calandria.
This modification is used when viscous liquids or liquids containing suspended
solids are evaporated. Such units are employed in evaporative crystallization.
In other forced circulation evaporators, the tube bundle becomes, in effect,
a simple heat exchanger, through the tubes of which the liquid is pumped.
Commonly, the opposing head suppresses boiling in the tubes. Superheating
occurs and the liquid flashes into a mixture of liquid and vapor as it enters
the evaporator body.
9.4.3 Film Evaporators
In the calandria’s short tubes an intimate mixture of vapor and liquid is discharged
at the top. If the tube length is greatly increased, progressive phase
separation occurs until a high-velocity core of vapor is formed, which propels
an annular film of liquid along the tube. This phenomenon, which is one stage
of flow when a liquid and a gas pass in the same direction along a tube, is
employed in film evaporators. The turbulence of the film gives very high heat
transfer coefficients, and the bubbles and vapor evolved are rapidly swept into
the vapor stream. Although recirculation may be adopted, it is possible, with
the high evaporation rates found in long tubes, to concentrate the liquid suffi-
ciently in a single pass. Since a very short residence time is obtained, highly
thermolabile materials may be concentrated at relatively high temperatures.
Film evaporators are also suitable for materials which foam badly. Various
types have been developed, but all are essentially continuous in operation,
their capacity ranging from a few gallons per hour upward.
The climbing film evaporator, which is the most common film evaporator,
consists of tubes 460 to 910 cm long and 2.5 to 5.1 cm in diameter mounted
in a steam chest [Figure 9.3(b)]. The feed liquid enters the bottom of the tubes
and flows upward for a short distance before boiling begins. The length of
this section, which is characterized by low-heat-transfer coefficients, may be
minimized by preheating the feed to its boiling point. The pattern of boiling
136 Chapter 9
and phase separation follows, and a mixture of liquid and vapor emerges from
the top of the tube to be separated by baffles or by a cyclone separator. Climbing
film evaporators are not suitable for evaporating viscous liquids.
In the falling film evaporator the liquid is fed to the top of long heated
tubes. Since gravity assists flow down the tube, this arrangement is better
suited to the evaporation of moderately viscous liquids. The vapor evolved is
usually carried downward, and the mixture of liquid and vapor emerges from
the bottom for separation. Even distribution of liquid must be secured during
feeding. A tendency to channel in some tubes leads to drying in others.
The rising-falling film evaporator concentrates a liquid in a climbing
film section and then leads the emerging liquid and vapor into a second tube
section which forms a falling film evaporator. Good distribution in the falling
film section is claimed, and the evaporator is particularly suitable for liquids
which increase greatly in viscosity during evaporation.
In mechanically aided film evaporators a thin film of material is maintained
on the heat transfer surface irrespective of the viscosity. This is usually
achieved by a rotor, concentric with the tube, which carries blades that scrape
the tube or ride with low clearance in the film. Mechanical agitation permits
evaporation of materials which are highly viscous or have a low thermal conductivity.
Since temperature variations in the film are reduced and residence
times are shortened, the vacuum evaporation of viscous thermolabile materials
9.4.4 Efficiency of Evaporators
In the pharmaceutical industry economic use of steam may not be of overriding
importance because the small scale of the operation and the high value of the
product do not justify the additional capital costs of improved heating effi-
ciency. In other industries heating costs require more efficient use of heat.
This efficiency is secured by utilizing the heat content of the vapor emerging
from the evaporator, assumed, until now, to be lost in a following condensation.
Two methods commonly used are multiple-effect evaporation and vapor
In multiple-effect evaporation, the vapor from one evaporator is led as
the heating medium to the calandria of a second evaporator, which, therefore,
must operate at a lower temperature than the first. This principle can be extended
to a number of evaporators, some stages working under vacuum. The
limit is set by the relation of the cost of the plant and the vacuum services to
the cost of the steam saved.
Evaporation and Distillation 137
In evaporators employing vapor recompression, the vapor emerging is
compressed by mechanical pumps or steam jet ejectors to increase its temperature.
The compressed vapor is returned to the steam chest.
9.4.5 Vapor Removal and Liquid Entrainment
Vapor must be removed from the evaporator with as little entrained liquid as
possible. The two determining factors are the vapor velocity at the surface of
the liquid and the velocity of the vapor leaving the evaporator. On a small
scale, surface vapor velocities will be low but with increase in scale, the adverse
ratio of surface area to volume creates higher velocities. Droplets formed
by the bubbles bursting at the boiling surface may then be projected from the
surface. In addition, foam may form. Various devices may be used to control
entrainment at or near the surface. A high vapor space is provided above the
boiling liquid to allow large droplets to fall and foam to collapse. Baffles
may be used in the vapor space to arrest entrained droplets. Where allowable,
antifoaming agents, such as silicone oils, can be used to depress foaming.
Stokes’ law shows that vapor of particular characteristics will carry
droplets upward against the force of gravity. Any entrained liquid not intercepted
in the evaporator body is, therefore, carried forward in the highervelocity
stream of the vapor uptake. Some droplets are caught here, the quantity
depending on duct geometry and vapor velocity. At atmospheric pressure,
the latter might be 17 m s1. In vacuum evaporation much higher velocities
may be used. When the quantity of entrained liquid is high, the vapor is commonly
led to a cyclone separator, which is used with frothing materials, and
to the vapor-liquid mixture leaving a climbing film evaporator. In the separator
the entrained liquid is flung out to the walls by centrifugal force and may be
collected or returned to the evaporator. The vapor is led to a condenser.
9.4.6 Evaporation Without Boiling
During heating, some evaporation takes place at the surface of a batch of liquid
before boiling begins. Similarly, liquids which are very viscous or which froth
excessively may be concentrated without boiling. The diffusion of vapor from
the surface is then described by equation 3.5:
(PAi PAg) (3.5)
138 Chapter 9
where NA is the number of moles evaporating from unit area in unit time, kg
is the mass transfer coefficient (proportional to the gas velocity) across the
boundary layer, R is the gas constant, T is the absolute temperature, PAi is the
liquid vapor pressure, and PAg is the partial pressure of the vapor in the gas
Distillation is a process in which a liquid mixture is separated into its component
parts by vaporization. The vapor evolved from a boiling liquid mixture
is normally richer in the more volatile components than the liquid with which
it is in equilibrium. Distillation rests upon this fact. Although multicomponent
mixtures are most common in distillation processes, an understanding of the
operation can be based on the vapor pressure characteristics of two component
or binary mixtures. Binary systems in which the liquids are immiscible are
discussed first. Discussion of the separation of miscible liquids by fractionation
forms most of the remainder of the section.
9.6 BINARY MIXTURES OF IMMISCIBLE
LIQUIDS: STEAM DISTILLATION
If the two components of a binary mixture are immiscible, the vapor pressure
of the mixture is the sum of the vapor pressures of the two components, each
exerted independently and not as a function of their relative concentrations in
the liquid. This property is employed in steam distillation, a process particularly
applicable to the separation of high-boiling-point substances from nonvolatile
impurities. The steam forms a cheap and inert carrier. The principles
of the process, however, apply to other immiscible systems.
If a mixture of water and a high-boiling liquid, such as nitrobenzene,
is heated, the total vapor pressure increases and ultimately reaches the external
pressure. The mixture boils and the vapors evolved are condensed to give a
liquid mixture which separates under gravity. In practice, the vapors are produced
by blowing steam into the liquid in a manner which gives intimate
contact between the phases. Since both components contribute to the total
pressure, the boiling temperature must be lower than the boiling point of either
component. In the case of nitrobenzene and water, the boiling point at atmospheric
pressure is about 372 K. To distill nitrobenzene alone at this temperaEvaporation
and Distillation 139
ture, a pressure of 20 mm Hg must be imposed. Steam distillation, therefore,
permits the distillation of water-immiscible materials of high boiling point
without the use of high temperatures, which might cause decomposition, or
high vacua. The method, however, only separates such materials from nonvolatile
constituents. If volatile impurities are present, they appear in the distillate.
The composition of the distillate is calculated in the following way. For
two components, A and B, the total vapor pressure, P, is the sum of the vapor
pressures of the components, PA and PB. Since the partial pressure of a component
in a gaseous mixture is proportional to its molar concentration, the vapor
where nA and nB are the number of moles of A and B in the vapor, respectively.
If WA and WB are the weights of A and B in the vapor, then
where MA and MB are the respective molecular weights. The distillate obtained
from the vapor is WA WB. Therefore,
Percentage of A in distillate
The ratio of immiscible organic liquid to water in the distillate is increased
if the former has a high molecular weight or a high vapor pressure.
Steam distillation under vacuum may be employed when the thermal
stability of the material prohibits temperatures of about 373 K. A further variant
is the introduction of unsaturated steam under conditions in which no condensation
to water takes place. Only two phases, the liquid being distilled and
the mixed vapors, are then present. The external pressure no longer fixes the
temperature, as in a three-phase system, and any convenient value can be
The chief uses of steam distillation are the purification and isolation of
liquids of high boiling point, such as aniline, nitrobenzene, or ?-dichlorobenzene,
and in the preparation of fatty acids and volatile oils. Many of the latter
are prepared by introducing steam into a mixture of the comminuted drug
and water. The method is also used to remove odoriferous elements, such as
140 Chapter 9
aldehydes and ketones, from edible oils. Dehydrating a material by adding a
volatile water-immiscible solvent, such as toluene, and distilling the mixture
is a form of steam distillation. The solvent separates in the condensate and
may be returned to the still.
9.7 BINARY MIXTURES OF MISCIBLE
9.7.1 Relation of Vapor Pressure and Mixture
When the two components of a binary mixture are completely miscible, the
vapor pressure of a mixture is a function of mixture composition as well as
the vapor pressures of the two pure components. If the liquids are ideal, the
relationship of vapor pressure and composition is given by Raoult’s law. At
constant temperature the partial vapor pressure of a constituent of an ideal
mixture is proportional to its mole fraction in the liquid. Thus, for a mixture
of A and B,
PA P°AxA (9.7)
where PA is the partial vapor pressure of A in the mixture, P°A is the vapor
pressure of pure A, and xA is its mole fraction. Similarly,
PB P°B xB (9.8)
The total pressure of the system, P, is simply PA PB.
These relations can be expressed graphically. If the vapor pressure at a
given temperature of each pure component is marked on a graph of vapor
pressure versus mole fraction, the total vapor pressure at the same temperature
of a liquid mixture of any composition falls on the straight line joining the
vapor pressures of the two components. The partial pressure of each component
is indicated by the diagonals of this figure. The principle is shown in
Figure 9.4. A separate relation must be constructed for each temperature.
Very few liquid mixtures rigidly obey Raoult’s law. Consequently, the
vapor pressure data must be determined experimentally. Mixtures which deviate
positively from the law give a total vapor pressure curve that lies above
the theoretical straight line. Negative deviations fall below the line. In extreme
cases deviations are so large that a range of mixtures exhibits a vapor pressure
higher or lower than either of the pure components.
Evaporation and Distillation 141
FIGURE 9.4 (a) Vapor pressure of an ideal binary mixture; (b) phase diagram.
Returning to ideal systems, the partial pressure of a component in the
vapor is proportional to its mole fraction. For component A,
PA yAP (9.9)
where PA is the partial pressure of A in the vapor and yA is its mole fraction.
Since PA P°AxA,
If A is the more volatile component, P°A P; therefore, yA xA; i.e., the
vapor is richer in the more volatile component than the liquid with which it
is in equilibrium.
9.7.2 The Relation of Boiling Point and
For the purposes of distillation, curves relating vapor pressure and composition
are usually replaced by boiling point curves. These are determined by experi142
FIGURE 9.5 Temperature-composition diagrams for a binary mixture: (a) minimum
azeotrope; (b) maximum azeotrope.
ment at the given pressure. Figure 9.5(a) represents a system in which the
vapor pressure of some mixtures is greater than the vapor pressure of the pure,
more volatile component. This system exhibits a minimum boiling point, and
the composition of the liquid at this point is Z. This mixture, which is a constant
boiling or azeotropic mixture, evolves on boiling a vapor of the same
composition. In the binary system described in Figure 9.5(b), mixtures are
formed with a vapor pressure less than that of the less volatile component.
The maximum boiling point is given by the azeotropic mixture, Z.
Systems forming minimum boiling mixtures are common, one example
being ethyl alcohol and water, where, the azeotrope contains 4.5% by weight
of water. The boiling point at atmospheric pressure is 351.15 K, 0.25 K lower
than the boiling point of pure alcohol. Maximum boiling mixtures are less
common. The most familiar example is hydrochloric acid, which forms an
azeotrope boiling at 381 K and containing 20.2% by weight of hydrochloric
Mixtures forming azeotropes cannot be separated into the pure components
by normal distillation methods. However, separation into the azeotrope
and one pure component is possible. Efficient fractionation of the mixture M
of Figure 9.5(a) gives the azeotrope Z as distillate and pure B as the residue.
The composition of the azeotropic mixture of a system is a function of
the total pressure, and it is possible in some cases to eliminate the constant
boiling mixture by altering the pressure at which the distillation is performed.
For example, at pressures less than 100 mm Hg, ethyl alcohol and water do
not form an azeotrope, and can be completely separated.
Evaporation and Distillation 143
FIGURE 9.6 Vapor-liquid equilibrium diagrams.
9.7.3 Vapor-Liquid Equilibrium Diagrams
Vapor-liquid equilibrium diagrams (Figure 9.6) are an alternative and convenient
method of recording distillation data. They consist of a conventional
graph relating the mole fraction of the more volatile component in the liquid,
X, to the mole fraction of the more volatile component in the vapor, Y. An
ideal binary system is shown in Figure 9.6(a). The temperature varies along
each of the curves, and the diagram is only applicable to the pressure at which
the variables were measured. Curves of minimum boiling mixtures and maximum
boiling mixtures are drawn in Figure 9.6(b) and Figure 9.6(c), respectively.
9.8 SIMPLE OR DIFFERENTIAL
In simple or differential distillation, the vapor evolved from the boiling mixture
is immediately removed and condensed. For the system in Figure 9.7(a),
the liquid of composition x1 evolves a vapor of composition y1. Its removal
impoverishes the liquid in the more volatile component. The composition of
the liquid moves toward pure B and its boiling point increases. There is, therefore,
a progressive change in the vapor composition, the mole fraction of the
more volatile component steadily decreasing. Unless the boiling points of the
two pure components differ widely, a reasonable degree of separation is not
possible. The method may be used to remove low-boiling-point solvents from
144 Chapter 9
FIGURE 9.7 (a) Three ideal stages in a fractional distillation and (b) the plate column
associated with the fractional distillation.
9.9 RECTIFICATION OR FRACTIONATION
In simple distillation, vapor enrichment is small. In fractionation, a term synonymous
with rectification, the vapor leaving the boiling liquid is led up a
column to meet a liquid stream or reflux which originates higher in the column
as part of the condensate. In a series of partial condensations and vaporizations,
the rising vapor becomes richer in the more volatile component at the
expense of the falling liquid, and high degrees of separation are possible. The
columns, called fractionating columns, are of two basic types: packed columns
and plate columns.
Packed columns are used for laboratory and small-scale industrial distillation
and are usually operated as a batch process. The column consists of
a vertical, hollow, cylindrical shell containing a packing designed to offer a
large interfacial contact area between liquid and vapor. The form of the packing
varies, but Raschig rings, which consist of small metallic or ceramic cylinders,
are the most commonly used. Other shapes are saddles, Pall rings, Lessing
rings, and meshes of woven wire or expanded metal. In a packed column,
countercurrent interaction between the rising vapor and the falling liquid occurs
throughout the column length. The distillation rate and the size and shape
of the packing must be chosen to give efficient support for the liquid phase,
phase movement, and phase interaction. High rates of vapor flow may arrest
or reverse the downward movement of liquid. This ultimately causes column
flooding and determines the upper end of the operating range. The column
Evaporation and Distillation 145
efficiency is also decreased if the falling liquid fails to wet all the available
packing surface, a condition which determines the lower limit of column operation.
In general, packed columns operate under widely varying conditions
without serious loss of efficiency.
9.9.1 Plate Columns
A plate column consists of a series of plates or trays on which the liquid is
retained for some period during its movement down the column. The rising
vapor is bubbled through this liquid, providing intimate contact between the
phases. Liquid in reflux moves downward between plates and is usually carried
by a downcomer. Contact between the vapor and liquid takes place in stages.
Plate columns operate efficiently over a limited range of conditions. They are
mainly used in large-scale, continuous installations in which the conditions
of distillation can be closely maintained.
9.9.2 Principles of Continuous and Batch
Figure 9.7(a) is the boiling point curve of a binary mixture. If a mixture of
composition x1 is boiled, a vapor of composition y1 is evolved, and condensation
gives a liquid of composition x2. This is an ideal distillation stage. A
second stage gives a liquid of composition x3, and, in this example, a further
stage would give the more volatile component in an almost pure form.
These conditions are approached in continuously operated fractionating
columns. In such columns, operating with continuous feed and product withdrawal,
the composition of the liquid and vapor at any point does not vary
with time. The process is examined with reference to the plate column in
Figure 9.7(b). Let the composition of the liquid on plate 3 be x1. The vapor
received at this plate from the plate below is bubbled through the liquid on
the plate. Some of the less volatile component is condensed, increasing the
mole fraction of the more volatile component in the bubbles. The latent heat
evolved by this condensation vaporizes some of the liquid on the plate. This
vapor is richer in the more volatile component than the liquid is. By these
two mechanisms the vapor which will leave the plate moves toward equilibrium
with the liquid on the plate. If equilibrium could be achieved, maximum
enrichment of the vapor would occur corresponding to the appropriate horizontal
line linking vapor-liquid equilibrium concentrations on the boiling point
curve. For the system in Figure 9.7(b), this line is x1y1. Two more ideal distilla146
tion stages at plates 2 and 1 complete the separation of this mixture. In practice,
equilibrium is not achieved at the plates due to limited contact between the
phases. Enrichment is therefore less than that at an ideal stage and the discrepancy
is a measure of plate efficiency.
Under steady column conditions, the concentration of the more volatile
component in the liquid on any plate is maintained by the overflow or reflux
of liquid richer in the more volatile component from the plate above. This is
true of all parts except the top plate. Here, the mole fraction of the more
volatile component must be maintained by returning part of the condensate
from the last stage to the top plate. This is known as reflux return, and the
reflux ratio is the ratio of the condensate returned to the column and the amount
withdrawn as product. This ratio markedly affects the degree of separation
occurring in a given column. If the proportion of the condensate to be returned
to the column is increased, the mole fraction of the more volatile component
in the liquid on the top plate is increased. The mole fraction of this component
in the emerging vapor is also increased and a purer product is obtained. By
the increased overflow of liquid from plate to plate down the column, this is
also true of all plates. Thus, by increasing the reflux ratio, the enrichment
obtained with a given number of plates is increased. The amount of product,
however, is decreased. A column operating at total reflux, in which the whole
of the distillate is returned to the column, achieves a given enrichment with
a minimum number of plates. This column, however, gives no product at all,
and an economic compromise is sought between a short column with a small
number of plates operating with high reflux ratio and a long column of many
plates operating with a low reflux ratio.
Algebraic and graphical methods are used to calculate the theoretical
number of plates required to separate a mixture in a column operating with
a known reflux ratio. In a packed column, enrichment of the vapor takes place
continuously as the column is ascended. The enrichment taking place over a
certain length of the column corresponds to the enrichment secured at a plate
which behaves ideally. This correspondence is expressed as the height equivalent
of a theoretical or ideal plate (HETP). This concept allows the account
given for plate columns to be directly applied to packed columns. The packing
height required for a separation is simply the product of the HETP and the
number of ideal stages required. The HETP is not constant for a given packing,
but depends on the physical properties of the liquid and the vapor, such as
density and viscosity, and on the distillation rate.
In batch distillation, steady-state conditions are never achieved, and the
concentration of the more volatile component in the still or at any point in
Evaporation and Distillation 147
the column falls as the rich product is withdrawn from the top. The concentration
of the more volatile component in the product also falls. To maintain a
given product specification, it may be necessary to increase the reflux ratio
from time to time. Alternatively, the reflux ratio could be so chosen that the
average composition of the product complies with the specification, the first
distillate being enriched and the last depleted of the more volatile component.
Most distillations, whether operated as batch or continuous processes,
are applied to mixtures of more than two components. If the boiling points
of the components differ widely, the process may be treated as successive
distillation of two component mixtures. If a mixture of three components, A,
B, and C, is batch-distilled, a column with sufficient plates will initially separate
the most volatile component, A, with a high purity. As distillation progresses,
the concentration of A in the distillate falls, and, ultimately, the column
fails to produce a distillate of the required quality. An intermediate fraction
is then distilled, consisting of A and B, until the distillate contains the required
amount of B. After this fraction is collected, a second intermediate fraction
is distilled to leave component C in the still. Intermediate fractions can be
distilled with subsequent batches. A similar separation could be accomplished
with two continuous columns, one separating A from B and C and another
separating B from C.
To avoid thermal decomposition of a component in a mixture, distillation
may be performed at a reduced pressure. In addition to the general principles
we have described, the following factors may be important. The pressure
drop associated with the flow of vapor up the column, which is relatively small
in atmospheric distillation, may become significant, producing a damaging
increase in the temperature of the liquid in the still. Second, in packed columns,
flooding occurs at lower distillation rates due to the high velocity of
the rising vapor.
9.10 SEPARATION OF AZEOTROPES AND
LIQUIDS OF SIMILAR VOLATILITY
Systems which form azeotropes cannot be separated by fractional distillation,
although formation of the azeotrope can sometimes be precluded by changing
the distillation pressure. Problems of separation are also found with mixtures
of liquids with similar volatility. Separation of these systems can be facilitated
by adding a third component. If this component forms one or more azeotropes
with the original components of the mixture, the process is called azeotropic
148 Chapter 9
distillation. The addition of a relatively nonvolatile component which alters
the relative volatility of the original components gives a process known as
In azeotropic distillation of minimum-boiling binary mixtures, the third
component either forms a new binary azeotrope of lower boiling point or a
ternary azeotrope of lower boiling point containing the original components
in different proportions. The newly formed azeotrope must be easily separated
after distillation. The process is illustrated by the dehydration of alcohol with
benzene. The binary azeotrope of ethyl alcohol and water boils at 351.15 K,
the ternary azeotrope of benzene, water, and alcohol boils at 337.8 K, and the
binary azeotrope of benzene and alcohol boils at 341 K. Distillation of the
alcohol-water azeotrope with benzene yields the ternary azeotrope, which separates
on condensation to give two layers, one of which contains almost all the
water. In a batch process the column then gives the benzene alcohol azeotrope,
leaving anhydrous alcohol in the still. In a continuous process the various
stages are each performed on a different column.
Extractive distillation is illustrated in the separation of benzene and cyclohexane
by phenol addition. The relative volatility of the original components
is modified so that cyclohexane is recovered as the distillate, leaving a
mixture of phenol and benzene which is passed to a second column for separation.
The phenol, which is added to the top of the column, appears to aid
separation by preferentially dissolving benzene during its downward passage.
This leads to the term extractive distillation.
9.11 MOLECULAR DISTILLATION
Molecular distillation is carried out without boiling at very low pressures,
around 0.001 mmHg. At these pressures molecular collisions in the evolving
vapor and their reflection back to the liquid surface are greatly decreased, and
the mean free path of the molecules is of the same order as the distance between
the evaporating surface and a condenser placed a short distance away.
It then becomes possible to distill liquids of very high boiling point, although
the degree of separation cannot exceed one theoretical plate. The process is
therefore used primarily to concentrate nonvolatile components in a high-boiling-
point medium. The vitamins in cod liver oil can be concentrated in this
way. For separating liquids of comparable volatility several separate distillation
stages are necessary.
Since agitation due to boiling is absent, an alternative method of maintaining
the more volatile component at the evaporating surface must be
Evaporation and Distillation 149
FIGURE 9.8 Large-scale molecular still.
adopted. In the industrial molecular still in Figure 9.8, the feed is introduced
at the bottom of a heated conical rotor and flows upward as a thin liquid layer
under the action of centrifugal force. The residue is caught in a gutter at the
top. The vapor is condensed on a concentric, water-cooled condenser a short
distance away and discharged.
The student of pharmacy will have used filtration extensively in the collection
of precipitates in chemical analyses or in the preparation of parenteral fluids
and will, therefore, anticipate the definition of filtration as the removal of
solids suspended in a liquid or gas by passage through a pervious medium on
which the solids are retained. The pervious medium or septum is normally
supported on a base, and these, together with a suitable housing providing
free access of fluid to and from the septum, comprise the filter.
10.1 APPLICATIONS OF FILTRATION
The applications of filtration are diverse. They may, however, be classified as
clarification or cake filtration.
Very high standards of clarity are imposed during the production of pharmaceutical
solutions. The aim may be simply the presentation of an elegant prod-
uct, although complete freedom from particulate matter is obviously necessary
in the manufacture of most parenteral solutions. The solids are unwanted and
are normally present in a very small concentration. Clarification may be carried
out by the use of thick media that allow for the penetration and arrest of
particles by entrapment, impingement, and electrostatic effects. This leads to
the concept of depth filtration in which particles, perhaps a hundred times
smaller than the dimensions of the passages through the medium, are removed.
For this reason, such filters are not absolute and must be designed with suffi-
cient depth so that the probability of the passage of the smallest particle under
consideration through the filter is extremely small.
Depth filtration differs fundamentally from the use of media in which
pore size determines the size of particle retained. Such filters may be said to
be ‘‘absolute’’ at a particle diameter closely related to the size of the pore,
so there is a relatively sharp division between particles that pass the filter
and those that are retained. An analogy with sieving may be drawn for this
mechanism. The life of such filters depends on the number of available pores
for fluid passage. Once a particle is trapped at the entrance to the pore, the
pore’s contribution to the overall flow of liquid is very much reduced. Coarse
straining with a wire mesh and the membrane filter employ this mechanism.
Sterilization of liquids by filtration could be regarded as an extreme
application of clarification in which the complete removal of particles as small
as 0.3 106 m must be ensured.
10.1.2 Cake Filtration
The most common industrial application is filtration of slurries containing a
relatively large amount of suspended solids, usually 3% to 20%. The septum
acts only as a support in this operation. The actual filtration is carried out by
the solids deposited as a cake. In such cases, solids may completely penetrate
the septum until the deposition of an effective cake occurs. Until this time,
cloudy filtrate may be recycled. The physical properties of the cake largely
determine the methods employed. Often, washing and partial drying or dewatering
are integral parts of the process. Effective discharge of the cake completes
the process. The solids, the filtrate, or both may be wanted.
10.2 FILTRATION THEORIES
Two aspects of filtration theory must be considered. The first describes the
flow of fluids through porous media. It is applicable to both clarification and
152 Chapter 10
cake filtration. The second—which is of primary importance only in clarification—
examines the retention of particles in a depth filter.
10.2.1 Fluid Flow Through Porous Media
The concept of a channel with a hydraulic diameter equivalent to the complex
interstitial network that exists in a powder bed leads to the equation
where Q is the volumetric flow rate, A is the bed area, L is the bed thickness,
?P is the pressure difference across the bed, and ? is the fluid viscosity. The
permeability coefficient, K, is
where ? is the bed porosity and S0 is the bed’s specific surface area by volume
10.2.2 Factors Affecting Filtration Rate
Equation 10.1 may be used as a basis for discussing those factors that determine
the filtration rate.
The filtration rate at any instant of time is directly proportional to the pressure
difference across the bed. In cake filtration, deposition of solids over a finite
period increases bed depth. If, therefore, the pressure remains constant, the
filtration rate falls. Alternatively, the pressure can be progressively increased
to maintain the filtration rate.
Conditions in which the pressure is substantially constant are found in
vacuum filtration. In pressure filtration it is usual to employ a low constant
pressure in the early stages of filtration, for reasons to be given. The pressure
is then stepped up as the operation proceeds.
This analysis neglects the additional resistance derived from the supporting
septum and the thin layer of particles associated with it. At the operation’s
beginning some particles penetrate the septum and are retained in the capillaries
in the manner of depth filtration while other particles bridge the pores at
the surface to begin the cake formation. The effect of penetration, which is
analogous to blinding a sieve, is to confer a resistance on the cake-septum
junction which is much higher than the resistance of the clean septum with a
small associated layer of cake. This layer may contribute heavily to the total
resistance. Since penetration is not reversible, the initial period of cake filtration
is highly critical and is usually carried out at a low pressure. The amount
of penetration depends on the septum structure, the size, shape, and concentration
of the solid particles, and the filtration rate.
When clarifying at constant pressure, a slow decrease in filtration rate
occurs because material is deposited within the bed.
The inverse relation between flow rate and viscosity indicates that, as expected,
higher pressures are required to maintain a given flow rate for thick
liquids than are necessary for filtering thin liquids. The decrease in viscosity
with increase in temperature may suggest the use of hot filtration. Some plants
(e.g., the filter press) can be equipped so that the temperature of hot slurries
can be maintained.
In cake filtration a suitable filter area must be employed for a particular slurry.
If this area is too small, the excessively thick cakes produced necessitate highpressure
differentials to maintain a reasonable flow rate. This is highly important
in the filtration of slurries giving compressible cakes. When clarifying,
the relation is simpler. The filtration rate can be doubled by simply doubling
the filter area.
The permeability coefficient may be examined in terms of its two variables:
porosity and surface area: Evaluation of the term ?3/(1 ?)2 shows that the
permeability coefficient is a sensitive function of porosity. When a slurry is
filtered, the cake porosity depends on the way in which particles are deposited
and packed. A porosity or void fraction from 0.27 to 0.47 is possible in the
regular arrangements of spheres of equal size. Intermediate values are normally
obtained in the random deposition of deflocculated particles of fairly
regular shape. A fast deposition rate, given by concentrated slurries or high
flow rates, may give a higher porosity because of the greater possibility of
bridging and arching in the cake. Although theoretically the particle size has
no effect on porosity (assuming that the bed is large compared with the parti154
cles), a broad particle size distribution may lead to a reduction of porosity if
small particles pack in the interstices created by larger particles.
Surface area, unlike porosity, is markedly affected by particle size and
is inversely proportional to particle diameter. Hence, as commonly observed
in the laboratory, a coarse precipitate is easier to filter than a fine precipitate
even though both may pack with the same porosity. Where possible, a previous
operation may be modified to facilitate filtration. For example, a suitable particle
size may be obtained in a crystallization process by control of nucleation,
or the proportion of fines in milling may be reduced by carefully controlling
residence times. In most cases, however, control of this type is not possible,
and, with materials that filter only with difficulty, much may be gained by
conditioning the slurry, an operator that modifies the porosity and specific
surface of the depositing cake.
In clarification, high permeability and filtration rate oppose good particle
retention. In the formation of clarifying media from sintered or loose particles,
accurate control of particle size, specific surface, and porosity is possible, so
a medium can be designed that offers the best compromise between permeability
and particle retention. This analysis of permeability can be accurately
applied to these systems. Due to the extremes of shape, this is not so of the
fibrous media used for clarification. Here it is possible to develop a material
of high permeability and high retentive capacity. However, such a material is
intrinsically weak and must be adequately supported.
10.2.3 Particle Retention in a Depth Filter
Theoretical studies of particle retention have been restricted to granular media
of a type used in purifying municipal water. The aim is to predict the variation
of filtrate quality with influent quality or time and then estimate the effect of
removedsolidsonthe permeability of the bed.Suchstudies havesomebearingon
the use of granular, sintered, or fibrous beds used for clarifying pharmaceuticals.
The path followed by the liquid through a bed is extremely tortuous.
Violent changes of direction and velocity occur as the system of pores and
waists is traversed. Deflection of particles by gravity or, for very fine particles,
by Brownian movement brings particles within range of the attractive forces
between particles and the medium and causes arrest. Inertial effects—that is,
the movement of a particle across streamlines by virtue of its momentum—
are considered to be important only when particles are removed from gases.
In liquid-solid systems, density differences are much smaller.
Opportunity for contact and arrest depends on the surface area of the
bed, the tortuosity of the void space, and the interstitial speed of the liquid.
Since the inertial mechanism is ineffective, increase in interstitial velocity
decreases the opportunity for contact and retention of particles by the medium.
Therefore, a filter’s efficiency decreases as the flow rate increases. However,
efficiency increases as the density or size of the influent particles increases
and decreases as the particle size in the bed decreases. Each layer of clean
filter is considered to remove the same proportion of particles in the influent.
where C is the concentration of particles entering element of depth dx. The
value of K, which is a clarifying coefficient expressing the fraction of particles
that deposit in unit depth of the bed, changes with time. Initially, the rate of
removal increases and the efficiency of filtration improves, perhaps, as has
been suggested, because the particle deposition in the bed is at first localized
and the surface area and tortuosity increase. Later, the removal efficiency decreases
because deposition narrows the pores, reduces convolutions and surface
area, and increases the interstitial liquid velocity. The failure of the medium
to adequately retain particles or the decrease in permeability and
filtration rate eventually limit filter life. If deposition is reversible, then permeability
and retentive capacity can be restored by vigorous backwashing. Alternatively,
the medium should be cheap and expendable.
10.2.4 Conditioning of Slurries
The permeability of an ideal filter bed, such as that formed by a filter aid, is
about 7 1013 m2. This is more than 10,000 times the permeability of a
precipitate of aluminum hydroxide. Therefore, modifying the slurry’s physical
properties, called slurry conditioning, can be a powerful tool for a filtration
engineer. Two methods, flocculation and addition of filter aids, are discussed.
Flocculation of slurries is a common procedure in which the addition of
flocculating agents is permissible. The aggregates or flocs, which are characterized
by a high sedimentation rate and sedimentation volume, form cakes with a
porosity as high as 0.9. Since this is also associated with a decrease in specific
surface, flocculation gives a marked increase in permeability. However, such
coagulates are highly compressible and are therefore filtered at low pressures.
Filter aids are materials added in concentrations of up to 5% to slurries
that filter only with difficulty. The filter aid forms a rigid cake of high porosity
and permeability due to favorable shape characteristics, a low surface area,
and a narrow particle size distribution, properties that can be varied for different
operations. This structure mechanically supports the fine particles origi156
nally in the slurry. Diatomite, in the form of a purified, fractionated powder,
is most commonly used. Other filter aids include a volcanic glass, called Perlite,
and some cellulose derivatives.
Filter aids cannot easily be used when solids are wanted. Their excellent
characteristics, however, lead to their use as a ‘‘precoat’’ mounted on a suitable
support so that the filter aid itself forms the effective filtering medium.
This prevents blinding the septum. Precoat methods take several forms and
are discussed in Section 10.3.
10.2.5 Cake Compressibility
In the theory of cake filtration, the permeability coefficient was considered
constant. The observation that a cake may be hard and firm at the cake septum
junction and sloppy at its outer face suggests that the porosity may be varying
throughout the cake depth. This variability could be due to decreased hydrostatic
pressure from a maximum at the cake face to zero at the back of the
supporting septum. The hydrostatic pressure must be balanced by a thrust,
originating in the viscous drag of the fluid as it passes through the cake, transmitted
through the cake skeleton, and varying from zero at the cake face to
a maximum at the back of the septum equal to the pressure difference. The
relation between this compressive stress and the pressure applied across the
cake is represented in Figure 10.1.
FIGURE 10.1 Stress distribution in a filter cake.
We have so far considered that no deformation occurs under this stress;
i.e., the cake is perfectly rigid. No cake, in fact, behaves in this way. However,
some, such as those composed of filter aids or of coarse, isodiametric particles,
approximate closely to a perfectly rigid cake. Others, such as cakes deposited
from slurries of heavily hydrated colloidal particles, are easily deformed so
that the permeability coefficient, until now assumed constant, is itself a function
of pressure, so equation 10.1 no longer applies. This effect can be so
marked that a pressure increase actually decreases the filtration rate. Most
slurries’ behavior is between these two extremes.
10.2.6 Cake Washing and Dewatering
Cake washing is of great importance in many filtration operations because the
filtrate retained in the cake can be displaced by pure liquids. Filtration equipment
varies in its washing efficiency, and this may influence the choice of
plant. If the wash liquids follow the same course as the filtrate, the wash rate
will be the same as the final rate of filtration, assuming that the viscosities of
the two liquids are the same and that the cake structure is not altered by,
for example, peptization following the removal of flocculating electrolytes.
Washing takes place in two stages. The first involves removing most of the
filtrate retained in the cake by simple displacement. In the second, longer
stage, filtrate removal from the less accessible pores occurs by a diffusive
mechanism. These stages are shown in Figure 10.2.
FIGURE 10.2 Displacement of filtrate by displacement washing.
158 Chapter 10
Efficient washing requires a fairly cohesive cake that opposes the formation
of cracks and channels which offer a preferential course to the wash liquid.
For this reason, cakes should have even thickness and permeability.
Subsequent operations, such as drying and handling, are facilitated by
removing the liquid retained in the cake after washing, which occupies from
40% to 80% of the total cake volume. Removal is achieved by blowing or
drawing air through the washed cake, leaving liquid retained only as a film
around the particles and as annuli at the points of contact. Since surface area
and the number of point contacts per unit volume increase as the particle size
decreases, the effectiveness of this operation, like washing, decreases with
cakes composed of fine particles.
The method by which filtrate is driven through the filter medium, and cake
if present, is used to classify filters as follows:
1. Gravity filters
2. Vacuum filters
3. Pressure filters
4. The centrifuge
Each group may be further subdivided into filters employed in continuous or
batch processes, although, due to technical difficulties, continuous pressure
filters are uncommon and expensive. The general principles of each group are
discussed and illustrated by several widely used filters.
10.3.1 Gravity Filters
Gravity filters employing thick, granular beds are widely used in municipal
water filtration. However, the low operating pressures, usually less than 1.03
104 N/m2, give low filtration rates unless very large areas are used. Their
use in pharmacy is quite limited. Gravity filters using suspended media composed
of thick felts are sometimes used for clarification on a small scale. On
a somewhat larger scale, a wooden or stone tank, known as a nutsche, is used.
The nutsche has a false bottom, which may act as the filter medium, although,
more commonly, the bottom is dressed with a cloth. The slurry is added and
the material filters under its own hydrostatic head. The filtrate is collected in
the sump beneath the filter. Thorough washing is possible either by simple
displacement and diffusion or by resuspending the solids in a wash liquid and
refiltering. The nutsche is comparatively difficult to empty, and labor costs
10.3.2 Vacuum Filters
Vacuum filters operate at higher pressure differentials than gravity filters. The
pressure is limited naturally to about 8.27 104 N/m2, which confines their
use of vacuum filters to the deposition of fairly thin cakes of freely filtering
materials. Despite this limitation, the principle has been successfully applied
to continuous and completely automatic cake filtration, for which the rotary
drum filter [Figure 10.3] is most extensively used. A typical construction may
be regarded as two concentric, horizontal cylinders, the outer cylinder being
the septum with a suitable perforated metal support. The annular space between
the cylinders is divided by radial partitions producing a number of peripheral
compartments running the length of the drum. Each compartment is
connected by a line to a port in a rotary valve which permits the intermittent
application of vacuum or compressed air as dictated by the different parts of
FIGURE 10.3 Rotary vacuum filter.
160 Chapter 10
the filtration cycle. The drum is partially immersed in a bath to which the
slurry is fed. The complete cycle of filtration, washing, partial drying, and
discharge is completed with each revolution of the drum and usually takes
from 1 to 10 min. The relative lengths of each part of the cycle, indicated by
the segments superimposed on the figure, depend on the cake-forming characteristics
of the slurry and the importance of the associated operations of washing
and drying. They may be varied by immersion depth and rotation speed so
that each compartment remains submerged until an adequate cake is formed.
Washing and dewatering can be carried out to the standard required during
the remaining part of the cycle. The slurry must be effectively agitated during
operation or sedimentation will cause the preferential deposition of the finer
particles, giving a cake of low permeability. Agitation, of course, must not
erode the deposited cake. Maintaining a suspension of very coarse particles,
therefore, becomes difficult or impossible, and other methods of feeding must
Filtration may be followed by a brief period of draining in which air is
drawn through the cake, displacing retained filtrate. Washing is usually carried
out with sprays, although devices which flood the cake have been used. Dewatering,
again achieved by drawing air through the cake, is followed by discharge.
A scraper knife, assisted by compressed air which causes the septum
to belly against the cutting edge, is commonly used. Highly cohesive cakes,
such as those encountered in the removal of mycelial growth from antibiotic
cultures, may be removed by means of a string discharge. A series of closely
spaced, parallel strings run on the cloth around the drum. At the discharge
section the strings lift the cake away from the cloth and over a discharge roller
after which the strings are led back to the drum.
Other variants of rotary drum filtration include top-feed filtration and
precoat filtration. As mentioned, slurries containing coarse particles cannot be
effectively suspended by the method described. Such materials, which give
rapid cake formation and fast dewatering, may be filtered by applying the
slurry to the top of the drum by using a feed box and suitable dams. Sedimentation
in this case assists filtration.
Precoat filtration using a rotary drum is applied to slurries containing a
small amount of fine or gelatinous material which plugs and blinds the filter
cloth. Filtration is preceded by the deposition of a filter aid on the drum to a
depth of up to 4 ins. Blinding of the surface layers occurs during filtration,
but these layers are removed at the discharge section by a slowly advancing
knife so that a clean filtering surface is continually presented to the slurry.
The depth of cut depends on penetration of the precoat by the slurry solids
and is usually about 105 m. This method has allowed the filtration of slurries
which could not previously be filtered or which demanded the addition of
large quantities of a filter aid.
For filtration on a smaller scale the nutsche is used. A vacuum is drawn
on the sump of the tank, which gives a much faster filtration rate than in a
10.3.3 Pressure Filters
Due to the formation of low-permeability cakes, many slurries require higherpressure
differentials for effective filtration than can be applied by vacuum
techniques. Pressure filters are used for such operations. They may also be
used when the operation’s scale does not justify installing continuous rotary
filters. Usually, operational pressures of 6.89 104 to 6.89 105 N/m2 are
applied across stationary filter surfaces. This arrangement prohibits continuous
operation because it is difficult to discharge the cake while the filter is under
pressure. The higher labor costs of batch operation are, however, offset by
lower capital costs.
The most commonly used pressure filter is the plate-and-frame filter
press [Figure 10.4]. It consists of a series of alternating plates and frames
mounted in line on bars which provide support and facilitate assembly and
cake discharge. The filter cloth is mounted on the two faces of each plate, and
FIGURE 10.4 The filter press: plates and frame.
162 Chapter 10
the press is assembled by moving the plates and frames together with a hand
screw or hydraulic ram. This provides a series of compartments, the peripheries
of which are sealed by the machined edges of the plates and frames uniting
on the filter cloth, which acts as a gasket. Dripping often occurs at this point,
so the press is less suitable for noxious materials. The dimensions of each
compartment are determined by the plate area and the intervening frame thickness.
These dimensions and the number of compartments used depend primarily
on the volume of slurry to be handled and its solids content. The plate
faces are corrugated by grooves or ribs which effectively support the cloth,
preventing distortion under pressure and allowing free discharge of the filtrate
from behind the cloth. A section of the assembled filter press is given in Figure
Coincident holes, shown in the top left-hand corner of both plates and
frames, provide, on assembly, a channel for the slurry and, simultaneously,
entry into each compartment through an entry port in each frame. All compart-
FIGURE 10.5 Assembled filter press showing a frame and two plates. Movement
of liquid during (a) filtration and (b) washing.
ments therefore behave in the same way with the formation of two cakes on
the opposing plate faces. Discharge of filtrate after passage through cake,
cloth, and corrugations takes place through an outlet in the plate shown diametrically
opposite the frame entry port. Filtration may be continued until the
cake entirely fills the compartments or the accumulation of cake gives unsatisfactory
Washing may be carried out by simply replacing the slurry with wash
liquids and providing for its separate collection. This method, however, gives
inefficient washing due to erosion and channeling of the cake. Where efficient
washing is required, special washing plates alternate with the other plates described.
These plates contain an additional inlet which leads the wash liquid
in behind the filter cloth. During washing, the filtrate outlet on the washing
plate is closed so that the wash liquid flows through the cloth and first cake
in a direction opposite to that taken by the filtrate. The wash liquid then follows
the course of the filtrate through the cake and cloth of the opposite plate. A
diagram of liquid flow during washing is given in Figure 10.5(b).
The development of filter media in sheet form with high wet strength
and the ability to retain extremely fine particles extends the application of the
plate-and-frame filter to clarification. Such media occur in various grades and,
when used in apparatus similar to that described, may be used to clarify or
sterilize liquids containing a very low proportion of solids. In sterilization by
sheet filtration, the operation is carried out in two stages. The solution is first
clarified. The very clean filtrate is then passed through the sterilizing sheet
under a relatively low pressure. Before the operation, the assembled filter is
sterilized by steam. The washing apparatus, assembled with suitable sheets,
may also be used for air filtration.
Other filters widely used for clarification are the Metafilter and the
Streamline filter. The former consists of numerous closely spaced rings, usually
made of stainless steel, mounted on a rod. The rod is fluted to provide
channels for filtrate discharge. The passage of filtrate between the rings is
provided by scallops stamped on one side of each ring which maintain a ring
spacing of between 1 105 and 8 105 m. This construction provides a
robust support for the actual filtering medium. It is mounted in a suitable
pressure vessel, and large filters consist of several units. For clarification the
filter is first coated by circulating filter aid of the correct grade. The finest
materials are suitable for bacteria removal. The coat acts as a depth filter.
Filter aids may also be added to the liquid to be clarified.
The Streamline filter employs paper disks compressed to form a filter
pack. The filtrate passes through the minute interstices between the disks, leaving
any solids at the edge. This is the principle of edge filtration. Other filters,
164 Chapter 10
composed of metal plates or wires, operate on the same principle and are used
for coarse clarification.
Many small-scale filters consist simply of a fixed, rigid medium, robust
enough to withstand limited pressures, mounted in a suitable housing. Such
filters, which are also vacuum-operated, are used to clarify by depth filtration.
Media are composed of sintered metals, ceramics, plastics, or glass. Filters
prepared from closely graded and sintered ceramic powders are suitable for
sterilizing solutions by filtration on a manufacturing scale.
10.4 FILTER MEDIA
The choice of filter medium for a particular operation demands considerable
experience. In clarification, high filtration rates and the retention of fine particles
are opposing requirements. Permeability and retentive capacity can be
determined and used to guide small-scale experiments with the materials to
be filtered, facilities for which are often made available by filter manufacturers.
Other relevant factors are filtrate contamination by the medium and associated
housing, adsorption of materials from solutions, and, where necessary, the
medium’s ability to withstand repeated sterilization.
In cake filtration the medium must oppose excessive penetration and
promote the formation of a junction with the cake of high permeability. The
medium should also give free discharge of cake after washing and dewatering.
10.4.1 Rigid Media
Rigid media may be loose or fixed. The former is exemplified by the deposition
of a filter aid on a suitable support. Filtration characteristics are governed
mainly by particle size, size distribution, and shape as described earlier. These
factors may be varied for different filtering requirements.
Fixed media vary from perforated metals used for coarse straining to
removal of very fine particles with a sintered aggregate of metal, ceramic,
plastic, or glass powder. The size, size distribution, and shape of the powder
particles together with the sintering conditions control the size and distribution
of the pores in the final product. The permeability may be expressed in terms
of the constant in equation 10.1. Alternatively, the medium may be characterized
by air permeability. The maximum pore size, which is important when
selecting filters for sterilization, may be determined by measuring the pressure
difference required to blow a bubble of air through the medium while it supports
a column of liquid with a known surface tension.
10.4.2 Flexible Media
Flexible media may be woven or unwoven. Filter media woven from cotton,
wool, synthetic and regenerated fibers, glass, and metal fibers are used as septa
in cake filtration. Cotton is most widely used, and nylon is predominant among
synthetic fibers. Terylene is a useful medium for acid filtration. Penetration
and cake discharge are influenced by the way in which fibers are twisted and
plied and by the adoption of various weaves such as duck and twill. The choice
of a cloth often depends on the chemical nature of the slurry.
Nonwoven media occur in the form of felts and compressed cellulose
pulps and are used for clarification by depth filtration. A disadvantage, unless
the medium is carefully prepared, is the loss of fibrous material from the filter’s
downstream side. The application of sheet media has already been discussed.
High wet strength is conferred on paper sheets by resin impregnation. An
alternative manufacture employs asbestos fibers supported in a cellulose
10.5 AIR FILTRATION
Removing particulate matter from air along with controlling humidity, temperature,
and distribution is the purpose of air conditioning. Solid and liquid particles
are most commonly arrested by filtration, although other methods, such
as electrostatic precipitation, cyclones, and scrubbers, are used in some circumstances.
The objective may be simply to provide comfortable and healthy
conditions for work, or it may be dictated by the operations proceeding in the
area. Some industrial processes demand large volumes of clean air.
This section is concerned mainly with air filtration, the objective of
which is the reduction or complete removal of bacteria. This is applied, with
varying stringency, to several operations associated with pharmacy. Where
sterilization is the objective and the presence of inanimate particles is of secondary
importance, other methods, such as ultraviolet radiation and heating,
must be added.
Bacteria rarely exist singly in the atmosphere but are usually associated
with much larger particles. For example, it has been shown that 78% of particles
carrying C. welchii were greater than 4.2 106 m. The average diameter
exceeded 10 106 m. On this basis it has been suggested that air filters
which are 99.9% efficient at 5 106 m are adequate for filtering air supplied
to operating theaters and dressing wards. On the other hand, filters used to
clean air supplied to large-scale aerobic fermentation cultures must offer a
166 Chapter 10
very low probability that any organism will penetrate during the process. This
became important in the deep culture production of penicillin when the ingress
of a single penicillinase-producing organism could be disastrous. Similarly,
stringent conditions are laid down for the air supply to areas where sterile
products are prepared and handled.
10.5.1 Mechanism of Air Filtration
A theoretical foundation for air filtration by passage through fibrous media
was laid in the early 1930s by studies of the flow of suspended particles around
various obstacles. In studies of the filtration of smokes (Hinds, 1982) it has
been shown that the following five factors operate simultaneously in arresting
a particle during its passage through a filter, although their relative importance
varies with the type of filter and the conditions under which it is operated.
1. Diffusion effects due to Brownian movement
2. Electrostatic attraction between particles and fibers
3. Direct interception of a particle by a fiber
4. Interception as a result of inertial effects acting on a particle and
causing it to collide with a fiber
5. Settling and gravitational effects
Air filters operate under conditions of streamline flow, as indicated by
the streamlines drawn around a cylindrical fiber in cross section in Figure
10.6. It was assumed that particle capture takes place if any contact is made
during the particle movement around the fiber. Once capture occurs, the particle
is not reentrained in the airstream but is deposited deeper in the bed. Never-
FIGURE 10.6 Inertial capture of a particle by a fiber.
theless, some fiber filters are treated with viscous oils, presumably to make
capture more positive and to reduce reentrainment.
If a particle remains in a streamline while passing around the fiber, capture
occurs only if the particle radius exceeds the distance between streamline
and fiber, a dimension dependent on the particle and fiber diameters. This
mechanism, termed capture by direct interception, is independent of the air
velocity except insofar as the streamlines are modified by changes in air velocity.
Deviation of particles from streamlines can occur in various ways
(Hinds, 1982). The chance of capture increases if Brownian movement causes
appreciable migration across streamlines, an effect important only for small
particles (less than 5 107 m) and low air speeds, when the time spent in
the vicinity of a fiber is relatively large. These conditions also apply to capture
which is the result of electrostatic attraction.
The inertial mechanism depends on particle mass, fiber diameter, and
approach velocity. The particle deviates from the streamline and follows the
broken line in Figure 10.6. Capture occurs if the deviation, which increases
as the mass and velocity of the particle increase, brings the particle into contact
with the fiber.
The simultaneous operation of mechanisms, at least one of which demands
low air speeds and fine particles for effectiveness and another which
requires large particles traveling at high speeds, suggests that maximum penetration
could occur at an intermediate air speed. Conversely, there is, for any
given conditions, an optimal particle size for which the combined filtration
effects are a minimum and penetration is a maximum. A diagram of the mechanism
interaction is reproduced in Figure 10.7. Similar effects were demon-
FIGURE 10.7 Interaction of the mechanisms of particle arrest.
168 Chapter 10
FIGURE 10.8 Effect of airstream velocity on bacterial spores removal by a filter.
strated for bacterial aerosols by Humphrey and Gaden, who estimated the
efficiency with which a glass fiber mat collected B. subtilis spores atomized
as particles just over a micron in radius. The results are presented in Figure
10.8. A theoretical approach to the removal of industrial dusts has been developed
by Stairmand and Fuchs.
10.5.2 The Design, Operation, and Testing
of Air Filters
Granular beds, fibrous media, and absolute filters prepared from cellulose and
asbestos are used for high-efficiency air filtration. With fibrous and granular
filters, the fractional reduction in particle content is assumed to be the same
through successive incremental thicknesses of the filter. We may therefore
rewrite equation 10.2 as
where C represents the number of particles entering a section of thickness dx.
The constant k is a measure of the filter’s ability to retain a particle and is a
complex function of fiber diameter, interfiber distance, and the operational air
velocity. Integration between inlet and outlet conditions gives
If a certain filter thickness is capable of retaining 90% of the entering particles,
then, if 106 particles enter, 105 will penetrate. If six thicknesses are used, then
the preceding relation predicts that only one particle penetrates. The logpenetration
effect has been confirmed for fibrous filters and for granular
beds. It must be stressed, however, that fibrous and granular filters present
passages very much greater than the fine particles they remove. Absolute sterility
or absolute filtration at a certain particle size cannot be achieved. However,
design variables, such as fiber diameter, fiber packing density, filter
thickness, and air speed. For example, these variables may be varied to give
air which, for a given input contamination, is, with a high statistical probability,
In an early study, Terjesen and Cherryl used a bacterial aerosol and a
Bourdillon slit sampler to test the suitability of filters for air sterilization. They
showed that 0.075-m slabs of slag wool composed of fibers, most of which
were less than 6 106 m and compressed to a suitable density, gave sterile
air when operated for 15 days at a face velocity of 0.152 m s1. A similar
efficiency was found for filters composed of glass fibers of similar diameters.
Resin-bonded filter mats composed of glass fibers 12 106–13 106 m
in diameter have also been described. An assembly of these mats to give a
filter 0.304 m deep effectively removes bacteria.
Bacteria may be effectively removed by passing air through deep granular
beds of activated carbon, alumina, and other materials. Table 10.1 gives
data on the efficiency of alumina in a bed 0.381 m deep for removing Serratia
marcescens from air. The effect of two design variables, granule size and air
speed, is illustrated.
TABLE 10.1 Removal of Seratia marcescens
with a 0.3-m Bed of Alumina Granules
(m/min) Efficiency (percent removal)
8–16 mesh 16–32 mesh
24.4 — 92
73.2 88 99.4
146.3 98.7 99.9
219.5 99.86 —
170 Chapter 10
The extremely hazardous nature of radioactive dusts has promoted
the design of high-efficiency air filters for use where such materials are handled.
These filters may be used for any application requiring extremely pure
air. A medium in paper form was constructed from cellulose and asbestos.
This could be pleated round corrugated spacers to give a large filtering area
in a relatively small space. A paper composed of very fine glass fibers was
later developed which resisted temperatures up to 773 K and could, therefore,
The general object of all filter design is the virtual certainty of removing
the particles under consideration with a medium offering minimal resistance
to airflow. Unlike liquid clarifiers, air filters become more efficient with time
because accumulation of particles restricts passage through the medium. This
deposition causes an increase in the pressure differential required to maintain
a given flow rate. When the filter has become laden with a certain amount of
dust, it must be cleaned or replaced. The life of high-efficiency air filters may
be lengthened by first passing the air through a coarse, or ‘‘roughing,’’ filter
which removes the largest particles.
The use of bacterial aerosols as tracer organisms to test filter efficiency
has already been described. Other tests with inanimate dusts are more generally
used to evaluate filter performance. For general ventilation purposes two
tests are specified. The first determines gravimetrically the capacity of the
filter to hold dust and still function satisfactorily. A standard dust of 5 106
or 26 105 m is passed into the filter until a specified increase in airflow
resistance occurs. The second test, which is also applicable to high-efficiency
filters, determines the fraction of a methylene blue aerosol which passes
through the filter under given conditions. The aerosol is generated by atomizing
a 1% aqueous solution of methylene blue. The droplets dry to give a cloud
of particles, 90% of which are below 2 107 m. The test is therefore extremely
stringent. The cloud is passed through the filter at a constant rate (103
m3 min 1) and then through a strip of porous paper that collects any methylene
blue particles which have penetrated. The stain due to the dye, after intensifi-
cation in steam, is compared to a series of similar stains which correspond to
known volumes of unfiltered air. Thus, if 60 103 m3 of filtered air give a
stain which matches that produced by 1.2 105 m3 of unfiltered air, the
penetration is 0.02%. An alternative method of evaluating penetration employs
a cloud produced by the atomization of a solution of sodium chloride. After
passage through the filter, part of the air is passed through a hydrogen flame.
The intensity of the sodium flame produced is estimated with a photoelectric
10.6 THE CENTRIFUGE
An object moving in a circular path is subjected to an outward centrifugal
force which balances the centripetal force moving the object toward the center
of rotation. This principle is used in the mechanical separations called centrifugal
filtration and centrifugal sedimentation. In the former, a material is placed
in a rotating perforated basket lined with a filter cloth. This material is used
to separate a solid, which is retained at the cloth, from a liquid. It is essentially
a filtration process in which the driving force is of centrifugal origin. It in no
way depends on a difference in the density of the two phases.
In centrifugal sedimentation the separation is due to the difference in
the density of two or more phases. In this more important process, solid-liquid
mixtures and liquid-liquid mixtures can be completely separated. If, however,
the separation is incomplete, there will be a gradient in the size of the dispersed
phase within the centrifuge due to the faster radial velocity of the larger particles.
Operated in this way the centrifuge becomes a classifier.
10.6.1 Centrifugal Filtration
The filtration principles discussed previously can be directly applied to centrifugal
filtration, although theoretical predictions of filtration rate and spinning
time are uncertain. The process is widely used for separating crystals and
granular products from other liquors, but it is less effective if the slurry contains
a high proportion of particles less than 1 104 m. The advantages of
the process are effective washing and drying. Residual moisture after centrifugation
is far less than in cakes produced by pressure or vacuum filtration. By
this method the moisture content of a cake of coarse crystals can be reduced
to as low as 3%. This facilitates the drying operation which normally follows.
Enclosure of the centrifuge is easy so that toxic and volatile materials can be
A typical batch filter [Figure 10.9(a)] consists of a perforated metal basket
mounted on a vertical axis. The cloth used to retain solids is often supported
on a metal screen Baskets mounted as shown are emptied by shoveling
the cake. If, however, top suspension is used, the cake can be more easily
withdrawn through traps in the base of the basket. In batch operation considerable
time is lost during machine acceleration and deceleration. Machines operating
with continuous discharge of solids are used for separating coarse solids
during large-scale operations. Such machines are commonly constructed
with a horizontal axis of rotation.
172 Chapter 10
FIGURE 10.9 (a) Batch centrifugal filter, (b) supercentrifuge, and (c) solid bowl
10.6.2 Centrifugal Sedimentation
Particle motion in a liquid is described by Stokes’ equation. If its diameter is
d, the rate, u, at which it settles by gravity in a liquid of viscosity ? and density
? is given by equation 1.24:
where g in acceleration due to gravity and ?p is the particle density. In the
centrifuge the gravitational force causing separation is replaced by a centrifugal
force. If the particle has a mass m and moves at an angular velocity ? in
a circle of radius r, the centrifugal force is ?2r(m ml), where ml is the mass
of the displaced liquid. Therefore, ?2r/g is the ratio of the centrifugal and
gravitational forces in the given example. Its value can exceed 10,000. The
separation is, therefore, quicker, more complete, and more effective in systems
containing very fine particles that will not sediment by gravity because of
Expressing the particle mass in terms of its volume and effective density,
we can write the centrifugal force as
d2(?g ?)?2r (10.4)
In streamline conditions the opposing viscous force, given by equation 1.22,
is 3?d?u, u being the terminal velocity of the particle. Equating these expressions
? ?2r (10.5)
The sedimentation rate is proportional to the radius of the basket and
the square of the speed at which it rotates. Centrifugal sedimentors can be
divided into various types.
For operation at very high speeds, the centrifuge bowl is tubular with
a length-diameter ratio from 4 to 8. An example is the Sharples supercentrifuge
[Figure 10.9(b)] which operates at up to 15,000 rpm or, in turbine-driven laboratory
models, up to 50,000 rpm. The machine, which gives continuous discharge
of two separated liquids, is widely used in emulsion separation. It is
also an effective clarifier when the concentration of solids is very low. These
are periodically discharged by scraping the walls of the centrifuge tube. Uses
include cleaning fats and waxes, blood fractionation, and virus recovery.
Disk-type centrifuges introduce baffles into the bowl in order to decrease
the distance which particles travel before settling at the wall. They split the
liquid into layers in which separation occurs. The length-to-diameter ratio is
usually much smaller than in tubular bowl centrifuges and operational speeds
are lower. In batch processes the machine is discharged manually at intervals.
Larger machines continuously or intermittently discharge the solids as a thick
slurry through nozzles or valves at the basket periphery.
A solid bowl batch basket is shown in Figure 10.9(c). In this type of
machine liquids are discharged by weirs or skimmers. Two skimmers are
shown, each taking off a liquid phase. Solids are discharged manually at the
end of the process. In continuous models a conveying scroll, operating at a
slightly different speed from the basket, plows the solids to one end and discharges
the material as a damp powder.
Size Reduction and Classification
11.1 THE IMPORTANCE OF FINE PARTICLES
Although fine particles can be produced directly by controlled precipitation,
by crystallization, or by drying a fine spray of solution, in many cases the
material is powdered in some kind of mill. From our point of view, the most
important result of this operation is the increase in surface area of a given
weight of the powder and its influence on diffusional processes. A cube of
side 0.01 m has a surface area of 6 104 m2. If, by some ideal size reduction
process, this cube was divided into cubes of side 0.001 m, we would have a
thousand particles each with a surface area of 6 106 m2, and a total surface
area of 6 103 m2. A 10-fold increase in surface area has been given by a
10-fold decrease in particle size. Generalizing, we may say that the surface
area is inversely proportional to the particle size, assuming that the particle
shape remains the same.
The rate of most chemical and physical reactions involving solids and
liquids is greatly influenced by the area of interfacial contact. In chemical
reactions a reagent must diffuse toward the surface of the solid, the reaction
products must diffuse away, a procedure which depends, among other things,
Size Reduction and Classification 175
on the area between solid and liquid. The effect of particle size on dissolution
rate exemplifies another aspect of diffusion which is important to the
pharmacist. Most commonly, drugs are taken orally in the form of solid
particles, and absorption, which is usually rapid, must be preceded by dissolution.
A full discussion of the role of particle size in oral, parenteral, and
topical therapy may be found in Newman and Axon (1961) and Wagner
The rate at which fine chemicals or drugs are extracted from a vegetable
source is increased by an increase in surface area. Reducing particle size increases
the area available for materials transfer and decreases the distance over
which solvent and solute must diffuse; it also has a marked effect on drying
Other effects, not based on diffusion and its dependence on surface area,
are found in mixing and various formulation requirements. If we withdraw a
sample from a mixture of powders, it is unlikely to contain exactly the correct
proportion of ingredients. However, the larger the number of particles in the
sample, the closer the sample will represent the overall proportions of the
mixture. We can therefore increase the sample accuracy which might eventually
form a tablet or a capsule, by increasing the number of particles it contains—
that is, reduce the particle size of the mix components. Since difference
of particle size promotes segregation, the components should be produced with
a similar particle size distribution.
Formulation requirements often dictate the use of fine particles. Impalpability
and spreading are required of dusting and cosmetic powders. Particles
of 3.5 105–4.0 105 m can be detected as single particles when applied
to the skin and may give the impression of grittiness. Such powders should,
in general, be finer than 3.0 105 m. When powders are tinted, the particle
size of powder and pigment affect the final color. In tableting, careful size
reduction of imperfect tablets provides a material suitable for compression.
The flow properties of suspensions of high disperse phase concentration is
affected by particle size and size distribution. At a given disperse phase concentration,
decreasing particle size leads to increasing viscosity, whereas
broadening the particle size distribution leads to decreasing viscosity. Sedimentation
is a function of particle size.
Numerous examples have been quoted to stress the importance of fine
particles in pharmacy. Milling or grinding offers a method by which these
particles may be produced, size classification gives a means, where applicable,
of selecting a desired fraction or of removing oversize or undersize particles,
and size analysis provides the analytical tool by which these operations may
be assessed and controlled.
176 Chapter 11
11.2 FUNDAMENTAL ASPECTS OF
CRUSHING AND GRINDING
A basic study of crushing and grinding considers the physical properties of
the material, the crushing mechanism itself, and its relation to the mechanism
of failure. When a stress, which may be compressive, tensile, or shear, is
applied to a solid, the latter deforms. Initially, the deformation or strain is the
distortion of the crystal lattice by relative displacement of its components without
change of structure. Complete recovery follows stress removal, and behavior
is elastic. Figure 11.1 considers the deformation of a solid under a tensile
stress, and elastic behavior is shown over section AB. Below the elastic limit
(B) stress is proportional to strain and is related to it by various moduli. Beyond
the yield point (C) permanent or plastic deformation occurs, and, as
shown by release of stress at point D, all strain is not recoverable. Sliding
along natural cleavage planes is occurring in this region. Plastic deformation
is terminated by failure or fracture, which is normally a quite gradual and
reproducible process preceded by material thinning. The stress at point E is
a measure of the material’s strength. The area under the curve at any point
represents the strain energy per unit volume absorbed by the specimen up to
that strain. The limiting strain energy per unit volume is the energy absorbed
up to the point of failure.
An extensive period of plastic deformation is shown in Figure 11.1, and
the material would be classified as ductile. For the brittle materials normally
encountered in grinding, little plastic deformation takes place and the points
C and E almost coincide. Fracture is here explained in terms of cracks and
FIGURE 11.1 Tensile deformation of a ductile material.
Size Reduction and Classification 177
flaws naturally present in the material. It occurs suddenly and with shattering.
The energy employed in stressing the particle to the point of failure reappears
mainly as heat on release of strain in a manner analogous to the sudden release
of a stressed spring.
The theoretical strength of crystalline materials can be calculated from
interatomic attractive and repulsive forces. The strength of real materials, however,
is found to be many times smaller than the theoretical value. The discrepancy
is explained in terms of flaws of various kinds, such as minute fissures
or irregularities of lattice structure known as dislocations. They have the capacity
to concentrate the stress in the vicinity of the flaw. Failure may then
occur at a much lower overall stress than is predicted from the theoretical
considerations. Failure occurs with the development of a crack tip which propagates
rapidly through the material while penetrating other flaws which may,
in turn, produce secondary cracks. The strength of the material therefore depends
on the random distribution of flaws and is a statistical quantity varying
within fairly wide limits. This concept explains why a material becomes progressively
more difficult to grind. Since the probability of containing an effective
flaw decreases as particle size decreases, the strength increases until, with
the achievement of faultless domains, the material strength equals the theoretical
strength. This position is not realized in practice due to complicating factors
such as aggregation.
The strength of most materials is greater in compression than in tension.
It is therefore unfortunate that technical difficulties prevent the direct use of
tensile stresses. The compressive stresses commonly used in comminution
equipment do not cause failure directly but generate, by distortion, sufficient
tensile or shear stress to form a crack tip in a region away from the point of
primary stress application. This mechanism is inefficient but unavoidable. Impact
and attrition are the other basic modes of stress application. The distinction
between impact and compression is referred to later. Attrition, which is
commonly employed, is difficult to classify but is probably primarily a shear
In any machine one mode of stress application usually predominates. It
must be correctly chosen with respect to the mechanical properties of the material.
Compression, for example, is useless for comminution of fibrous or waxy
solids. Attrition is generally necessary for all fine grinding.
The deformation and subsequent failure of a brittle material are not only
a function of stress but also of the rate at which the stress is applied. Different
results may be obtained from slow compressive breaking and impact breaking
at the same energy. Particle shape, size, and size distribution may be affected.
In impact breaking the rate of stress application is so high that the limiting
178 Chapter 11
strain energy may be exceeded several times by the suddenness of the operation.
The reason is that fracture is time dependent, with a lag occurring between
the application of maximum stress and failure.
Stress application is further complicated by ‘‘free-crushing’’ and
‘‘packed-crushing’’ mechanisms. In free crushing, the stress is applied to an
unconstrained particle and released when failure occurs. In packed crushing,
the application of stress continues on the crushed bed of particles. Although
further size reduction occurs, the process is less efficient due to vitiation
of energy by the effects of interparticulate friction and stress transmission
via particles which do not themselves fracture. This is easily demonstrated
when a crystalline material is ground in a pestle and mortar. The fine powder
initially produced protects coarser particles. If the material is sieved and
oversize particles returned, the operation may be completed with far less
Free crushing is most nearly approached in the roller mill, which explains
the high efficiency of the machine, and, to a lesser extent, in other
continuous processes in which individual particles are presented to the grinding
media. Packed crushing occurs in ball mills.
11.3 GRINDING EFFICIENCY
Extensive investigation of the relation between the energy supplied to a mill
and the size reduction achieved has been carried out. The efficiency of the
process reflected by such a relation is of small importance in pharmacy because
the applications are limited. For completeness, however, they will be
Most of the energy supplied to the mill is ultimately dissipated as heat
due to mechanical inefficiency. Most of the remainder or net grinding energy
also appears as heat produced on the release of strain energy, a small part being
added to the internal energy of the system as, for example, surface energy.
Various hypotheses relate the net grinding energy applied to a process
and the size reduction achieved. The first, proposed by Karl von Rittinger in
1867, states that the energy necessary for size reduction is directly proportional
to the increase in surface area:
E k(Sp Sf) (11.1)
where E is the energy consumed, and Sp and Sf are the surface area of product
and feed materials, respectively. The constant k depends on the grinding unit
employed and represents the energy consumed in enlarging the surface area
Size Reduction and Classification 179
by one unit. The relation between surface area and particle size has already
been derived, and we may therefore write
where df and dp are the particle sizes of feed and product particles, respectively.
The hypothesis indicates that energy consumption per unit area of new
surface produced increases faster than the linear ratio of feed and product
dimensions, a phenomenon already noted and explained. The proportionality
of net energy input and new surface produced has been confirmed in some
Although Rittinger’s law is concerned with surfaces and not with the
energy associated with those surfaces, it is rational to relate crushing energy
consumed and the surface energy gained by increase of surface area, thereby
arriving at a measure of efficiency. In experiments in which single particles
are crushed, between 1% and 30% of the applied energy appears as surface
energy. In practical systems, when application of stress is less ideal, the net
grinding energy is 100 to 1000 times greater than that associated with the new
surface; i.e., the efficiency of the process, on this basis, is between 0.1% and
The relation of energy to surface area provides little information on the
grinding process and does not influence mill design. It provides, however, the
basis of some grindability tests in which a known amount of energy is supplied
to a mill and the increase in surface is measured. This application is restricted
to fine grinding.
Conversion of grinding energy to surface energy is neglected in Kick’s
law, enunciated in 1885. The law is based on the deformation and brittle failure
of elastic bodies and states that the energy required to produce analogous
changes of configuration of geometrically similar bodies is proportional to the
weight or volume of those bodies. The energy requirements are independent
of the initial particle size; they depend only on the size reduction ratio. Kick’s
law predicts lower energies than Rittinger’s relation. The theory, however,
demands that the resistance to crushing not change with particle size. The role
of flaws present in real materials is not considered, with the result that the
energy required for fine grinding, when the apparent strength may have greatly
risen, is underestimated.
A third theory of comminution, put forth by Bond, gives results intermediate
between the predictions of the laws of Kick and Rittinger. The theory
180 Chapter 11
rests upon three principles, the first of which states that any divided material
must have a positive energy register. This can only be zero when the particle
size becomes infinite. The input energy, E, for any size reduction process then
equals the product energy register minus the feed energy register. The energy
associated with a powder increases as the particle size decreases, and we may
assume that the energy register is inversely proportional to the particle size
to an exponent, n. Hence,
E Ep Ef
The second principle of Bond’s theory assigns to n a value of i, stating
that ‘‘the total work useful in breaking which has been applied to a stated
weight of an homogeneous material is inversely proportional to the square
root of the diameter of the product particles.’’
The third principle states that material breakage is determined by the
flaw structure. This aspect of size reduction has already been discussed.
An empirical, but realistic, approach to mill efficiency is gained through
experiments in which the energy consumed and size reduction achieved are
compared with values obtained in a laboratory test operating under free-crushing
conditions. All energy supplied in the latter is available for crushing, and
the test is assumed to be 100% efficient. Both slow-crushing and impact tests
are used. Many single particles may be simultaneously crushed, and the work
done may be measured. The latter is then related to the size reduction achieved.
Similar measurements can be made during practical milling, expressing the
efficiency of the process as a percentage of the free-crushing value. On this
basis, approximate efficiency of the roll crusher is 80%, the swing hammer
mill is 40%, the ball mill is 10%, and the fluid energy mill is only 1%.
11.4 OPERATION OF MILLS
In some operations, such as those in which ores are processed, size reduction
may constitute a major proportion of total process costs. The efficiency with
which energy is utilized is, therefore, of great importance. Drugs, on the other
hand, fall into a class of materials which is expensive and processed in relatively
small quantities. The contribution of grinding to total costs is, therefore,
smaller, and the choice of machine can usually be made on technological rather
than economic grounds. Generally, drugs are easy to grind. The operation is
classified as fine, grinding if the bulk of the product passes a 200 mesh screen
Size Reduction and Classification 181
(7.6 105 m), or as superfine grinding, if a powder of a few microns or less
is required. Most pharmaceutical grinding falls into these classes, although
coarser grinding is applied to vegetable drugs before extraction.
Heywood stated that any type of crushing or grinding machine exhibits
optimal comminution conditions for which the ratio of the energy to new surface
is minimal (Heywood, 1957). If finer grinding is attempted in such a
machine, the ratio is increased. Mills may thus become grossly inefficient if
called upon to grind at a size for which they were not designed. A limited size
reduction ratio is imposed on a single operation, larger ratios being obtained by
the adoption of several stages, each employing a suitable mill. The fluid energy
mill, which presents a size reduction ratio of up to 400, is exceptional.
A low retention time is inherent in free-crushing machines. Little overgrinding
takes place, and the production of excessive undersize material or
‘‘fines’’ is avoided. Protracted milling times are found with many slow-speed
mills, with the result that considerable overgrinding takes place. Accumulation
of product particles within the mill reduces the effectiveness of breaking
stresses, and the efficiency of milling progressively decreases. This is typical
of ‘‘open-circuit’’ grinding, in which the material is passed only once through
the mill and remains until virtually all has reached the required product size.
An overall increase in efficiency is secured in ‘‘closed-circuit’’ grinding. Product
particles are removed from the mill by means of a current of air or liquid
by screens. The removed product may then be classified and any oversize
material returned to the mill. Adoption of closed-circuit grinding techniques
is only possible on a relatively large scale. On a smaller scale the effect can
be simulated by periodic classification of the entire mill contents and the removal
of material which has reached the required size.
11.4.1 Dry and Wet Grinding
Between the approximate limits of 5% and 50% moisture, materials cake and
do not flow. Both factors oppose effective grinding. Dry grinding is carried
out at low moisture contents, the upper limit depending on the nature of the
material. Although 5% or more moisture may be permissible for vegetable
drugs, it would prove excessive during the milling of a coarse, impervious
Wet grinding is a common procedure when a fluid suspension is required,
and drying, which would prove a significant drawback, is unnecessary.
An excellent dispersion can be produced simultaneously, and, in some operations,
this provides the primary objective, size reduction being of secondary
182 Chapter 11
importance. Wet grinding may also be adopted when the size reduction
achieved during dry grinding is prematurely limited by aggregation.
Certain general advantages are secured during wet grinding:
Increased mill capacity
Lower energy consumption
Elimination of hazards from dust
Easier materials handling
The principal disadvantage, apart from the possible inclusion of a drying stage,
is the increased wear of the grinding medium.
Wear of grinding elements, which occurs in all mills, contaminates the product.
Contamination influences the choice of constructional materials, with ceramics
and stainless steel most commonly used. Contamination is normally
slight. However, in the protracted periods often associated with the production
of very fine powders, it may become severe. This is illustrated in Figure 11.2,
which shows a progressive increase in a sulfated ash value of the material due
to wear of the ceramic mill.
FIGURE 11.2 Contamination of griseofulvin during milling.
Size Reduction and Classification 183
Closed mills, which prevent the ingress of bacteria, must be used for
grinding sterile materials.
11.4.3 Temperature Sensitivity
Care must be exercised during milling of temperature-sensitive materials, especially
when a very fine product is required. Caking results if the softening
point is exceeded. Materials may be chilled before grinding, or facilities for
cooling the mill during grinding may be provided. Waxy solids can be successfully
ground with dry ice, the low temperatures conferring brittle characteristics
on the material. Chemical degradation may occur at high grinding temperatures.
Oxidative changes can be prevented by grinding in an inert atmosphere
such as nitrogen.
11.4.4 Structural Changes
Several examples of change of physical structure during very fine grinding
have been reported. Gammage and Glasson (1963) found changes in the crystal
form of calcium carbonate after ball milling. Distortion of the kaolinite
lattice during very fine grinding was reported by Gregg (1955). Changes such
as these could affect solubility and other physical characteristics which, in
turn, might influence formulation and therapeutic value.
11.4.5 Dust Hazards
Hazards from dust may become acute during dry grinding. Extremely potent
materials require machines to be dustproof and dustproof clothing and masks
to be given to operators. Danger may also arise from the explosive nature of
11.5 GRINDING EQUIPMENT
The following equipment is in regular use for dry-grinding pharmaceutical
materials: edge and end runner mills, hammer mill, pin mills, ball mills.
The fluid energy mill is becoming widely used for producing superfine
powders. The ball mill and the colloid mill are used for wet grinding and the
production of liquid dispersions. The end runner mill and adaptations of the
184 Chapter 11
roll mill may be used to comminute and disperse powders in semisolid bases
as, for example, in the production of ointments. These mills, and the vibratory
mill, are described in this section.
11.5.1 Edge and End Runner Mills
The edge runner mill consists of one or two heavy granite or cast iron wheels
or mullers mounted on a horizontal shaft and standing in a heavy pan. Either
the muller or the pan is driven. The material is fed into the center of the pan
and is worked outward by the muller action. While in the zone traversed by
the muller, comminution will occur by compression, due to the weight of the
muller, and by shear. The origin of the shear forces is indicated in Figure
11.3(a). The linear velocity of the pan surface will vary over the line of contact
between muller and pan. For efficient grinding this dimension is large compared
with the diameter of the pan. Muller and pan speeds may only coincide
on one hypothetical circle, at other positions a varying amount of slip must
occur. A scarper continually moves material from the perimeter of the pan to
the grinding zone.
The end runner mill is similar in principle and consists of a rotating pan
or mortar made of cast iron or porcelain. A heavy pestle is mounted vertically
within the pan in an off-center position [Figure 11.3(b)]. The mechanism of
size reduction is compression due to the weight of the pestle, and shear. The
latter is developed by the relative movement of muller and pan which varies
over the muller face. The muller is friction-driven by the pan through the
ground material. A scraper is used to redirect the material into the grinding
Both mills operate at slow speeds on a packed bed. Both produce moderately
fine powders and operate successfully with fibrous materials. Wet grinding
with very viscous materials, such as ointments and pastes, is also possible.
11.5.2 The Hammer Mill
The hammer mill typifies a group of machines operating at very high speeds
and acting primarily by impact on a freely suspended particle. The term disintegrator
is also used. High efficiency, which would be expected from the operation
of a free-crushing mechanism, is reduced because the blows delivered
are in excess of the minimum required for breakage.
A typical machine [Figure 11.4(a)] consists of a disk rotating at speeds
up to 8000 rpm. The higher speeds are used for fine grinding in relatively
Size Reduction and Classification 185
FIGURE 11.3 (a) Edge runner mill; (b) end runner mill.
small machines. A balanced number of hammers is fitted to the disk. The
hammers may be fixed or pivoted, presenting flat, knife, or file edges to the
material. The material is fed to the top or the center of the mill and is broken
by direct impact until fine enough to pass through the screen which forms the
lower part of the mill casing. A range of screens is normally provided. Due
to tangential exit, the product size is considerably smaller than the screen
apertures. The disk and hammers act as a centrifugal fan, drawing large volumes
of air through the mill. Entrained dust must be separated with a bag
filter or a cyclone separator.
186 Chapter 11
FIGURE 11.4 (a) Impact mill with pivoted hammers, (b) comminution mill, and (c)
The mill processes dry, crystalline materials, which do not soften under
milling conditions, and many crude drugs. Rotation speed and size and shape
of the screen apertures are interrelated factors controlling the product size.
A considerable amount of very fine powder is produced. A marked rise in
temperature can occur during passage through the mill with consequent risk
of fusion or decomposition of susceptible drugs.
Great versatility, derived from simple variation of screen, rotor speed,
and blade type, is characteristic of the refined mills commonly used in the
pharmaceutical industry. The Fitzmill (The Fitzpatrick Company of American
and Manesty Machines Ltd.) and the Apex Comminuting Mill (Apex Construction
Co., London) are mobile machines constructed largely of stainless
steel [Figure 11.4(b)]. Both offer a large screen area and operate at various
speeds. A reversible rotor permits the use of blades presenting either a flat
impact face or a cutting edge to the material. Materials are ground by highspeed
operation of the impact face. The knife edges may be used at lower
speeds for wet granulation and for precision reduction of the imperfect tablets
produced during dry granulation. The mill may be jacketed to control milling
temperatures. Mixing, wet grinding, and ointment milling may also be performed.
Size Reduction and Classification 187
11.5.3 The Pin Mill
Pin mills consist of two horizontal steel plates with vertical projections arranged
in concentric circles on opposing faces and becoming more closely
spaced toward the periphery. The projections of the two faces intermesh. The
material is fed through the center of the stationary upper disk onto the lower
revolving disk and is propelled by centrifugal action toward the periphery.
The passage between the pins provides size reduction by impact and attrition.
The material is collected in the annular space surrounding the disks and passes
to a separator. The large volumes of air drawn through the mill are discharged
through the separator. Absence of screens and gratings provides clog-free action.
The machine is suitable for grinding soft, nonabrasive powders, and low
milling temperatures permit heat-sensitive materials to be processed. The
fineness of the grind may be varied by the use of disks with different dispositions
11.5.4 The Ball Mill
The ball mill is widely used for fine grinding. Extremely fine powders may
be produced, although milling times are often protracted. Despite simple construction,
the mill is extremely versatile. It can be used for wet or dry grinding
in continuous or batch processes. The latter are usually imposed by the scale
of pharmaceutical operations. Since the mill is closed, sterility can be maintained
or an operation can be conducted in an inert atmosphere, if the process
demands such conditions. Materials of widely differing mechanical properties
can be ground by the combined effects of impact and attrition characteristic
of the mill.
In its simplest form the ball mill [Figure 11.4(c)] consists of a rotating,
hollow cylinder containing balls usually made of stainless steel or stoneware.
During grinding, the balls slowly wear and are eventually replaced. For general
purposes the mill contains balls of different sizes which perform different
functions. Mill loading varies. Typically, it is half-filled with balls, and the
material to be ground is added to overfill the interstices between the balls.
The apparent volume of the total charge is commonly 60% of the mill volume.
In operation the distance the charge moves up the mill casing depends on the
centrifugal force, a function of the speed at which the mill rotates and the
friction between charge and mill lining. These effects determine the pattern
of movement within the mill. At low grinding speeds the balls tumble, roll,
and jump down the free face of the charge, a pattern described as cascading.
With increased speed, the pattern progressively changes to cataracting in
188 Chapter 11
which the balls are carried almost to the top of the mill and fall directly onto
the charge below.
The grinding contributions of impact and attrition vary in these patterns
of movement. Attrition predominates in the cascading mill and depends to
some extent on the surface area of the balls. The effect can therefore be
enhanced by using small balls. Impact breaking becomes more important
in the cataracting mill, the most effective action being derived from the high
kinetic energy of the larger balls, a factor also influenced by the latter’s density.
If there is sufficient friction between the mill lining and the charge, the
latter ‘‘keys’’ to the mill at higher speeds and rotates with it. This is termed
centrifuging, and since there is no relative movement between the balls, no
grinding occurs. The speed marking the onset of centrifuging is called the
critical speed. Theoretically it represents conditions for which the centrifugal
and gravitational forces acting on a ball at the top of the mill are balanced.
If the mass of the ball is m, the gravitational force is given by mg and the
centrifugal force is mv2c
/r, where vc is the critical speed and r is the distance
of the ball from the axis of the mill, i.e., the radius of the mill minus the radius
of the ball. These may be equated to give
vc vgr (11.4)
In practice, centrifuging does not occur until well above the theoretical
critical speed, and it varies with mill loading and the amount of slip between
charge and lining. Mills usually operate at between 50% and 80% of the critical
speed. The lower speeds are used for wet grinding and very fine dry
If a low coefficient of friction permits extensive slipping between mill
and charge, centrifuging will not occur even at very high mill speeds. Under
these ‘‘supercritical’’ conditions the grinding action differs from the pattern
By correct choice of ball size, mill speed, and diameter, the ball mill
may be used to grind material of widely different particle size. In coarse dry
grinding, the energy associated with the largest ball falling the diameter of
the mill must be sufficient to break the largest particle. Very fine grinding,
on the other hand, is best effected by the attrition between a large number of
small balls. The most important limiting factor in the production of very fine
particles by milling is agglomeration. Ultimately, the reduction of new surface
by rebonding may equal the increase in surface due to fracture. This is shown
Size Reduction and Classification 189
FIGURE 11.5 Effect of particle agglomeration during milling.
as point A in the relation of specific surface area and milling time in Figure
11.5. With further grinding the effective particle size may actually increase.
Agglomeration during fine dry grinding is usually more severe than in wet
grinding. In both cases, however, additives can sometimes be used to limit its
The ball mill also provides a simple mechanical means of dispersing
solids in liquids. Wet grinding depends on the attrition characteristic of the
cascading mill: the smaller the balls the greater the effect, and the greater the
suspension viscosity. The latter should not prevent the correct movement of
the charge. Where their use is permissible, the addition of surface-active agents
may greatly accelerate the process by preventing reaggregation of the particles.
Surface-active agents can also alter the physical properties of the solid, lowering
the breaking strain and rendering the particle more brittle. A higher ratio
of solids to liquid, which aids efficient milling, is possible if the system is
In large-scale, continuous installations, the mill may be modified to
apply grinding forces appropriate to the size of particle being ground. In the
tube mill the ratio of length to diameter is greatly increased, and the mill is
divided into several compartments, each containing balls of different average
size. The coarse material first enters the compartment containing the largest
balls. It is then conveyed to successive compartments containing smaller balls
and capable of progressively finer grinding. In the Hardinge conical ball mill,
190 Chapter 11
natural segregation is induced by the conical shape. The largest balls operate
at the largest diameter and, through the kinetic energy acquired during the
extensive fall, create high-impact stresses suitable for breaking coarse particles.
The material first passes through this region. With further progress
through the mill, the greater surface presented by the smaller balls promotes
finer grinding by attrition.
11.5.4 The Vibratory Mill
In the ball mill the grinding energy is derived from the acceleration of the
balls in a gravitational field. Under normal conditions the latter limits the speed
at which a mill of a given diameter can be run and therefore limits the rate
at which energy can be applied to the process. Long milling times are characteristic
of the ball mill. The advantage of vibratory milling is centered mainly
on this limitation, since it is possible by this method to develop accelerations
much greater than those induced by the earth’s gravitational field. Grinding
can be more energetic and milling times can be greatly reduced.
A simple form of vibratory mill consists of a mill body containing the
grinding media, usually of porcelain or stainless steel balls. The mill body is
supported on springs which permit an oscillatory movement. This vibration
is usually, but not necessarily, in a vertical plane. The suspended mass is
maintained in a state of forced vibration by some means, such as the rotation
of a shaft on which unbalanced weights are mounted. The charge is subjected
to movements of high frequency and small amplitude. The resultant chattering
of the mill gives comminution by attrition. Characterized by relatively high
speed grinding, the vibratory mill is usually more flexible than the ball mill;
charging and discharging and adaption to continuous processing are much
easier. The more efficient use of the energy applied and the shorter grinding
times usually result in lower milling temperatures than are found in a ball
mill. Construction, however, is more complex and the feed size of the material
is limited to approximately 0.25 in. and less. The mill is not suitable for grinding
resilient materials which cannot be ground by impact since the shear forces
developed are less than those found in a ball mill.
A refined example of this principle is found in the Podmore-Boulton
Vibro-Energy Mill [Figure 11.6(a)]. This mill consists of an annular grinding
chamber generally accommodating a medium of small cylinders. These cylinders
align coaxially in a three-dimensional vibratory field to give close packing
and line contact between moving surfaces. This alignment, it is claimed, gives
Size Reduction and Classification 191
FIGURE 11.6 (a) Vibro-energy mill and (b) fluid energy mill.
preferential grinding of coarse material leading to products with narrow particle
11.5.5 The Fluid Energy Mill
The fluid energy mill offers an alternative method of producing very fine powders.
The term micronizer is in general use and is a trade name coined by a
company which originated a particular type of fluid energy mill. In all fluid
energy mills the grinding results mainly from attrition between the particles
being ground, the energy inducing movement of the particles being supplied
in the form of compressed fluids. Air and steam are widely used.
A common type of fluid energy mill is illustrated in Figure 11.6(b). The
material is blown into the grinding chamber through a venturi feed placed at
its perimeter. The compressed fluid enters the chamber through nozzles tangential
to a hypothetical circle within the grinding chamber. The particles are
violently accelerated by the rotating fluids and are subjected to the influence
of successive nozzles. Grinding results from impact between particles, which
192 Chapter 11
are then subjected to the intense classifying action of the circulating fluid.
Oversize particles remain in the grinding zone, while fine powder and spent
grinding fluid spiral to the central outlet.
For a given machine size reduction depends on the size of the feed, its
rate of introduction to the grinding chamber, and the pressure of the grinding
fluid. The most important machine factors are the grinding chamber geometry
and the number and angle of the nozzles.
Powders with all particles below a few microns may be quickly produced
by this method. The disadvantage of high capital and running costs may not
be so serious in the pharmaceutical industry because of the high value of the
materials which are often processed. For grinding drugs the mill is usually
made of stainless steel. Large volumes of air compressed to about 6.89 105
N/m2 must be provided.
11.5.6 Colloid Mills
Colloid mills are a group of machines used for wet grinding and dispersion.
They operate by shearing relatively thin layers of material between two surfaces,
one of which is moving at a high angular velocity relative to the other.
Although very fine dispersions can be produced, they are not, as the name
implies, of colloidal dimensions. Colloid mills are also widely used to prepare
A typical colloid mill consists of a stator and rotor with flat working
surfaces, often made of stainless steel or carborundum. The clearance is adjustable
from virtually zero upward. The rotor is rotated at several thousand revolutions
per minute, and the slurry of already fine material passes through the
clearance under the action of centrifugal forces. Surface-active agents fulfill
the same function in colloid mills as in ball milling.
11.5.7 Roller Mills
Roller mills may be used to grind pastes and other plastic dispersions. They
operate by inducing crushing and shearing forces in a thin layer of the paste
as it passes through the narrow clearance between two rollers. Commonly,
shear forces are intensified by the differing peripheral velocities of the rolls.
The clearance between the rolls is variable and depends on the plasticity of
the mass, the gap increasing as the stiffness of the material increases. With
thin pastes the milling action is similar to that of the colloid mill.
Size Reduction and Classification 193
11.6 CLASSIFICATION OR SIZE
In the chapter introduction the influence of particle size on several processes
was described. The operation in which particles of a suitable size are selected
and others rejected because they are too small or too large is called classification
or size separation. This process is also important in closed-circuit grinding,
when removing fine powders to promote flow, and when restricting particle
size distribution to prevent segregation or to enhance appearance.
Although various particle properties can be used to classify a powder,
only two are important. The first is based on the ability of a particle to pass
through an aperture, known as sieving or screening. The second employs
the drag forces on a particle moving through a fluid. The term classification
is sometimes restricted to this method of separation, but in this text
elutriation and sedimentation are used. In general, screening is applied to
the separation of coarse particles and elutriation and sedimentation to fine
11.6.1 Sieving and Screening
Sieves and screens are widely used in the classification of relatively coarse
materials. For very large particles, greater than a half-inch, a robust plate perforated
with holes is used. However, the pharmaceutical applications of
screening are with much smaller particles, and screens are in the form of woven
meshes. Unless special methods are used to prevent clogging and powder
aggregation, the lower useful limit resides in a cloth woven with 7900 meshes
per meter, corresponding to a mesh spacing between 7.0 105 and 8.0
105 microns. Fine screens of this type are extremely fragile and must be used
with great care.
A series of suitable sieve cloths are specified by the gauge of the wire
and the permitted weaving tolerances. In successive meshes of this series, the
mesh space alters by the factor 4v2. In the mesh series commonly chosen for
alternate screens are selected so that the mesh spacing decreases by v2 and
the area of the apertures is halved. For classification one or more meshes of
suitable weave can be chosen from this series and mounted in a frame.
194 Chapter 11
In operation the mesh should be lightly loaded so that all particles capable
of passing the mesh (undersize) have a chance to do so. The mesh must,
therefore, be agitated to ensure access of particles to the holes and to clear
holes blocked by particles just unable to pass. Under these conditions the rate
of sieving is proportional to the number of undersize particles on the screen.
It therefore decreases exponentially.
Most screening, particularly of coarse materials, is carried out dry. Wet
screening of dilute slurries is adopted for powders which aggregate strongly,
clog the mesh, or become electrostatically charged by the screen vibrations.
Sieving errors arising from the cohesion of small and large particles and the
retention of the former on a coarse mesh is avoided. Wet screening is particularly
useful if the subsequent process is wet and drying is unnecessary.
For small-scale classification, test sieves with meshes mounted on circular
brass frames, 8, 12, or 18 in. in diameter, rims on the lower edges enabling
them to nest with the sieve beneath. When the chosen sieves are equipped
with a lid and receiving pan, the agitated assembly becomes an effective smallscale
grading unit. Sieving is stopped when the rate at which particles pass
the mesh has reached some low value or after some predetermined time at
which the rate is known to be low.
Generally as the scale of the operation increases it becomes less precise.
For continuous screening, the feed material is made to move across the screen
to a point of discharge. The residence time on the screen is usually short, and
many undersize particles traverse it without falling through. With increased
sieving area the meshes become more fragile, and the finest meshes must be
supported with a coarser wire. An example of a large-scale separator utilizes
a circular screen, up to 5 ft in diameter, and vibrates in a horizontal plane,
the gyratory movement being imparted by an out-of-balance flywheel connected
to the assembly. In other machines the mesh is rectangular and inclined
at a shallow angle (5–30°). A gyratory movement is developed and the material
to be classified is fed to the top end. These machines may bear more than
one deck, thus allowing the powder to be separated into several fractions at
11.6.2 Elutriation and Sedimentation
The balance of the drag force on the particle and the forces promoting movement
occurs at the terminal velocity. This velocity depends, among other
things, on the particle size, and it is the property on which several classifiers
are based. The fluid is air or liquid. Liquid affords a higher precision because
Size Reduction and Classification 195
dispersion can be more thorough. High shear forces cannot be developed, and
dispersing agents cannot be used in air.
The simplest classifier is a rising current of fluid in which the particles
are suspended. In this case the force opposing the upward drag is gravitational.
If the opposition gives a terminal velocity greater than the current speed, the
particle will fall. This is the principle of elutriation, and the particle size, d,
at which the separation is made follows from a rearrangement of equation
1.24 for conditions in which Stokes’ law is valid:
d v 18?u
Here ?p ? is the density difference between solid and fluid, ? is the viscosity
of the fluid, and u is the speed of the upward current.
The elutriator in Figure 11.7(a) consists of three tubes. The first is smallest
in diameter and offers the highest upward liquid velocity. Coarse particles
with a high terminal velocity settle in this tube while the remainder are swept
to the bottom of the second. The diameter of the second tube exceeds that of
the first and elutriation speeds are lower. Only fine particles are swept into
the third tube, where the process is repeated at a finer size. In this way the
original slurry is divided into four fractions.
FIGURE 11.7 (a) Elutriator and (b) grade efficiency curve.
196 Chapter 11
FIGURE 11.8 Cyclone separator.
In practice, fluctuations in flow conditions due to natural convection and
a violation of the conditions for which Stokes’ law is valid blur the point of
separation. Evaluating the separation must, therefore, take account of the fine
particles which fall with the coarse particles and of the coarse particles which
move to the fine fraction. This is best expressed by a grade efficiency curve.
Returning to equation 1.24, a particle of size d should be stationary in the
elutriation tube. Due to fluctuating conditions it eventually resides with the
coarse or fine fractions, the chances being equal. The weight fraction in each
is, therefore, 0.5 at this size. We shall assume that of the particles which are
twice this size (2d), virtually all appear in the coarse product.
The weight fraction here is unity. Similarly, all particles of size 0.2d
move to the fine product, so the weight fraction in the coarse product is zero.
As shown in Figure 11.7(b), a sigmoid curve, passing through 0.5 at size d,
links these extremes. The closer these extremes and the steeper the curve, the
Size Reduction and Classification 197
more efficient is the separation. A grade efficiency curve of this type can be
used as an appraisal of any sedimentor or elutriator.
Gravitational sedimentation is not of great importance in small-scale
classification. Sedimentation in a spinning fluid stream is, however, widely
used. The most common classifier of this type is the cyclone separator in
Figure 11.8. The fluid enters tangentially and acquires an intense spinning
motion, spiraling downward into the cone before rising to the outlet as a central
core. The inlet speed is very high, so large angular velocities are developed.
Due to centrifugal force particles move radially across the spinning stream to
fall at the wall into the cone. Operated in this way complete separation of
solids occurs and the cyclone is, therefore, an effective air cleaner. Operated
with lower centrifugal forces the cyclone transports the finest particles to the
exhaust, leaving the coarser particles to fall into the cone. Cyclone classifiers
are designed for use with liquid or air.
The centrifuge is normally operated to completely separate two phases.
If, however, the rate at which the feed passes through does not allow all particles
to settle, the action of a classifier is developed. This is illustrated by a
solid bowl centrifuge which consists of a steel shell in the form of a frustum
mounted horizontally. It contains a conveying screw at the wall which rotates
at a slightly higher speed than the shell. Particles which settle at the wall are
conveyed to the narrow end of the shell and discharged. Fine particles are
entrained with the overflow to the other end.
Perry and Chilton (1973) defined mixing as an operation ‘‘in which two or
more ingredients in separate or roughly mixed condition are treated so that
each particle of any one ingredient is as nearly as possible adjacent to a particle
of each of the other ingredients.’’ The term blending is synonymous with
mixing, and segregation or demixing is the opposite. Mixing is a basic step
in most process sequences, and it is normally carried out
1. To secure uniformity of composition so that small samples withdrawn
from a bulk material represent the overall composition of the
2. To promote physical or chemical reactions, such as dissolution, in
which natural diffusion is supplemented by agitation
Mixing can be classified as positive, negative, or neutral. Positive mixing,
which applies to systems that, given time, would spontaneously and completely
mix, such as two gases or two miscible liquids. Mixing apparatus is
used on such systems to accelerate mixing. Negative mixing is demonstrated
by suspensions of solids in liquids. Any two-phase system, in which the phases
differ in density, will separate unless continuously agitated. Neutral mixing
occurs when neither mixing nor demixing takes place unless the system is
acted on by a system of forces. Examples are mixing solids with solids and
solids with liquids when the solids concentration is high.
Mixing must embrace all combinations of the three states of matter. The
theory of mixing should be able, when the system to be mixed has been de-
fined, to dictate the type and design of the mixer, such as volume, shape, and
type of impeller, and the process conditions, such as degree of agitation and
the time and power required. Theoretical knowledge is, however, insufficient
to predict mixer performance. More commonly, choice is based on broad empirical
principles which are then supported by practical tests.
12.2 THE SCALE OF SCRUTINY
Whether materials are satisfactorily mixed depends on the subsequent operations
in which the mixture plays a part. Any mixture, if examined on a small
enough scale, shows regions of segregation. An acceptable degree of mixing
is related to subsequent operations in a process sequence. The term scale of
scrutiny is used to describe the minimum size of the regions of segregation
in a mixture which would cause it to be regarded as insufficiently mixed. For
example, if a tablet is to contain 0.1 g of drug A and 0.1 g of drug B, the
powder from which the tablets are to be made must be sufficiently mixed so
that, on drawing a sample of 0.2 g from the mixture, the sample contains,
within narrow limits, the correct amounts of A and B. The way in which A
and B are dispersed within the sample may be of no importance as long as
the tablet is not divided. The scale of scrutiny is here determined by the tablet
weight. In general, a small scale of scrutiny is applied if the unit size of the
product is small and if too much or too little of one component is very undesirable.
Two further useful concepts to describe unmixedness are the scale of
segregation and the intensity of segregation. The scale of segregation is a
measure of the size of the regions of unmixed materials. In the preceding
example the intensity of segregation shows the extent to which A has been
diluted with B, and vice versa. These two concepts are usually interrelated.
A high intensity of segregation can be tolerated as long as the scale of segregation
is small. Alternatively, a larger scale of segregation may be tolerated if
the intensity of segregation is reduced.
200 Chapter 12
12.3 MIXING OF SOLIDS
Pharmacy offers many important examples of mixing solids. In several forms
of drug presentation, the attainment of accurate dosage depends on an adequate
mixing operation at some stage in production. Since the dose unit may be
small, say 0.1 g, a small scale of scrutiny is applied.
The mixing of all systems of matter involves a relative displacement of
the particles—whether molecules, globules, or small crystals—until a state
of maximum disorder is created and a completely random arrangement is
achieved. Such an arrangement for a mixture of equal parts of two components
is shown in Figure 12.1(b).
A ‘‘perfect’’ mixture, which, with a practical sample, would offer point
uniformity, is shown in Figure 12.1(a). Such an arrangement is, however, virtually
impossible, and no mixing equipment can do better than produce the
‘‘random’’ mixture in Figure 12.1(b). In such a mixture the probability of
finding one type of particle at any point in the mixture is equal to the proportion
of that type of particle in the mixture.
Mixing solids differs from mixing liquids in that the smallest practical
sample withdrawn from a mixture of two miscible liquids contains many millions
of particles. In solids mixing a small sample contains relatively few particles,
and examination of Figure 12.1(b) should show that such samples exhibit
FIGURE 12.1 Diagrammatic representation of (a) a perfect mix and (b) a random
considerable variation with respect to the overall mixture composition and
that this variation should be reduced as the number of particles in the sample
increases. Assessing the variation in, say, drug content in a series of samples
drawn from a mixture of powders is of great importance. The tablet machine
may be regarded as a volumetric sampling device, and the variation in drug
content between one tablet and the next is largely controlled by the mixing
stage which precedes it.
12.3.1 Some Properties of a Random Mixture
In 1943, Lacey (1953) showed that the variation in the composition of samples
drawn from a random mixture of two materials could be expressed by the
s vp(1 p)
where s is the standard deviation of the samples, p is the proportion of one
component, and n is the number of particles in the sample. The relation requires
that the two components be alike in particle size, shape, and density
and only be distinguished by some neutral property, such as color. If a very
large number of samples, each containing a given number of particles, is withdrawn
from a mixture of equal parts of two materials, the results of analysis
can be presented in the form of a frequency curve in which the samples are
normally distributed around the mean content of the mixture. A total of 99.7%
of the samples will fall within the limits p 0.5 3?. The standard deviation
of the samples is inversely proportional to the square root of the number of
particles in a sample. If the particle size is reduced so that the same weight
of sample contains four times as many particles, the standard deviation is
halved. The distribution of samples and the effect of size reduction are shown
in Figure 12.2.
In a critical examination of pharmaceutical mixing, Train showed that
samples of a random mixture of equal parts of A and B must contain at least
800 particles if 997 out of every 1000 samples (3?) were to lie between 10%
of the stated composition; i.e., the proportion, p, of A 0.5 0.05, whence
? 0.05/3 (Train, 1960). The effect of the number of particles in a sample
on the percentage variation about the mean content of a mixture of equal parts
A and B was summarized by Train [Figure 12.3]. The diagram may be used
to show that if, in the example, limits of 1% were substituted, 90,000 particles
must be present in each sample. The true standard deviation is symbolized
202 Chapter 12
FIGURE 12.2 Distribution of samples drawn from a mixture of equal parts A and
B. The broken line represents data for the coarser powder.
FIGURE 12.3 General theoretical relationship between number of particles and percentage
limit of ingredient for a 50:50 mix.
by ?. The standard deviation estimated by the withdrawal of a number of
samples is denoted by s.
If instead of equal parts A and B, the proportion of an active ingredient,
A, in the mixture were 0.1 (10%), imposition of limits of 10% (in 997 cases
out of 1000) requires that each sample contain over 8000 particles. If the
proportion of active constituent is 0.01 or 1%, a figure of 90,000 particles per
sample is obtained, and if the limits are reduced to1%, the figure is 9 million.
The theoretical derivation of these results is based on component particles
which are alike in size, shape, and density. This condition is not encountered
in the practical mixing of solids, and, as we shall see, any of these factors
may prevent the formation of a random mixture. The value of the number of
particles per sample derived in any example must therefore be raised if the
limits given are to be maintained.
As the proportion of an active ingredient in a mixture decreases, the number
of particles in each sample or dose must increase and materials of smaller
particle size must be used. This statement indicates the limitation of the mixing
of solids. Producing very fine powders is difficult and often attended by severe
aggregation, thus defeating the object of size reduction in the mixing process.
Where the proportion of active constituent is very small and is finally presented
in a small-dose unit, dry mixing of solids may fail to produce an adequate dispersion
of one component in another, and other methods, such as spraying a solution
of one component onto another, must then be adopted.
Another example of the relation of dose uniformity and number of particles
in the dose is two components which are separately granulated before
mixing. This procedure is sometimes adopted for reasons of stability during
granulation. The variation in samples drawn from such a system is much
greater than the variations in a mixture which was mixed before granulation,
because the effective number of particles in the sample is greatly reduced.
12.3.2 Degree of Mixing
A quantitative expression which defines the state of a mix is necessary if a
rational answer to the question, Is this material well enough mixed? is to be
made. Such an expression would also allow the course of mixing to be followed
and the performances of different mixers to be compared. The most
useful way to express the degree of mixing is to measure the statistical variation
in composition of a number of samples drawn from the mix. The scale
of scrutiny determines the size of the sample, and their number depends on
the accuracy required of the assessment.
204 Chapter 12
As already shown, a series of samples drawn from a random mix exhibits
a standard deviation of sr. An index of mixing, M, is given by
where s is the standard deviation of samples drawn from the mixture under
examination. This approaches unity as mixing is completed:
where s0 is the standard deviation of samples drawn from the unmixed materials.
It is equal to p(1 p), where p is the proportion of the component in the
mix. Its modification by Lacey, using the variance of the samples, to
gives a fundamental equation for expressing the state of the mixture, where
M? varies from zero to unity.
The binomial and Poisson distributions have also been used to examine
the state of a mixture. If the proportion of black particles in a random mixture
of black and white particles is p, the probability, P(x), of obtaining x black
particles in a sample of n particles is
xpx(1 p)nx (12.5)
If p is small (0.15) and n is large, the Poisson distribution can be used when
P(x) em(mx/x!) (12.6)
where m np, the mean number of black particles in the samples of n particles.
This relation may be used in an assessment of dry mixing equipment.
If m 20 and more than 10 samples are taken, then:
1. About 10 of the samples have the number of black particles outside
the limits m 1.7vm.
2. About 5% of the samples have the number of black particles outside
the limits m 2.0vm.
3. About 1% of the samples have the number of black particles outside
the limits m 2.6vm.
FIGURE 12.4 Variation in the number of black particles in samples drawn from a
tumbler blender for (a) p 0.01 and (b) p 0.7.
Results of such tests in which small cubes of polythene were mixed in
a double-cone blender are shown in Figure 12.4(a,b). The probability that the
results plotted in Figure 12.4(a) came from a random mixture is less than 0.01,
19 out of 34 samples exceeding the 1 in 10 limits. The densities of the two
components in this example were 0.92 and 1.2. The results in Figure 12.4(b)
were obtained when the components were of the same density and the probability
that the samples were drawn from a random mixture was 0.7.
Alternatively, satisfactory mixing may be established by imposing standards
dictated by the operations in which the mixture is to take part. The
variance of the samples at different times during mixing is shown in Figure
12.5. The samples, which in this case weighed 5 g, represent the ultimate
subdivision of a production size antibiotic mixture. An acceptable degree of
homogeneity was set at a standard deviation of 5%, giving a variance of
(0.05)2, and this was achieved after just over 100 revolutions of the mixer.
[The band around the experimental values of the variance defines the limits
within which the true variance lies (p 0.9).] By this method the suitability
of the machine and operating characteristics were established.
12.3.3 Mechanisms of Mixing and Demixing
The randomization of particles by relative movement, one to another, is
achieved by the following mechanisms:
1. Convective mixing: transferring groups of adjacent particles from
one location in the mass to another
206 Chapter 12
FIGURE 12.5 Decrease in the variance of samples drawn from a mixture of penicillin
(40%) and dihydrostreptomycin in a twin-shell blender.
2. Diffiusive mixing: distributing particles over a freshly developing
3. Shear mixing: setting up slip planes within the mass
All take place to some extent during mixing, but they vary in extent with the
type of mixer used. In general, a large diffusional element is necessary if the
scale of scrutiny is small. In addition, distortion of portions of the material
by intense shear forces, as in mulling, and the scattering of individual particles
by impact, processes normally associated with size reduction, are used for
some mixing operations.
Convective mixing predominates in machines utilizing a mixing element
moving in a stationary container. An example is the horizontal ribbon mixer.
Groups of adjacent particles are moved from one position to another, giving
a steady decrease in the scale of segregation.
Shear mixing occurs when a system of forces acting on the particles
induces the formation of a slip place. This gives relative displacement of two
regions. It occurs, for example, in shape rearrangement as the main charge
falls from end to end in a double-cone mixer. Train has stressed the importance
of expansion or dilation of the material, so shear forces may be effective
(Train, 1960). A practical corollary is that efficiency is reduced if the machine
Diffusive mixing predominates in tumbler mixers. Tumbling occurs as
the material is lifted past its angle of repose. Mixing occurs when a particle
changes its path of circulation through a collision or when it is trapped in
voids presented by another layer of particles.
The mild forces involved in these examples may be insufficient to adequately
disperse materials which tend to aggregate. The more energetic processes
of mulling and impact milling may then be used. Size reduction and
mixing are carried out simultaneously, although the former may be slight. An
example is the incorporation of ferric oxide and basic zinc carbonate in calamine
production. For mixing of this type the hammer mill, mullers, and ball
mills charged with small balls are frequently used. The material being processed
at any time must contain the correct amounts of materials. If the holdup
capacity of the mill is sufficiently large, this can be achieved by a correctly
proportioned feed. Otherwise, the product must be mixed a second time by
some other method to correct segregation of large-scale but small intensity.
If all particles in a mixture reacted equally to an applied force, then all
mixers would eventually produce a random mixture, although the time taken
would vary, the more efficient mixer producing a random mix more quickly.
The characteristics of real mixtures prevent this, and differences in particle
size, shape, and density oppose randomization. Of these, differences in particle
size are the most important. The role of these factors in opposing mixing and
promoting demixing is demonstrated in the analysis of horizontal drum mixing.
Movement of material in a radial plane is shown in Figure 12.6. The static
mass of particles is lifted past its angle of repose, and particles tumble down
FIGURE 12.6 Mechanism of radial mixing and demixing.
208 Chapter 12
the free surface, accelerating to the center of the mixer and then decelerating
before entering the static bed. The zone in which this takes place is the mixing
zone, and since it is in contact with the static bed, in which no mixing takes
place and which is moving in the opposite direction, a velocity gradient occurs
across the mixing zone; i.e., a layer of particles is passing over the layer beneath,
and so on. This zone is in an expanded state and particles are therefore
passing over voids in the layer beneath. Mixing occurs when a particle is
trapped by moving into a void, thus changing its path of circulation. This
mechanism suggests an optimal running speed. If it is too slow, not enough
events occur. If it is too fast, the capture time is insufficient.
As long as one type of particle is not preferentially caught, a random
mix eventually occurs in the radial plane. If, however, one component is
smaller, denser, or has certain shape characteristics, it is preferentially trapped
and moves into the lower layers of the mixing zone until it finally concentrates
as a central core running the length of the mixer. Similar effects occur in axial
mixing, and the final shape of the segregated zone formed under the influence
of axial and radial movement depends on the material’s flow properties. Similar
effects occur with a double-cone blender. Segregation also occurs with
such materials when they are dumped from the mixer.
In general, one component concentrates at one position in the mixer
when a simple-repetitive, symmetric movement occurs. Modern design tends
to the rotation of asymmetric shapes or to symmetric shapes rotated asymmetrically,
often with an abrupt reversal in charge movement. Even so, segregation
may still occur after a long period of mixing. The variance of samples
decreases during mixing to a minimum value, and is followed by a period of
demixing, the variance finally achieving a higher equilibrium value. It is therefore
possible to overmix.
12.3.4 Mixing Rate
Since mixing is a process of achieving uniform randomness, the mixing rate
is proportional to the amount of mixing still to be done. If, at the start of
mixing, a particle changes its path of circulation, it is most likely to find itself
in a different environment. The rate of mixing is therefore fast. At the end of
the process, the particle is less likely to find a different environment, and such
a change gives no useful mixing. Fewer mixing events take place, and the
mixing rate finally reaches zero. The mixing rate for any mixing mechanism
can be represented by the expression
k(1 M) (12.7)
where M, the mixing index, has already been defined. Integrating this equation
M 1 ekt (12.8)
The rate constant k depends on the physical nature of the materials being
mixed and on mixer geometry and operation.
12.4 MIXING MACHINES
12.4.1 Trough, Ribbon, and Paddle Mixers
A simple trough mixer consists of a semicircular trough in which an impeller,
such as paddles mounted at diverse angles on a shaft running the length of
the trough, rotates, thereby lifting and distributing the material in an irregular
manner. Convective and shear mixing occur. Some fine-scale diffusive mixing
occurs when the impeller lifts material clear of the main charge.
The ribbon mixer employs a ribbon-like conveying scroll. The helix,
which may be continuous or interrupted, is rotated in a semicircular trough,
and mixing again occurs through convection and shear, giving rapid coarsescale
dispersion. Two ribbons set to convey material in opposite directions
are frequently fitted to the shaft. Although little axial mixing in the vicinity
of the shaft occurs, mixtures with high homogeneity can be produced by prolonged
mixing even when components differ in particle size, shape, or density
or there is some tendency to aggregate.
12.4.2 Tumbler Mixers
Tumbler mixers operate by a mainly diffusive mechanism, their use is confined
to free-flowing and granular materials. The mild forces employed, which preclude
mixing materials which aggregate strongly, allows friable materials to
be handled satisfactorily. The more elaborate geometric forms are most commonly
used because movement of material in all planes, which is necessary
for rapid overall mixing, is induced. Internal baffles and lifter blades may also
be incorporated. For example, axial movement of material along the length
of a simple drum mixer is slow and can be enhanced by these methods.
12.4.3 Mullers and Impact Millers
The function of mullers and impact millers was discussed earlier.
210 Chapter 12
12.5 MIXING LIQUIDS
In mixing miscible liquids, any practical scale of scrutiny embraces a very
large number of particles. If, therefore, a mixture of liquids is randomized by
agitation, for all practical purposes it can be regarded as uniform. Miscible
liquids are classified as positive mixtures and would, given time, mix completely
without external help. The time required for mixing is reduced by
agitation during which the scale of segregation is reduced, allowing a fast
decay in the intensity of segregation by natural diffusion. In general, no great
problems are encountered unless the operational scale is very large.
Miscible liquids are most commonly mixed by impellers rotating in
tanks. These impellers are classified as
In conjunction with the design of the containing vessel, impellers provide
a. A region of intense shear near the impeller with the induction of
high-velocity gradients and turbulence within the liquid.
b. Projection of the disturbance as a flow pattern extending throughout
the volume of the container. This is dictated by the impeller’s type
and position, the tank design, and the material’s flow properties.
All the material should pass through the impeller zone at frequent intervals
of time, the design of the mixer preventing the formation of ‘‘dead’’
zones. The turbulent, high-velocity flow of liquid from the impeller causes
mixing by projecting eddies into, and entraining liquid from, the neighboring
zones. The thin ribbons of one component in another rapidly become diffuse
and finally disappear through molecular diffusion.
The flow pattern may be analyzed in terms of its three components of
motion: radial flow (i.e., perpendicular to the impeller shaft); longitudinal or
axial flow (i.e., parallel to the shaft); and tangential flow (i.e., a circular path
around the shaft). A satisfactory flow pattern depends on the correct balance
of these components. In a cylindrical tank, radial flow gives rise to axial flow
by reaction at the tank wall. Tangential flow receives no such modification.
Its predominance as laminar flow circulation supports stratification at various
levels. Furthermore, a vortex is created at the liquid surface which may penetrate
to the impeller, causing air to be dispersed in the liquid. In general, tangential
flow should be minimized by moving the impeller to an off-center
position, thus destroying mixer symmetry, or by modifying the flow pattern
with baffles. Tanks with vertical agitators may be baffled by one, two, or more
strips mounted vertically on, or just away from, the vessel wall. Baffles reduce,
but do not eliminate, tangential flow, whereas little modification of radial and
axial flow occurs. Baffles produce additional turbulence.
Additional factors must be applied to mixing two immiscible liquids.
This operation, encountered, for example, in liquid-liquid extraction, involves
the production and maintenance of a large interfacial contact area. In addition,
phase separation due to differences in density must be opposed by an adequate
axial flow pattern. The high rates of shear induced by propeller or turbine
rotation cause globules of the disperse phase to be drawn into an unstable
filament of liquid which breaks and re-forms into smaller globules. Unless
stabilized by surface-active agents, the reverse process—coalescence—occurs
in zones in which velocity gradients are small.
12.5.1 Paddle Mixers
Four types of paddle mixers are illustrated in Figure 12.7. The mixing element
is large in relation to the vessel and rotates at low speeds (10–100 rpm). A
simple paddle, with upper and lower blades, suitable for mixing miscible liquids
of low viscosity is shown in Figure 12.7(a). A tangential flow pattern
predominates with zones of turbulence to the rear of the blades. The gate
paddle in Figure 12.7(b) is suitable for mixing liquids of higher viscosity, and
the anchor paddle in Figure 12.7(d), with low clearance between pan and
blade, is useful for working across a heat transfer surface. Stationary paddles
intermeshing with the moving element suppress swirling in the mixer in Figure
12.7(c). In the other examples baffles are necessary. Unless paddle blades are
pitched, poor axial turnover of the liquid occurs. Hence, paddles are not suitable
for mixtures which separate.
12.5.2 Propeller Mixers
Propellers are commonly used for mixing miscible and immiscible liquids
of low viscosity. The marine propeller is typical of the group. High-speed
rotation (400–1500 rpm) of the relatively small element provides high shear
rates in the vicinity of the impeller and a flow pattern with mainly axial and
tangential components. They may be used in unbaffled tanks when mounted
in an off-center position or inclined from the vertical. Horizontal mounting
in the side of the vessel is frequently used when the scale of the operation is
212 Chapter 12
FIGURE 12.7 Paddle mixers.
Turbine designs are intermediate between paddles and propellers. Turbines
are effective mixers over a wide viscosity range and provide a very versatile
mixing tool. The ratio of radial to tangential flow, which are the predominating
components with this impeller, increases as the operating speed increases.
Pitched-blade turbines are sometimes used to increase axial flow Baffles must
be used to limit swirling unless a shrouded turbine is used. With this impeller
a discharge with no tangential component is produced.
12.5.4 Mixing Liquids and Solids
Examples of solid-liquid mixing occur during dissolution and crystallization
and in controlling chemical reactions between solids and liquids. Alternatively
randomization of materials for subdivision and presentation may be the object,
as, for example, in toothpaste production.
The flow properties of a liquid-solid mixture alter markedly with change
in the ratio of the two phases. At low, solid-disperse phase concentrations,
flow properties are Newtonian and mixing by impellers is satisfactory as long
as flow components oppose settling. Under such conditions it may be desirable
to increase impeller size and decrease its speed. For a given power input,
improved flow patterns are produced at the expense of turbulence. Unless the
difference in density between solid and liquid is small, paddles are ineffective
for suspending solids. Otherwise, the discussion presented for mixing liquids
may be applied.
Anomalous flow characteristics are exhibited at higher disperse phase
concentrations in which the apparent viscosity is a function of the shear rate.
The apparent viscosity may increase or, more commonly, decrease as speed
impeller increases. Mixing is achieved by suitable impellers, notably the turbine,
as long as adequate flow patterns in the entire volume of the mixing
vessel are created. Turbulence is less effective as a mixing mechanism, and
regimes of laminar flow will be extensive.
Further increase in apparent viscosity occurs at higher disperse phase
concentrations. This is often associated with the development of a yield value.
Unlike true liquids, shear forces must exceed a certain level before deformation
occurs. Since the shear forces developed by particles suspended in liquids
are small, sedimentation does not occur and the mixture may be classified as
neutral. Mixing by impellers is precluded if the apparent viscosity is very high,
because the projection of adequate flow patterns is impossible. Alternative
methods must be used in which the mixing element visits all stations in the
mixing vessel. For thin pastes, machines typified by the domestic food mixer
are used. Imposition of planetary movement on the rotation of the mixing
element causes all parts of the mix to be sheared at intervals. Very high shear
rates are produced as the element sweeps out zones close to the container wall.
In other machines, the containing vessel rotates.
For thicker pastes and plastics, a kneading, stretching, and folding action
is employed. The sigma blade, mounted axially in a trough, is a commonly
used mixing element. Intense shear is induced by the close clearance between
element and container. Simultaneous transport around the trough occurs, so
all portions of the mass are periodically deformed. Considerable variation in
rheological properties may occur during mixing, and robust mixer construction
The differential speed of the rolls of the roll mill induces high shear
rates in the material. This machine is suitable for paste mixing. With more
fluid dispersions, the ball mill and the colloid mill may be used. Solids which
214 Chapter 12
aggregate may be successfully dispersed, although subsequent stability may
require a deflocculating agent.
Blending solids with very small quantities of liquid, an operation commonly
used for granulating powders, presents extreme problems of uniformity.
If the material does not become plastic and pasty, it will not mix by shear
deformation in the manner described. Mixing is then best achieved by spraying
the liquid as fine droplets onto a highly mobile powder which is continually
and rapidly developing new surfaces. In this way all particles can be exposed
to the spray. A closed ribbon mixer, planetary mixer, or sigma blade mixer
can be used. Alternatively, tumbler mixers can be fitted with a spray device.
If the solid is itself a mixture, the material must be completely mixed before
liquid is added. Otherwise, homogeneity is difficult to achieve.
Solid Dosage Forms
Earlier the subject of powders was addressed from a physicochemical standpoint.
The unit processes involved in incorporating powders in solid dosage
forms must also be considered. Solid dosage forms can be divided into granules,
capsules, and tablets for oral delivery, and inhalation products. Note that
solid particulates might also play a role in certain parenterals in the form of
Solid dosage forms are the most desirable final products of a development
process that begins with drug discovery, proceeds through bulk product
manufacturing, preformulation, and formulation characterization to one of the
products mentioned. Figure 13.1 illustrates an abbreviated sequence of steps
through which the drug passes to the final dosage form.
Most solid dosage forms are intended for oral ingestion. The drug released
from the dosage form is available at the site of absorption or action
within the gastrointestinal tract.
Preformulation studies are required before a formulation is developed.
By studying the properties of the drug it is possible to delineate a course of
action for composing the formulation. The properties studied are
216 Chapter 13
FIGURE 13.1 Drug to the final dosage form.
• Organoleptic properties
• Particle size, shape, and surface area
• Parameters affecting absorption (dissociation constant, partition coefficient)
• Crystal properties and polymorphism
• Stability (chemical and physical)
• Compatibility (with excipients and potential packaging materials)
• Miscellaneous physicochemical properties
Solid Dosage Forms 217
Problem solving in service of formulation development can be derived
from knowledge of these properties. Each item has been covered in depth
elsewhere and is beyond the scope of this volume.
The additives employed in solid dosage forms are categorized as diluent,
glidant, lubricant, disintegrant, and binder. Several candidates from each category
may be considered as components of a possible dosage form. Lubricants
and disintegrants play a more substantial role in compressed tablet dosage
forms than they do in granules or capsules. This will be discussed in more
The simplest form of solid dosage form employs granules prepared from the
drug and other components in stable aggregates in sizes large enough to facilitate
accurate manipulation and dispensing in bulk and at the level of the unit
Following particle size reduction and blending the formulation may be
granulated (Carstensen, 1993), which provides homogeneity of drug distribution
in the blend. In addition, it may help flow properties and powder compression
characteristics. Large granules can be prepared from primary particles by
drying from a slurry (with techniques described elsewhere in this text) or by
spraying with granulation solution. Figure 13.2(a) shows a top-spray granulator.
An alternative method [Figure 13.2(b)] employs an auger to force the
blend between rollers, thereby forming a compressed solid that disintegrates
into large aggregates (Doelker, 1994).
The steps involved in granulation begin with transferring powders to a
mixer and blending the product. The granulation solution can be added, and
coarse milling or wet granulation begun. Finally, the product is dried and
milled to an appropriate size. If the powder is unstable in the presence of polar
solvents, it may be compressed directly. Granulation increases the uniformity
of drug distribution in the product, improves the powder flow rate and uniformity
of flow, and, if used as an aid to tableting, assists in compression and
More sophisticated approaches to combining the drug and excipients
into a free-flowing large particle size to improve homogeneity, handling, and
218 Chapter 13
FIGURE 13.2 (a) Top-spray granulator; (b) granulator with an auger to force the
blend between rollers.
drug-release characteristics include spray-drying, fluid-bed-drying, extrusion
spheronization, and microsphere or microcapsule formulation. All of these
processes are governed to some degree by fundamental fluid flow, heat, and
mass transfer phenomena.
13.2 HARD CAPSULES
Hard capsules have traditionally been manufactured from gelatin. The gelatin
is obtained from bone or skin (calf or pig) acid or alkali treatment over a
Solid Dosage Forms 219
period of weeks, in some cases as long as 30 weeks (pork skin, 1–5% HCL).
The product pH is adjusted, and a hot water extraction is followed by filtration,
concentration, and solidification. The final product is milled to size.
Capsule shells are prepared by dipping manganese bronze pins into a
bath of molten gelatin. Once removed from the bath the gelatin solidifies on
the pins. The caps and bodies are then dried and trimmed. Colorant or titanium
dioxide (for opacity) is added as part of this process.
The need for capsules with different physicochemical properties, to aid
in stability for example, has promoted a search for alternative materials. In
addition, individuals who, for strict religious or health reasons, cannot ingest
gelatin need alternative products. In this regard starch and hydroxypropylmethyl
cellulose (HPMC) have been developed. There is no reason to believe
that other film-forming polymers might not be useful in this regard. One significant
issue that must be considered is the moisture content of the capsule.
Gelatin is known to optimally contain 5–15% moisture. Below 5% the shell
becomes brittle and may shatter. Above 15% the gelatin distorts, and the shape
of dosage form, if not its integrity, is challenged. The presence of a nutrientrich
environment and moisture may offer an ideal situation for microbial
growth and enzyme action. Control of microbial growth is therefore a serious
consideration in the preparation of capsule products.
Various capsule sizes are manufactured, as shown in Figure 13.3. There
are no strict rules for predicting required capsule size. Capsules are selected
based on their capacity and the nature of the formulation to be added. The
bulk density and compressibility of the product (drug and excipients) dictate
the quantity of drug that can be placed within a capsule of known volume.
Since the drug dose required to achieve a therapeutic effect can be estimated
for new compounds and is known for existing compounds, this information
can be used in conjunction with the capsule volume to select an appropriate
FIGURE 13.3 Different capsule sizes.
220 Chapter 13
The requirements for capsule production depend on the scale of manufacturing.
Extemporaneous preparation (6–12) usually employs enough of the
product formula to fill one more capsule than required, to account for loss
of fill in manipulation. Special consideration should be given to controlled
substances where all of the drug must be accounted for. Industrially (thousands)
the amount necessary to fill the desired number can be prepared because
the error will be small on such a large scale. The operations involved in largeor
small-scale capsule filling are the same. The capsules as supplied in random
orientation must be rectified into a bodies-down, caps-up orientation. The two
shells are then separated, and the capsule is filled with product formulation.
Various methods are available to fill the capsules. For small-scale production,
a plate or single capsule filling method is employed. On a larger scale, tamping,
intermittent compression, continuous compression vacuum, or auger filling
may be employed (Figure 13.4). The shells are then joined and sealed,
and the completed product is discharged as shown in Figure 13.5. Different
FIGURE 13.4 Capsule filling: (a) tamping, (b) compression, and (c) auger filling.
222 Chapter 13
FIGURE 13.5 Capsule manufacturing process.
locking mechanisms have been developed for capsules shown in Figure 13.6.
A cleaning and polishing step also follows the manufacturing procedure to
improve product appearance.
The product is visually inspected following production, its potency and
uniformity are evaluated, and it is transferred hygienically to the final packaging.
If the product is hygroscopic, it may be necessary to package capsules
FIGURE 13.6 Capsule locks.
Solid Dosage Forms 223
with desiccant to avoid moisture uptake. Alternatively, impervious packaging
materials, such as aluminum blisters, may be used. Capsules are easier to prepare
than tablets, are quite flexible with respect to dose, and easily combined
with other solid dosage forms since other capsules or tablets can be incorporated
into larger capsules.
Additional processes are required for tablet production beyond those described
previously. Because these processes are not ubiquitous in pharmaceutical manufacturing,
they are dealt with only briefly here. Many of them are required
for all solid dosage forms. Each process must be conducted while balancing
the effects of the respective excesses.
Compressed solids, tablets, or caplets are prepared by placing the blend
of component additives in a cylinder or die, above a movable piston or punch.
An upper punch is brought into the top of the piston, and pressure applied to
the distal ends of the punches forces the powder into a compact (Figure 13.7).
Product quality depends on the cohesive forces acting on the powder under
compression. These cohesive forces are influenced by the selection of additives
in the dosage formulation. One method of evaluating tablet manufacture
considers the effect of applied pressure on porosity of the compressed powder
(Carstensen, 1993). Data may be plotted as the negative natural logarithm of
porosity against applied pressure in the form of a Heckel plot (Heckel, 1961).
The slope is proportional to the yield value (?, elastic limit) 1/3?.
The tooling of a tablet press varies according to the tablet design. Consideration
must be given to the distribution of forces across the faces of the
tablet punches as they are brought together to compress the tablet in the die.
As more unusually shaped tablets are produced and more elaborate embossing
tools are required, the forces are not distributed evenly across the punches,
and care must be taken if they are to have a reasonable useful life-span. Mathematically,
finite element analysis can be used to characterize these forces and
to calculate the requirement for preserving the tools for extended periods.
Coating is achieved by placing a batch of tablets in a coating pan and
spraying or coating from solution with the required polymer. The Accela-Cota
(Figure 13.8) is one of the more common coating systems.
Tablets have been prepared with different characteristics and for different
purposes. The most common tablets are uncoated, coated, chewable, or
effervescent. Some specialized dosage forms have been developed for sublin224
FIGURE 13.7 Tablet manufacture.
gual and buccal delivery. A typical uncoated conventional tablet might have
the composition shown in Table 13.1. Examples of such systems include generic
aspirin and Valium. These tablets are designed for rapid dissolution.
Tablets may be coated for a variety of reasons, including better appearance,
taste masking, ease of swallowing, protection from light, protection from
gastrointestinal irritation, facilitate tablet printing, and control release. The
formulation of a coated tablet is similar to an uncoated tablet. Usually it is
coated from a solution of polymer, e.g., methylcellulose, enteric polymer.
Bayer aspirin or erythromycin products are examples of coated tablets.
Chewable tablets are usually flavored and contain addtives that contribute
to a smooth texture, including glycerin and sugars such as mannitol and
sorbitol. An example is Tylenol chewable tablets.
Effervescent tablets are formulated such that an acid-base reaction occurs
when they are combined with water. This is achieved by using weak acids
(e.g., citric, malic, tartaric, or fumeric acids) or bases (e.g., sodium or potasSolid
Dosage Forms 225
FIGURE 13.8 Accela-Cota. (Courtesy of Thomas Engineering, Hoffman Estates, Illinois.)
TABLE 13.1 Tablet Composition
Drug Generic aspirin, Valium
Filler Lactose, sucrose, phosphates
Binder Starch, polyvinylpyrollidone, cellulosics
Glidant Talc, silicon dioxide
Lubricant Magnesium stearate
Disintegrant Starch, sodium starch glycolate
226 Chapter 13
sium carbonates) in the product. The best known of these products is Alka-
Sublingual tablets are designed to disintegrate and dissolve instantly.
Hence, they must have structural integrity sufficient for storage, transport, and
administration but capable of dissolution on the oral mucosa under the tongue.
Nitroglycerin tablets designed for treating angina are prepared in a compositionally
simple formulation of lactose massed with 60% ethanol. This route
of administration is intended to avoid first-pass liver metabolism. Testosterone
tablets have been prepared for buccal delivery by slow dissolution. The tablet
does not contain a disintegrant and is intended to have an extended residence
time in the buccal cavity at the rear of the mouth. Since release is not immediate
drug dosage may be significantly reduced by this route.
13.4 INHALATION PRODUCTS
Solid particles are employed in two types of inhalation product: the pressurized
metered dose inhaler (pMDI) and the dry powder inhaler (DPI). In both cases
the method of choice for manufacturing particles in an appropriate size range
to deposit in the lungs (5 µm) is attrition milling by air jet mill.
The pMDI product is prepared as a nonaqueous suspension in which
surfactant is used to disperse the drug particles in high-vapor-pressure propellants.
Once the particles are prepared the product formulation depends only
on the particle dispersion in suspension, their ease of redispersion, and their
physical stability upon aerosolization. Figure 13.9 shows a typical filling line
for pMDI product.
Dry powder inhaler formulations usually involve a combination of the
micronized drug with a carrier, notably lactose. The carrier particles are usu-
FIGURE 13.9 Metered dose inhaler filling line.
Solid Dosage Forms 227
ally larger than the drug particles and outside the range required for lung
deposition (30 µm). The purpose of these large particles is to help disperse
the respirable drug particles carrying them into the inspiratory airflow where
they are stripped from the surface as a function of the large shear forces. These
formulations are prepared in capsules, blisters, or reservoir devices. The filling
technology has been developed to accurately meter small doses into the unit
Other methods of particle preparation have been evaluated, including
spray-drying and supercritical fluid manufacture. The capacity to manufacture
particles with known and optimized particle size, shape, and surface characteristics
is intriguing, and it seems likely that these methods will become more
significant in the future and may even surpass micronization for aerosol delivery
Sterilization processes do not result in a product that can be described as absolutely
sterile or nonsterile. The process is a statistical phenomenon. A variety
of techniques are available, including heat, radiation, ethylene oxide, and sterile
14.1 THERMAL STERILIZATION
The use of heat to sterilize depends on the magnitude (T), duration (t), and
amount of moisture present:
It is thought that the heat coagulates protein in the living cell. The temperature
required for this phenomenon to occur is inversely proportional to moisture
14.1.1 Dry Heat
Relatively stable substances that resist degradation at high temperatures (313
K) are suitable candidates for dry heat sterilization. Two hours exposure at
353 K or 45 min at 433 K kills spores as well as vegetative forms of microorganisms.
These exposure periods do not include the lag time from loading
of the oven until sterilization temperature is achieved. The lag time depends
on the geometry and operating features of the oven and characteristics of the
The oven types that can be employed are natural and forced convection,
both of which are described in Chapter 6. The forced convection oven offers
the advantages of uniformity of heat distribution and reduction in lag time in
comparison with the natural convection system. This method is reserved almost
exclusively for glass or metal, since other materials char (cellulose),
oxidize (rubber), or melt (plastic) at these temperatures.
14.1.2 Moist Heat
Moist heat offers the advantage of greater effectiveness at low temperatures.
The thermal capacity of steam is much greater than that of hot air. Spores
and vegetative forms of bacteria may be effectively destroyed in an autoclave
employing steam under pressure, either 1.03 105 N/m2 at 394 K for 20 min
or 1.86 105 N/m2 at 405 K for 3 min. The lag time to complete exposure
of the material to be sterilized is important.
Ultraviolet light is frequently used to reduce airborne microbial contamination
and to sterilize surfaces. Both are usually achieved with mercury vapor lamps
having an emitted light of 2.537 107 m.
Radiation sterilization uses the ionizing radiation of X-rays and gamma
rays. X-rays are derived from bombardment of a heavy-metal target with electrons.
Gamma rays are obtained from atomic nucleus decay from the excited
state to the ground state.
The energy evolved from radiation can be equated to photon behavior
E h?, ?
230 Chapter 14
where E and ? are the energy and frequency of a photon respectively, h is
Planck’s constant, and C and ? are the speed and wavelength of light, respectively.
The energy absorbed from the radiation sources equates to the dose:
1 rad 100 erg/g of material absorbing
There are a variety of radiation sources. 60Cobalt (60Co) decays to 59Co
in the core of a nuclear reactor to emit two photons (1.17 106 eV and 1.33
106 eV) and an electron (0.31 106 eV). The half-time for decay is 5.3
years. 137Cesium (137Cs) decays to emit one photon (0.661 106 eV). Cesium
has a 33-year half-life. An electron beam can be accelerated to an energy
equivalent to 5 106–10 106 eV. At energies below 5 106 eV penetration
is insufficient for sterilization. Penetration depth can be correlated with energy
levels. For example, materials with density equivalent to water (? 106 g
m3) are penetrated 5 107 m/eV. 60Co gives rise to radiation that penetrates
0.3 m through water. Accelerating electrons have high dose rate and exposure
is only required for seconds. 60Co has a lower dose rate, so an exposure for
hours is required.
Ionizing radiation arises from the photoelectric effect, the Compton effect,
or ion pair production. Gamma radiation causes local and intense damage
and may break chemical bonds. The primary target is the deoxyribonucleic
acid (DNA) of the microorganism. In addition, free radicals may be formed,
i.e., peroxides that result in intracellular and extracellular peroxides by a chain
reaction, that cause damage.
14.2.1 Resistance to Damage
Damage depends on the amount of energy absorbed relative to the number
and resistance of the microorganisms being irradiated. Unicellular organisms
have greater resistance than multicellular ones. Gram-positive bacteria have
greater resistance than Gram-negative bacteria. Finally, bacterial spores have
greater resistance than vegetative forms. Viruses are more resistant than bacteria.
The energy required to reduce the population of viruses by 90% (Dvalue)
is 5 105 rad. Fungi are equivalent to bacterial spores in their resistance.
To evaluate the dose several parameters must be known. What magnitude
of source (e.g., 60Co) is available? A typical source is between 0.5–2
106 Curies (Ci), where 1 Ci is 3.7 1010 disintegrations/s. The product geometry
and the speed of the conveyor carrying it to the source must be known.
The dose can be evaluated by a variety of dosimetric techniques. In bulk or
ampules containing liquids, ferric ammonium sulfate and ceric sulfate can
be used to show an absorbance change, evaluated by UV spectrophotometry.
However, this is accurate only for 60Co and 137Cs.
Radiochromic solids can be utilized and evaluated by visible spectrophotometry.
Amber and red polymethylmethacrylate are used to evaluate 0.1–1.0
106 or 0.5–5.0 106 rad, respectively. Nylon film is examined for opacity
following exposure and may be used to evaluate exposures of 0.1–5.0 106
Validation requires determination of the bioburden and the Dvalue.
These represent the dose required to achieve sterilization and the estimated
The dose may be regarded as overkill if low Dvalues are obtained. Bacillus
pumulis exhibit inherently high resistance to gamma-ionization radiation
with Dvalues of 0.15–0.22 106 rad. The Food and Drug Administration
would like a 12-log reduction in microorganisms. The dose required is approximately
2.6 106 rad.
14.2.2 Product Development
The product, container, and closure must be evaluated for physical and chemical
stability. A number of radiation-induced changes can potentially occur.
The product may change in color, odor, flavor, potency, biocompatibility, and
toxicity. The container may lose rigidity, become brittle, label adhesion, or
become leachable. The product and container may be assessed by exposure
to multiple doses and single high doses of radiation. The long-term stability
can then be evaluated under ambient storage conditions, at elevated temperatures,
and under worst-case shipping conditions.
Dose mapping can be performed by determining the minimum radiation
point in the load. Multiple dosimeters can be used to view the vertical quadrant
through the load. Dosimeters are routinely set to measure the minimum dose.
14.3 ETHYLENE OXIDE
Ethylene oxide is a gaseous alkylating agent used as a surface sterilant. It
alkylates proteins, RNA, and DNA in microorganisms, and replaces labile
oxygen with ethylene hydroxide. Bulk crystalline materials can occlude vegetative
bacterial cells or spores, with crystals. Consequently, ethylene oxide will
not reach them. The final step prior to sterilization is aseptic recrystallization.
232 Chapter 14
Ethylene oxide is colorless and aromatic. The threshold limit for the
odor is 700 ppm. The OSHA specification for worker exposure is 10 ppm.
The toxicity of ethylene oxide is similar to ammonia. It causes conjunctival
and respiratory irritation, dizziness, headaches, and vomiting, is known to be
mutagenic, and may be carcinogenic. Some by-products of ethylene oxide (bp
283.8 K) are ethylene glycol (bp 471.9 K) and ethylene chlorhydrin (bp 401.4
K). Pure ethylene oxide is flammable and explosive. It is generally mixed with
propellant (88:12) or carbon dioxide (90:10). Ethylene oxide polymerizes in
the liquid state and may plug lines or spray polymerized sludge on the product.
The product expires in 90–120 days because of the polymerization.
Ethylene oxide inactivates all microorganisms. The cidal rate depends
on the gas concentration, sterilization temperature, exposure time, and water
content of the microorganism. Inactivation follows classical first-order kinetics
and is irreversible. Relative humidity is synergistic with ethylene oxide. At
30–60% relative humidity the microorganism hydrates. The water acts as a
vehicle to transport the gas through polyethylene and polypropylene. Polystyrene
traps ethylene oxide and dissipates it over years and thus is not appropriate
for ethylene oxide sterilization. Temperatures of 313–333 K are suitable
for heat labile items. Cycle times are longer if temperatures, relative humidities,
or ethylene oxide concentrations are lower. Generally, concentrations of
350–700 mg/mL are employed. Cycle times vary from 4–12 hr.
Following sterilization the load is degassed, a dynamic process wherein
filtered air is passed over the product for 12–72 hr. Degassing is usually performed
in the treatment chamber but may be moved to a sterile facility. The
process is monitored with Bacillus subtilis var. niger as a biological indicator.
Spore strips (106 spores/strip) can be purchased for this purpose. During validation
the load is probed with thermocouples in addition to B. subtilis spore
strips. Gaseous mixture is sampled from different points in the sterilizer for
gas chromatographic analysis.
14.4 STERILE FILTRATION
Several filter geometries are available to perform sterile filtration, including
flat membranes in a stainless steel press (0.293 m), pleated membranes
housed in stainless steel cartridges, and stacked plates in the form of flat segments
of membrane filters.
Matrix filters consist of fibers with pores having a depth of up to 1.2
104 m. Cellulose nitrate may be dissolved in the highly volatile solvents
amyl acetate, ether, or dioxane. A gel-forming solvent, such as acetone, ethaSterilization
nol, or propanol, may be added. The mixture is poured on a flat plate and
placed in a controlled temperature environment to dry. Pore size depends on
the gel-forming solvent concentration. Other substances, such as other cellulose
esters, acetate, and butyrate, polyamides (nylon), polysulfones, fluorocarbons
(Durapore membranes), either polyvinylidenedifluoride (hydrophobic)
or surface-modified with organic amides (hydrophilic); acrylic polymers;
and polyvinyl chloride, may be used as filter material. To make some membranes
hydrophilic surfactants may be added, including Tween 80, Triton X-
100, hydroxypropyl cellulose, and glycerol. Sieve filters are made of polycarbonate
(Nucleopore 105 m thick). Collimated uranium fission products form
nucleation tracks in film. Etching chemical exposure determines pore size.
14.4.1 Adsorption and Screening
When wetted almost all membrane filters have negative charge. Bacteria have
a similar negative charge and do not necessarily remain on the filter. Filters
with other characteristics can be selected under these circumstances. Positively
charged (AMF Zeta Plus Membrane) or protein- and peptide-adsorbing (Pall
Posidyne Nylon 66) filters can be selected.
Ionic strength, pH, pressure, and flow rate all effect particle adsorption.
The flow rate Q through a filter is
where Ci is the inherent resistance of the filter to flow (a function of void
volumes), A is surface area, P is pressure, and V is viscosity.
Filters are related according to nominal pore size and absolute pore size
(the largest pore in the filter). Hence, a pore size distribution exists.
14.4.2 Filter Integrity
Filter integrity can be evaluated by several techniques. The destructive test
involves filtering a suspension of bacterial cells (Pseudomonas diminuta,
0.3 106 m) through a 2 107 m filter. Six liters of suspension containing
1 1010 org/L grow up on an agar plate. Downstream of a 106-m filter there
should be nothing and an 8-log reduction should have occurred. The bubble
point test, performed before and after sterile filtration, assumes that pores can
be characterized as capillaries. When totally wetted all capillaries should be
234 Chapter 14
full of water or solution. The pore length is generally much greater than the
diameter. Pressure is applied to the wetted filter. The bubble point pressure
(P) may be described as follows:
where ? is the surface tension (7.2 N/m2), ? is the contact angle, and D is the
14.4.3 Product Development Considerations
A specified area of filter must be soaked in a specified volume of product for
a designated time. The accelerated stability of a product in the presence of a
filter can be performed at 313–333 K for 60 days. The extent of damage,
nature and quantity of extractables, and potency of active ingredients must be
evaluated prior to selection of a filter for a particular process.
Bioprocess engineering utilizes microbial growth to produce therapeutic
agents of biological origin. In the current climate of recombinant (DNA) technology
this often means using host microorganisms as expression vectors for
a product, most frequently a protein or peptide.
Many of the principles employed in bioprocess engineering encompass
fundamentals and unit processes described elsewhere in the text. All of the
fundamentals apply, namely fluid flow and heat and mass transfer. Therefore,
unit processes such as pumping (pumps and pipes), sterilization, filtration,
heating, and ventilation have an application in bioprocessing. This section
covers topics not dealt with earlier: pharmaceutical water systems, bioreactor
design, integration and control systems, and product purification.
15.1 PHARMACEUTICAL WATER SYSTEMS
In general, pharmaceutical water systems employ combinations of technologies
described earlier. However, since the objective is unique, we review some
of these methods while introducing issues which are specifically related to the
236 Chapter 15
production of different qualities of water (Kuhlman and Coleman, 1991). Table
15.1 summarizes water treatments and uses.
15.1.1 Pretreatment and Sources of Water
Potable (drinking) water is not suitable for pharmaceutical purposes. The EPA
limits allow 500 recoverable microorganisms per milliliter, none of which
can be coliform organisms in drinking water. Drinking water requires further
treatment in order to meet the requirements for use in pharmaceutical processes.
Water is pretreated to remove materials likely to be detrimental to the
purification equipment. This pretreatment takes many forms. A multimedia
bed (different gravels in a carbon steel vessel) is used to remove solids from
the municipal water. Common problems include high bacterial or particulate
counts in the effluent. This technique is highly inefficient because the container
is susceptible to corrosion, the media is porous, and the piping contains dead
legs, cracks, and crevices.
15.1.2 Water for Injection
Water for injection (WFI) is prepared following pretreatment and further purifi-
cation, including ion exchange, distillation, and reverse osmosis.WFI must contain
50 recoverable bacterial colonies or less per milliliter for immediate use. Its
preparation by distillation or reverse osmosis renders it sterile, from which it
must be protected from contamination by endotoxins or microorganisms.
TABLE 15.1 Water Treatment
Type of water Treatment steps
Water source (reservoir, ground) Prefilter, sand, gravel
Chemical treatment (Cl, Fl)
Drinking water Multiple ion exchange (anion, cation)
Charcoal (Cl, Fl)
Multiple filters (size discrimination)
Source: Modified from Groves (1988).
Zeolite water softener is an exchanger that replaces calcium ions with magnesium
ions. Regeneration of the resin is necessary and usually conducted with
brine. Consequently, chloride ions which attack certain types of composite
membranes may enter the feedwater stream. Bacteria may also propogate in
Activated carbon filters employ a carbon steel tank filled with gravel
and covered with activated charcoal (anthracite). Again, this is a source of
bacteria and chloride ions.
Deionized water is produced by passing treated water through a mixed
bed or a two-bed cation/anion exchange resin system. The resulting water is
deionized because hydrogen ions replace cations and hydroxyl ions replace
anions. Deionized water has little or no bacteria and is easily regenerated.
The potential for microbial contamination during some of these purifi-
cation procedures renders additional steps necessary to prepare water suitable
for pharmaceutical processing.
Distillation separates water from other soluble and insoluble components by
elevating the temperature to that at which vapor forms (100°C) in a boiling
chamber and then condensing the vapor into a receiving vessel. The nature
of hydrogen bonding of water imparts a unique property to water. Although
it can be raised to 100°C with a relatively small amount of energy (80 kcal),
it takes almost seven times this amount (540 kcal) to break the hydrogen bonds
and release the water as steam at the same temperature. Consequently, in the
condensation phase eight times as much water at 5°C (refrigeration temperature)
is required to condense the water as steam. These large exchanges of
heat may be used in an efficiently designed still to heat up water entering a
second still. Alternatively the combined gas law can be utilized by compressing
vapor and therefore elevating its temperature (vapor compression still).
Reverse osmosis units vary in design, construction materials, and membrane
type more than any other unit in the pretreatment process. Usually it is a singlepass
system (may not eliminate chlorides). Transmembrane pressures must be
maintained. Osmosis is the process whereby a solution separated from pure
water by a semipermeable membrane induces movement of water toward the
238 Chapter 15
region of high solute concentration. This would ordinarily give rise to an osmotic
pressure. If pressure is applied against the osmotic pressure head, the
flow of water can be induced in the opposite direction, thereby reversing osmosis.
This process, which may be regarded as a form of filtration, removes
materials of sizes down to 200 D molecular weight in a sequence that usually
removes particulates and viable microorganisms and contaminating molecules
sequentially according to size (i.e., large particles, bacteria, viruses, pyrogens,
and ions). Softened pH-adjusted water is used to maximize the efficiency of
ion removal. The ionic radius affects ions removal, with multivalent ions more
readily removed than monovalent ions.
15.1.3 Storage and Distribution
The water temperature at the point of use must be such that the water can be
handled without risk. A recirculating ambient loop or a heat exchanger at the
point of use may be required. A sophisticated system of loops and heat exchangers
is required to elevate the water temperature before it returns to a
storage tank. One approach is to maintain an ambient loop during the day and
heat the water during the night. If the water is maintained at ambient temperatures
for not more than 24 hr, the conditions do not violate cGMP regulations.
15.1.4 Quality Control
Conductivity and resistivity are convenient on-line measures that ensure water
quality. As it circulates, water loses resistivity, stabilizing at about 5 M?/cm.
Some corrosion may take place in the distribution system, which may ultimately
lead to adulteration of the water.
Endotoxin levels are monitored by sampling. Sampled water may be
subjected to the limulus amebocyte lysate test to measure the presence of
endotoxin. This in vitro assay was predated by rabbit pyrogen testing, which
involves monitoring the rabbit’s core body temperature in response to injection
with a water sample. Endotoxin may cause mild immune responses which will
be detected by an increase in body temperature.
Validation of any process is required in pharmaceutical manufacturing. The
validation master plan outlines the required content and method of preparing
validation documentation. Validation is integral to the start-up of the entire
plant. Three major sections of the validation procedure are
1. Installation qualification (IQ): establishes and documents that the
unit or system was installed correctly per the manufacturer’s speci-
2. Operational qualification (OQ): establishes and documents that the
unit or system operates as intended
3. Production qualification (PQ): establishes and documents that the
unit or system can fulfill its intended purpose on a reproducible
basis when challenged with realistic worst-case conditions
The master plan should include a listing of documentation included in
validation files for each system (reference files, vendor data, calibration reports,
standard operating procedures, and inventories). Critical path schedules,
manpower estimates, operator responsibilities, auditing procedures, and outside
validation resources should be included in validation documentation.
Outside validation resources should be recruited. They may include purchase
of validation protocols from commercial vendors, acquisition of data
on validation exercises from equipment vendors, use of testing laboratories for
performance qualification, contracting with other qualified agencies to perform
water sampling, and, in the extreme case, contract with a qualified agency to
perform the entire validation exercise (including writing protocols and performing
validation testing). The scale of operation and internal resources dictate
which option to select.
15.2 CELL KINETICS
The principles of bioreactor design require understanding the phenomena intended
to take place in these controlled environments. This relates to the
growth kinetics of prokaryotic or eukaryotic cells derived from animal, plant,
or microbial origins. The complexity of biochemical reactions and transport
phenomena render accurate predictive mathematical modeling impossible
since the system consists of multiple phases having many components. Attempts
have been made to estimate growth kinetics based on a matrix combining
unstructured or structured approaches to distributed or segregated models
(see Table 15.2).
240 Chapter 15
TABLE 15.2 Various Models for Cell Kinetics
Population Unstructured Structured
Distributed Single cells are homogeneously Cell aggregates are homogedistributed
throughout the neously distributed throughout
culture the culture
Segregated Single cells are heterogeneously Cell aggregates are heterogedistributed
throughout the neously distributed throughout
culture the culture
Source: Modified from Lee (1992).
15.2.2 Growth Cycle
The growth cycle of cells has been documented for over a century. It consists
of six phases which describe cells growth from an initial period of accommodation
or acclimatization through to exhaustion or overpopulation of the environment.
The lag phase, which occurs when cells are introduced into a medium,
is a period of time when no net change in cell number occurs. This
phase is followed by an accelerated growth phase when the cell numbers start
to increase and the division rate increases to reach a maximum in the exponential
growth phase, where the division rate is proportional to d Ln Cn0/dt, which
is constant at maximum value. Following this maximal growth rate a deceleration
in both growth and division occurs. The cell population finally reaches
a maximum value, but the death of growing cells occurs as nutrients are depleted.
15.2.3 Monod Kinetic Parameters
Much has been written regarding the growth of cells in fermenters and chemostats
(Lee, 1992). The kinetic considerations in these systems are briefly summarized
The Monod equation is an empirical expression describing the effect of
substrate concentration on the specific growth rate, and it takes a form similar
to Michaelis-Menton enzyme kinetics or the Langmuir adsorption isotherm:
where µ and µmax are growth rate and specific growth rate at half-maximum
value, and Ks and Cs are a system coefficient and concentration of the limiting
substrate in the medium, respectively.
Monod kinetic parameters specific growth rate at half-maximum, and
the system coefficient cannot be estimated with a series of individual studies
as easily as Michaelis-Menton kinetics for enzyme action. The initial reaction
rate can be measured accurately as a function of substrate concentration for
enzymes. Cell cultures undergo an initial lag phase in growth in which Monod
kinetics do not apply. Even though the Monod equation has the same form
as the Michaelis-Menton equation, the rate equation is different.
The Michaelis-Menton equation describing enzyme activity takes the
where Cp, Cs are product concentration and substrate concentration, respectively,
and Km is the rate constant. The Monod equation takes the form
Note that the cell concentration term Cx, in the Monod equation is absent from
the Michaelis-Menton equation.
Measuring the steady-state substrate concentration at various flow rates,
one can test various kinetic models and estimate the value of the kinetic parameters.
A linear relationship can be derived:
where µ is equal to the dilution rate (D) for a chemostat. If a certain microorganism
follows Monod kinetics, the plot of 1/µ versus 1/Cs yields the values
of µmax and Ks by reading the intercept and the slope of the straight line. This
plot is the same as the Lineweaver-Burk plot for: Michaelis-Menton kinetics.
Since 1/µ approaches infinity as the substrate concentration decreases, the
data is weighted too heavily at low substrate concentrations and insufficiently
at high substrate concentrations. Nevertheless, this approach has the advantage
of showing the relationship between the independent (Cs) and dependent variables
(µ). Figure 15.1 illustrates the manner in which the specific growth rate
may be derived from a plot of reciprocal dilution rate versus reciprocal substrate
242 Chapter 15
FIGURE 15.1 Reciprocal dilution rate for a chemostat plotted against reciprocal substrate
15.3 BIOREACTOR DESIGN
A bioreactor is a device within which biochemical transformations are caused
by the action of enzymes or living cells. The simple method of shaking cells in
a flask to enhance oxygenation through the liquid surface and to aid mass transfer
of nutrients without cell damage has to be scaled up for industrial processing.
The use of biotechnology in the manufacture of pharmaceuticals is of
increasing interest. Consequently, these techniques require attention in the
planning of unit processes.
Bioprocessing can be considered in terms of small-scale bioreactors, or
fermenters, and the translation of such processes into large-scale economically
viable production operations (Klegerman and Groves, 1992; Tatterson, 1994).
Bioprocessing is by no means a new field. The topicality of this subject is
due to the increasing interest in the use of isolated cells and microorganisms
as manufacturing tools. It might well be argued that the technology was developed
millenia ago for the purposes of wine and beer production. More recently,
FIGURE 15.2 Types of bioreactors.
the use of attenuated microorganisms or isolated antigenic materials for vaccination
resulted in further developments. In the last decade interest in genetic
engineering and manipulation of the genetic code of certain microorganisms
has produced a revolution in pharmaceutical manufacturing.
The major difference between a biotechnological process and other pharmaceutical
manufacturing operations is the need for a bioreactor (Figure 15.2).
A bioreactor may be required to produce expressed proteins utilizing bacteria,
yeast, insect, or mammalian cells [ref]. Table 15.3 illustrates the various processes
(Prokop and Bajpai, 1991). It would be difficult to describe the various
TABLE 15.3 Biotechnological Processing
Stage Activity Impact
First Reactions: catabolic, anabolic, enzymatic, degrada- Molecular
tion, and stoichiometric
Second Metabolite translocation; compartment differentia- Individual cells
tion; genetic changes
Third Growth; dispersed, segregated, and mixed culture Population of cells
Fourth Reaction mixers: mass and heat transfer; dynamics Bioreactor
and control; coupled to processes
Fifth Separation unit operations; process synthesis and in- Process design
tegration; quantitative and qualitative evaluation
for process design
244 Chapter 15
FIGURE 15.3 Bioreactors: (a) stirred tank reactor; (b) airlift fermenter.
bioreactor elements and their permutations. Some of the simplest examples
of bioreactors are shown in Figure 15.3.
Some important factors in bioreactor design are (1) sterility, (2) broth
rheology, (3) mass transfer, (4) mixing, (5) heat transfer, (6) suspension homogenization,
and (7) shear sensitivity of microorganisms. The importance
of these design considerations depends on the nature of the biological systems
The presence of organized structures in the form of mycelial cells or biopolymers
tends to induce non-Newtonian properties in broth. The power law of
plastic systems (Martin, 1993) may be employed to describe broth rheology.
The viscosity and shear rate are related to the concentration of cell mass in
the system. These correlations are species-specific and depend on the stage
of growth in the cell cycle.
15.3.3 Mass Transfer
Although all nutritient, waste product, and cell integrity issues in growth
may be considered in terms of mass transfer, the most notable of these
is oxygen transfer for aerobic growth. A maximum uptake rate of oxygen
exists for any system, and the design should be based on an understanding
of this limitation. Also the oxygen uptake rate of cells shows a saturation
dependence on dissolved oxygen concentration. Assuming a pseudo steady
state of dissolved oxygen concentration, a design value of gas-liquid mass
transfer coefficient ?La for a biological system can be specified for a specific
Maximum oxygen demand
C*L CL, critical
The gas-liquid mass transfer coefficient often changes during the course of
fermentation because of changes in broth rheology or through additives, such
as antifoaming agents.
Concentration and temperature are influenced by mixing in bioreactors. Total
homogeneity within a system is rarely, if ever, achieved and local variations
in mixing within vessels may affect growth, metabolism, or other molecular
expression phenomena. Operating conditions influence terminal mixing time
(time to reach designated variability associated with complete mixing)
and mean circulation time (time to circulate through specific region once).
Characterization of mixing times and the influence of geometric features of
reactors under different operating conditions and scales of operation (bench,
pilot, and full scale) are important if efficiency (time and cost) is to be optimized.
15.3.5 Heat Transfer
Heat is dissipated mainly by convection across the walls of the jacket or coils.
In aerated systems, metabolic heat production is correlated with oxygen uptake
rate. The maximum metabolic load should be considered in design calculations
as in gas-liquid oxygen transfer.
Handbook values are available for heat transfer on the jacket side, vessel
side, and in tubes. In general, heat transfer becomes a problem only in very
large scale operations and in dense microbial populations,which are frequent
with recombinant cells. In other cases, gas-liquid mass transfer and mixing
are the major concerns.
246 Chapter 15
Agitation is required to maintain suspensions of the cells. Agitated bioreactors
are designed to maintain complete suspension (no cell mass at the bottom of
the reactor) or a homogeneous suspension. These terms imply stable flocculations
(aggregates) in suspension or homogeneous cell distribution throughout
The mechanism of shear damage to the cells is not clear. Mycelial or
protozoan cells exhibit shear-rate-limited growth, and cell damage has been
monitored by analyzing the concentration of low-molecular-weight nucleotides
in the culture broth.
15.4 BIOPROCESSING PLANT DESIGN
The foregoing discussion focused on major elements of bioprocessing activities,
namely water treatment and reactor design. Heating, ventilation, and air
conditioning (HVAC) and steam production, described elsewhere in this text,
are also requirements for bioprocessing. The design of a bioprocessing plant
is subject to current good manufacturing practices (cGMPs), which emphasize
control and reproducibility. It is clear that the application of such principles
to other pharmaceutical processes of a more mechanical nature may readily
be achieved. The biological nature of the processes being controlled challenges
the engineers and scientists involved.
As with any regulated process specifications must be prepared in advance
and acceptance criteria established for subsequent quality control
checks. Validation of the facility and process should be considered essential to
design, construction, and start-up. Documentation of design and construction
ensures appropriate specifications for subsequent validation.
15.5 PROTEIN PURIFICATION
The purpose of bioprocess engineering is to utilize resources necessary to
promote the growth of microorganisms in a controlled environment for the
purpose of producing a product of biological origin. Note that additional processing
is required to purify the product obtained from these systems. The
purification from cell culture of soluble proteins may be conducted by combining
traditional purification steps (Harrison, 1994). These steps are shown in
Table 15.4. Each step focuses on particular physicochemical properties; for
TABLE 15.4 Purification Steps of Soluble Proteins
Chromatography Adsorption Ion exchange (IEC) Hydrophobic
interaction (HIC) Gel Affinity Highpressure
liquid chromatography (HPLC)
Precipitation Ammonium sulfate
Buffer exchange Ultrafiltration
example, ion exchange, hydrophobic interaction, and gel chromatography separate
molecules based on charge, hydrophobicity, and molecular size, respectively.
Inclusion bodies with complex tertiary structures undergo additional
steps, including washing, solubilizing, and refolding of proteins before further
purification steps are adopted.
As with all of the foregoing processes, validation of purification steps
is required. Indeed, the sequence of designing protein purification processes
may be described as follows (Nelson, 1991):
• Stepwise recovery yields
• Impurity removal
• Scalability of protein purification steps
• Validation of protein purification steps
Biotechnological innovation occurs as the result of complex integrated
bioprocesses based on molecular and cellular biology. The key processes have
been described briefly in this chapter, and discourses of some length are available
on each of these topics in the literature. Since the next generation of
pharmaceutical products is likely to be developed by these methods, readers
are strongly encouraged to familiarize themselves with these topics and with
the more fundamental issues of molecular and cellular biology not covered in
this text (Bolsover et al., 1997).
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Absorption, 52, 175, 176
Acetone, 113, 232
Additives, 189, 217, 245
Adhesion, 69, 70
Adiabatic cooling line, 84, 87, 98
Adiabatic saturation temperature
Adsorption, 120, 164
Langmuir isotherm, 240
Aerosol(s), 78, 216
bacteria, 168, 169, 170
methylene blue, 170
Agglomeration (see Aggregation)
Aggregation, 76, 177, 188, 189,
193, 194, 203, 209, 214, 216
Agitated vessels, 49, 136
Agitation, 160, 211, 246
Agitator blades, 102, 210, 211
Air, 34, 52, 69, 83, 85, 112, 164,
165, 185, 187, 194
conditioning, 79, 80, 246
filter (see Filter(s): air)
flow, 101, 105, 170
molecular weight, 82
temperature, 81, 108
velocity, 90, 102, 167, 169
Alcohol, 113, 148
sulfate, 231, 247
Amyl acetate, 232
of inclination, 71
of repose, 70
Antibiotics, 103, 104, 160, 205
Antifoaming agents, 137, 245
Asbestos, 165, 170
Ascorbic acid, 87
Aseptic conditions, 103, 104, 231
Aspirin, 87, 224, 225
Atomization, 106, 170
Auger feed, 217, 220, 221
Azeotrope(s), 142, 147
Bacillus pumulis, 231
Bacillus subtilis, 168, 232
Bacteria, 79, 103, 104, 165, 183,
229, 230, 233, 237, 238,
Bacterial aerosols (see Aerosol(s):
Baffles, 125, 209, 211
Barrel roller, 77
Benzene, 113, 148
Bernoulli theorem, 6, 9, 12
Binder, 75, 217, 225
Bioprocessing, 235, 243
Bioreactor design, 235, 239, 242
Blades (see Agitator blades)
Blending (see Mixing)
Blisters, 78, 227
Blood components, 103
Blower(s), 29, 34
Boiling, 37, 49, 108, 131
liquid(s), 76, 126, 128, 129,
point, 96, 130, 135, 138, 139,
141–143, 145, 148
Bond angles, 68
Bond’s theory, 180
Boundary layer, 2, 22, 25, 60, 61
Bourdillon slit sampler, 169
Bourdon gauge, 5
Bragg’s law, 68
Bubbles, 48, 49, 76, 104, 137,
point, 233, 234
Cake(s), 112, 124, 150–160, 164
Caking, 75, 102, 160
Calandria, 112, 126, 134, 135
Capillary, 27, 152, 233
forces, 3, 93, 96
Capsule(s), 78, 216, 219, 222,
Cell, 228, 233, 243, 244, 246
growth kinetics, 239
Cellulose, 156, 165, 225, 229
force (see Force: centrifugal)
Centrifugation, 56, 117, 188
Centrifuge, 158, 172, 173
Ceric sulfate, 231
137Cesium, 230, 231
Charge, electric, 69
reaction, 67, 124, 212
Chlorinated hydrocarbons, 114
Chutes, 72, 75
Citric acid, 224
Clarification, 150–152, 170
Classification, 174, 179, 192, 193
Clostridium welchii, 165
60Cobalt, 230, 231
of contraction, 12
of discharge, 10–12
of friction, 188
Coffee, 108, 110
Cohesion, 69, 70
Colorant, 219, 225
Columns, 144, 145
Comminution (see Milling)
Common ion, 123
Compressibility, 3, 155, 217
Compression, 156, 176, 217, 220,
Compressor(s), 29, 30, 217
Compton effect, 230
Concentration gradient(s), 15, 64,
Condensate, 112, 117, 129, 146
Condensation, 51, 67, 93, 145
Condenser(s), 104, 117, 137, 149
Conduction, 15, 36, 40, 41, 61, 96,
Contact angle, 234
Contamination, 40, 111, 182, 236,
Convection, 36, 41, 61, 97, 205
Cooling, 37, 103, 119
Crushing (see Milling)
Crystal, 171, 177, 183, 200
growth, 68, 118–121, 124
lattice, 69, 120, 183
material, 177, 178, 186
Crystallization, 56, 63, 64, 67, 76,
113, 115, 117–119, 123,
125, 135, 154, 174, 212,
Cyclone(s), 106, 136, 137, 165,
185, 196, 197
Decomposition, 102, 132,
Degradation, 132, 135, 183,
Demixing (see Segregation)
Density, 3, 4, 7, 23, 29, 35, 51,
62, 171, 199, 216
bulk, 66, 71, 73, 75, 108
fluid, 20, 36, 134, 211, 213
particle (see Particle density)
surface energy, 68
true, 68, 73
Deoxyribonucleic acid (DNA),
recombinant technology, 235
Dewatering, 157, 160, 164
Dew point, 52, 85
Dies, 75, 78, 223
Differential scanning calorimetry,
Diffusion, 3, 15, 52, 56–58, 61,
62, 92, 93, 114–116, 120,
137, 157, 159, 165, 174,
Brownian, 154, 167, 172
vapor, 50, 92, 96
Diffusivity, 58–60, 62, 115
Diluent, 217, 225
fluid flow, 18, 25
heat transfer, 44
mass transfer, 62
Disintegrant, 217, 225, 226
Disperse systems, 1, 213
Dispersing agents, 195
Dissociation constant, 216
Dissolution, 56, 63–65, 68, 111,
115, 116, 175, 212, 216,
Distillation, 56, 64, 128, 138, 139,
143, 146–148, 236, 237
Dose, 67, 72, 203, 219, 231
batch, 87, 98
hot air ovens, 98, 108
continuous, 87, 105
drum dryers, 108
fluidized bed, 96, 101, 102,
spray, 67, 76, 96, 105, 107,
Drying, 34, 56, 57, 63, 64, 86, 87,
89, 90, 92, 94, 95, 98,
104–106, 158, 160, 171,
174, 175, 182
constant rate period, 92, 96
first falling rate period, 92, 95
freeze, 102–104, 117
rate curve, 92
second falling rate period, 92, 95
Duhring’s rule, 130, 131
Dust(s), 120, 168, 175
Dye, 13, 14
Eddies, 11, 15, 25, 57, 210
Electromagnetic waves, 37
Electron(s), 36, 79
precipitation, 79, 151, 165
Elutriation, 101, 193, 195–
Endotoxins, 236, 238
Energy, 67, 230
friction degradation, 8, 10,
grinding, 178–180, 182
kinetic, 25, 29, 32, 119
pressure, 25, 29, 32
Enteric polymer, 224
Enzyme(s), 110, 219
Ethanol, 142, 226, 232
oxide (see also Sterilization),
Euler’s law, 68
Eutectic mixture, 103
Evaporation, 57, 86, 89–94,
96, 105, 108, 112, 128,
Evaporator(s), 37, 45, 131, 133,
forced circulation, 135
Excipient, 77, 108, 217, 219
Extemporaneous preparation, 220
Extraction, 64, 110, 112, 115, 116,
148, 181, 211, 247
Extract(s), 96, 108, 112, 175
Fatty acids, 139
Ferric oxide, 207
glass, 169, 170
Fick’s law, 58, 60
Filler (see Diluent)
coefficient(s), 42, 43, 45, 51,
two-film theory, 63
area, 153, 170
bag, 106, 185
media, 164, 168
pressure, 158, 161, 171
resistance, 152, 153
vacuum, 158, 159, 171
Filtration, 29, 56, 117, 150–152,
157, 159, 160, 162–165,
170, 171, 233, 235
centrifugal, 171, 172
sterile (see Sterilization)
Flocculation, 155, 157
Flow, 15, 18, 24, 69, 115
axial, 210, 211
friction head, 8
laminar, 10, 13, 14, 19, 22, 28,
46, 57, 61, 173, 213
powder, 72, 86
properties, 77, 117, 175, 213,
radial, 210, 212
rate-volumetric, 10–12, 17, 23,
27, 133, 152, 233
tangential, 210, 212
turbulent, 10, 13–16, 18, 21,
22, 41, 46, 57, 60, 61, 63,
64, 102, 135, 210, 211,
flow, 1, 218
incompressible, 8, 9
non-Newtonian, 2, 244
velocity, 22, 42, 76
viscosity (see Viscosity: fluid)
Fluidization, 66, 75, 101, 125
Food and Drug Administration,
centrifugal, 32, 171, 172, 197
drag, 24, 194, 195
frictional, 22, 23, 76
viscous, 25, 156
gravitational, 69, 172, 195, 197
momentum, 69, 194
shear, 195, 207, 211, 213, 227
van der Waals, 69
viscous, 16, 22, 25, 173
Formulation, 183, 215, 220
Fourier’s equation, 38
Fractionation, 138, 144
Friability, 97, 189
Friction, 15, 35
factor, 20, 21
Frothing, 97, 104
Fruit juice, 102
Fumeric acid, 224
Gamma (?) rays, 229
Gas(es), 29, 46, 57, 58, 60, 62, 63,
66, 69, 76, 85, 90, 107,
108, 150, 154, 245
Gelatin, 93, 218, 219
Gel chromatography, 247
Glass(es), 36, 118, 165
Globules, 200, 211
Granular solids, 72, 75, 91, 93, 95,
98, 102, 154, 168, 169, 171
magnesium trisilicate, 88
tablet, 100, 102
Granulating fluid, 76, 214, 217
Granulation, 66, 75, 100, 216, 217
compression, 217, 218
top-spray, 217, 218
Grashof number, 45
Gravitational constant, 4
Gravity, 51, 66, 77, 154
Grinding (see Milling)
Head (see also Pressure):
loss of, 11, 13
constant source, 49
flux, 48, 49, 96, 129
of crystallization, 117
of evaporation, 81–83
of fusion, 103
of sublimation, 105
radiant, 105, 228
sensitive materials. (see Thermolabile
Heat exchanger, 125
Heating, 105, 165, 235, 246
Heat transfer, 36, 38, 76, 81, 82,
97, 100, 126, 128, 129,
211, 218, 244, 245
coefficient, 42, 43, 48, 52, 83,
125, 126, 129, 131, 134,
convective, 96, 245
steady-state, 37, 40
High performance liquid chromatography,
Hopper(s), 71, 72, 75, 78, 221
Humidification, 79, 84
Humidity, 69, 79, 82, 85, 87, 88,
90, 92, 98, 165
relative, 80, 88, 232
diameter, 24, 28, 152
Hydrochloric acid, 142, 219
Hydrostatic(s), 3, 156
head, 131, 158
Hydroxyl ions, 237
dew point, 81
wet bulb depression, 81, 83
Hygroscopicity, 216, 222
Impeller(s), 75, 126, 209–
Inclusion bodies, 247
Incompressibility, 3, 4, 6, 8, 9
capture, 166, 167
effects, 22, 23
dry powder, 226
pressurized metered dose,
area of, 107, 174, 211
Interstices, 3, 27, 116, 152,
Interstitial velocity, 153, 154
exchange, 236, 237, 247
Ionic strength, 233
Jacket, 128, 245
Kick’s law, 179
energy, 6, 8, 9, 10, 11
surface reaction, 121
Kirchhoff’s law, 52
Kozeny’s equation, 29
Lactose, 88, 108, 225, 226
Latent heat of evaporation, 81
Lattice group, 68
Leaching, 64, 110, 112, 114
Limulus amebocyte lysate,
Lineweaver-Burk plot, 241
Liquid(s), 1, 15, 29, 56, 60,
66, 143, 150, 154, 159,
163–165, 171, 173, 174,
175, 194, 199, 210–213,
viscous, 79, 131, 135, 136
Liquor(s), 109, 123, 124, 170
Lubricant, 217, 225
Lyophilization (see Drying:
Malic acid, 224
Manganese bronze pins, 219
Manometer, 5, 9, 13
Mass transfer, 56, 61, 76, 81, 107,
114, 116, 218, 244
coefficient, 63, 65, 82, 83, 90,
interfacial, 63, 64
Mechanical energy, 6, 8, 14
Media, 151, 152, 164, 165, 168
Meniscus, 88, 93, 94
Menstruum, 112, 115
Mesh (see Screen)
Metal(s), 36, 38, 164, 165
Michaelis-Menton kinetics, 240,
Microorganisms, 230, 242, 244
Milling, 67, 102, 114, 154, 175,
176, 177, 180, 181, 188,
192, 201, 226
ball, 183, 189, 207, 213
colloid, 192, 213
edge runner, 183, 184
fluid energy (micronizer), 191,
hammer, 183, 184, 186, 207
media (balls), 190
muller, 206, 207, 209
pin, 183, 187
roller, 192, 213
vibratory, 190, 191
paddle, 209, 211
planetary, 213, 214
ribbon, 209, 214
tumbler, 207, 209, 214
Mixing, 58, 77, 106, 198, 199,
208, 212, 213, 217, 244,
convective, 205, 209
degree of, 200
diffusive, 206, 207, 209
index of, 204, 209
rate, 208, 209
shear, 206, 209
Mixture(s), 202, 204, 205, 207
Moisture, 79, 228
content, 68, 79, 86, 87, 89, 219
critical content, 92, 94, 95
Molecules, 200, 238
Momentum, 15, 23
transfer, 14, 15
Monod equation, 240, 241
Mucosal irritation, 232
Mycelial growth, 160, 244, 246
Nitrobenzene, 138, 139
Nonporous materials, 87, 91
Nucleation, 118–122, 125, 154
Nusselt number, 45
Nutsche, 158, 161
Nux vomica, 110
Occupational Safety and Health
Odoriferous elements, 139
Ointments, 184, 186
Organoleptic properties, 216,
Orifice, 11, 73
area of, 12
reverse, 236, 237
Osmotic effects, 93
Paddle(s), 112, 210, 212
Pan speed, 76
Parenterals, 150, 151, 175, 215
Particle(s), 28, 29, 66–68, 94,
108, 152–154, 160, 170,
178, 192, 202, 203, 205,
207, 213, 215, 227,
density, 26, 172, 201, 203, 209,
packing, 72, 73, 75, 78
shape, 66, 68, 74, 101, 122,
164, 201, 203, 209, 216,
size and distribution, 66, 74–77,
94, 95, 101, 113–115, 122,
126, 154, 155, 158, 164,
169, 175, 177, 179, 189,
194–196, 201, 203, 209,
size reduction, 174, 179, 180,
Particulate matter, 151, 165
Partition coefficient, 216
Pastes, 184, 192, 213, 214
Percolation, 111–113, 116
Permeability, 28, 29, 111–
113, 115, 154, 155, 158,
coefficient, 27, 28, 152, 153,
pH, 123, 124, 219, 233
Phase diagram, 141
Photoelectric cell, 170
Pipe, 13, 15, 16, 18, 24
diameter, 15, 16, 20, 23, 46
length, 16, 41
roughness, 15, 20, 21
Pitot tube, 12
Planck’s constant, 229, 230
Planetary mixer, 77
Plastic(s), 36, 164, 192, 213,
Poiseuille’s law, 15, 16, 21, 28
Polyamides (nylon), 233
Polymorphism, 68, 216
Polyvinyl chloride, 233
Pore(s), 88, 94, 95, 152, 157, 164,
Porosity, 28, 29, 73, 74, 115, 153,
Porous materials, 3, 38, 151, 152,
170, 175, 236
Potency, 108, 222, 231
Pour, 69, 74
Powder(s), 66, 113, 156, 164, 173,
175, 192–194, 202, 203,
feeding/filling, 66, 86
flow (see Flow: powder)
sample thieves, 77
transport, 66, 77
Power, 9, 15, 20
Prandtl number, 45, 63
Precipitation, 67, 123, 124, 150,
Pressure, 4, 7, 9, 29, 58, 62, 67,
93, 105, 106, 113, 127,
129, 153, 156, 223, 233
atmospheric, 5, 102
bubble point, 234
difference, 152, 156, 164
drop, 15, 16, 35, 76, 147
energy, 6, 7, 9, 11
head/height, 5, 8, 33
partial, 58, 82, 90, 138
vapor, 88, 103, 130, 131, 138,
140, 141, 226
batch-operated, 37, 49, 133
Propellers, 210, 212
Protein(s), 103, 123, 132, 228,
231, 233, 243, 247
Pseudomonas diminuta, 233
Psychrometric charts, 80, 83, 88
Pump(s), 29, 37, 104
impeller, 32, 34
positive displacement, 30
priming, 30, 34
reciprocating, 30, 31
Punch(es), 75, 221
Purification, 117, 216
Purity, 118, 122, 216
rabbit test, 238
Radiation, 36, 52, 83, 100, 230
sterilization (see Sterilization: radiation)
Radius of curvature, 93
mixture, 205, 207, 208
number tables, 77
Randomization, 205, 213
Raoult’s law, 130, 140
Rectification, 144, 222
Reflux, 145, 146, 147
Resistance, 28, 42
thermal, 37, 38, 40
experiment of, 13–15, 22
number, 20, 23, 35, 62, 63
Rheology, 213, 244, 245
Ribbon blender, 77
Ribonucleic acid (RNA), 231
Rittinger, Karl von, 178
Rittinger’s law, 179
Rollers, 75, 192
Rotation, 186, 190, 211, 213
Salted out, 123
Sampling, 201, 205
Saturation curve, 84
Scale, 38, 131, 137
of scrutiny, 199, 203, 210
Scrapers, 131, 184
Screen(s), 75, 180, 185
Screening (see Sieving)
Sedimentation, 56, 160, 166, 175,
193, 197, 213
Segregation, 198, 199, 207, 208,
Semipermeable membrane, 237
Separation, 113, 129, 194, 195
particle size (see Classification)
phase, 136, 211
Septum, 150–153, 155, 156, 165
Serratia marcescens, 169
Shape (see Particle[s]: shape)
stress, 2, 16, 21, 22, 25, 71,
Sieving, 193, 194
Silica gel, 85
Silicon dioxide, 225
Silicone oils, 137
Size distribution (see Particle[s]:
size and distribution)
Slurry, 30, 32, 108, 116, 151,
160, 162, 171, 194, 195,
at drying surface, 92, 108
chloride, 123, 130, 170
starch glycolate, 225
Solid(s), 36, 56, 91, 117, 129, 150,
152, 154, 159, 165, 171,
173–176, 199, 212, 213,
dosage forms, 215–217, 226
waxy, 100, 183
Solubility, 68, 115, 123, 129,
Solute, 114, 116, 130, 157,
Solution(s), 86, 105, 114, 150,
151, 164, 234
spray, 174, 203, 217
Solvent(s), 99, 111, 112, 114, 115,
175, 217, 247
Specific heat, 37
Specific surface area, 68
Spinning disk, 106
Split cylinder, 71
Split plate, 71
Spore(s), 168, 229, 230
Spray drying (see Dryer: spray)
Stability, 89, 91, 117, 214, 216,
Stagnant fluid, 57, 60
Stagnation point, 12
Starch, 219, 225
Steam, 49, 79, 99, 129, 136, 139,
jet ejectors, 137
Stefan-Boltzmann law, 53
Sterile products, 166, 183, 244
Sterilization, 151, 163, 164, 165,
170, 228, 232, 235
heat, 228, 229
ethylene oxide, 228, 231
filtration, 228, 232
radiation, 228, 229
temperature, (see Temperature:
Stirrers, 125, 126
Stokes’ law, 26, 137, 172, 195,
Storage, 69, 71, 124, 231
stability, 88, 89
Streamline(s), 6, 13, 15, 16, 25,
27, 57, 173
Stress, 156, 175, 176, 178
Sublimation, 102, 117
Suction potential, 93, 94
Supercooling, 103, 118
Supercritical fluid, 227
Supersaturation, 120, 121, 122, 125
active agents, 189, 192, 211
area, 28, 29, 95, 152–155,
175, 178, 179, 182, 189,
tension, 3, 69, 76, 93, 106, 164,
Surfactant (see Surface: active
Suspension(s), 86, 105, 116, 195,
Tablet(s), 67, 72, 75, 78, 108, 216,
buccal, 224, 226
chewable, 223, 224
coating, 223, 225
machine/press, 201, 223
Tartaric acid, 224
Temperature, 36, 37, 58, 68, 83,
90, 92, 98, 102, 105, 107,
108, 114, 165, 183, 185
absolute, 37, 53, 131
adiabatic saturation, 83
boiling, 129, 131
gradient(s), 3, 38, 42, 43, 96,
sterilization, 229, 232
web bulb, 81, 82, 84, 87, 92,
Tensile strength, 68, 71
conductivity, 38, 39, 42, 51, 54
resistance, 40, 52
stability, 87, 115, 122, 129, 132
Thermolabile material(s), 107,
108, 123, 131, 133, 136,
Titanium dioxide, 219
Triton X-100, 233
Tube (see Pipe)
Turbine(s), 112, 210, 212, 213
Turbulence (see Flow)
Tween, 80, 233
Unit operations, 72
Vacuum, 100, 102–104, 131, 136,
152, 159, 161
Vapor(s), 48, 50, 100, 117, 136,
pressure (see Pressure: vapor)
Vaporization, 51, 86, 93, 128
Variable area meter, 13
V blender, 77
Velocity, 9, 10, 12, 15, 28, 76,
108, 129, 154, 210
gradient(s), 1, 2, 8, 17, 25, 208,
terminal, 108, 173, 194, 195
Vena contracta, 12
Ventilation, 34, 235, 246
Venturi meter, 10, 11
water treatment, 236
Vibration, 73, 74, 190
Virus(es), 173, 230, 238
Viscosity, 1, 15, 19, 23, 29, 51,
62, 106, 116, 129, 134,
175, 211, 213
fluid, 16, 20, 152, 195
Void(s), 112, 115, 154
volume, 28, 66, 74
Volatile materials, 171
Volume of fluids, 3
Washing, 160, 164
Water, 2, 4, 28, 35, 48, 86, 113,
142, 148, 234
hot, 79, 99
for injection, 236
molecular weight, 90
sensible heat of, 81
vapor, 79, 85, 90, 104, 117
Wavelength of light, 229, 230
Weight, 67, 72, 75
Wettability, 51, 217
Wetting, 40, 99
Yield, 118, 122
Zeolite, 236, 237
Zinc carbonate, 207