The Theory
`
`and Practice of Industrial
`
`4 Pharmacy
`
`LEON LACHMAN, Ph.D.
`Lachman Consultant Services, Inc.
`Garden City, New York
`
`HERBERT A. LIEBERMAN, Ph. D.
`H. H. Lieberman Associates, Inc.
`Consultant Services
`
`Livingston, New Jersey
`
`JOSEPH. L. KANIG, Ph.D.
`Kanig Consulting and Research Associates, Inc.
`Ridgefield, Connecticut
`
`THIRD EDITION
`
`FEBIGER- 1986- PHILADELPHIA
`
`TEVA EXHIBIT 1013
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`RBP_TEVA05022354
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`TEVA EXHIBIT 1013
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`

`
`Lea 8c Febiger
`600 Washington Square
`Philadelphia, PA 19106-4198
`UTSA.
`(215) 922-1830
`
`Library of Congress Cataloging in Publication Data
`Main entry under title:
`
`The Theory and practice of industrial pharmacy.
`
`.
`_
`Includes bibliographies and index.
`I. Lachman, Leon,
`1. Pharmacy.
`2. Drug trade.
`l929~
`.
`II. Lieberman, Herbert A., 1920~
`III. Kanig, Joseph L., 1921-
`[DNLM: 1. Drug
`Industry.
`QV 704 T396]
`RSl92.L33 1985
`ISBN 0-8121~0977—5
`
`84-27806
`
`Gl5’.l9
`
`First Edition, 1970
`Second Edition, 1976
`
`Copyright © 1986 by Lea 8c Febiger. Copyiight under the
`International Copyright Union. All Rights Reserved. This
`book is protected by copyright. No part of it may be repro-
`duced in any manner or by any means without wiitten pe1'~
`mission from the publisher.
`PRINTED IN THE UNITED STATES OF AMERICA
`
`Print No, 4 3 21
`
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`

`
`Contents
`
`;
`
`Section 1.
`
`Principles of Pharmaceutical Processing
`
`3
`1. Mixing
`EDWARD G. RIPPIE
`
`21
`2. Milling
`EUGENE L. PARROT .
`
`47
`. Drying
`ALBERT s. RANKELL, HERBERT A. LIEBERMAN, ROBERT F. SCHIFFMANN
`
`. Compression and Consolidation of. Powdered Solids
`KEITH MARSHALL
`
`66
`
`. Basic Chemical Principles Related to Emulsion and Suspension
`Dosage Forms
`100
`STANLEY L. HEM, JOSEPH R. FELDKAMP, JOE L. WHITE
`
`. Pharmaceutical Rheology
`JOHN H. WOOD
`
`. Clarification and Filtration
`s. CHRAI
`
`123
`
`146
`
`Section II. Pharmaceutical Dosage Form Design
`8. Preformulation
`171
`EUGENE F. FIESE, TIMOTHY A. HAGEN
`
`197
`9. Biopharmaceutics
`K.C. KWAN, M.R. DOBRINSKA, J.D. ROGERS, A.E. TILL, K.C. YEH
`10. Statistical Applications in the Pharmaceutical Sciences
`SANFORD BOLTON
`
`243
`
`Section III. Pharmaceutical Dosage Forms
`
`_
`293
`11. Tablets
`GILBERT S. BANKER, NEIL R. ANDERSON
`
`1
`346
`12. Tablet Coating
`JAMES A. SEITZ, sIIAs1II P. MEHTA, JAMES L. YEAGER
`
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`
`374
`. Capsules
`Part One Hard Capsules
`VAN B. HOSTETLER
`
`374
`
`Part Two Soft Gelatin Capsules
`J.P. STANLEY
`
`Part Three Microencapsulation
`J.A. BAKAN
`
`398
`
`412
`
`. Sustained Release Dosage Forms
`NICHOLAS G. LORDI
`
`430
`
`15. Liquids
`_].C. BOYLAN
`
`457
`
`,
`
`R
`
`479
`16. Pharmaceutical Suspensions
`NACIN K. PATEL, LLOYD KENNON*, R. SAUL LEVINSON
`17. Emulsions
`502
`MARTIN M. RIECER
`
`18. Semisolids
`
`534
`
`BERNARD IDSON, JACK LAzARUs*
`19. Suppositories
`564
`LARRY J. COBEN, HERBERT A. LIEBERMAN
`20. Pharmaceutical Aerosols
`589
`JOHN J. SCIARRA, ANTHONY J. CUTIE
`21. Sterilization
`619 ‘
`KENNETH E. AVIS, MICHAEL J. AKERS
`22. Sterile Products
`639
`KENNETH E. AVIS
`
`Section IV. Product Processing, Packaging, Evaluation, and
`Regulations
`
`23. Pilot Plant Scale—Up Techniques
`SAMUEL HARDER, GLENN VAN BUSKIRK
`
`681
`
`711
`24. Packaging Materials Science
`CARLO P. CROCE, ARTHUR FISCHER, RALPH H. THOMAS
`
`733
`
`25. Production Management
`J.V. BATTISTA
`V 760
`26. Kinetic Principles and Stability Testing
`LEON LACHMAN, PATRICK DELUCA, MICHAEL J. AKERs
`27. Quality Control and Assurance
`_ 804
`LEON LACHMAN, SAMIR A. HANNA, KARL LIN
`28. Drug Regulatory Affairs
`856
`WILLIAM R. PENDERGAST, RAYMOND D. McIvIURRAY*
`
`INDEX
`
`883
`
`*Deceased.
`
`xii - Contents
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`
`Drying
`
`ALBERT S. RANKELL, HERBERT A. LIEBERMAN,
`and ROBERT F. SCHIFFMANN
`
`There is hardly a pharmaceutical plant engaged
`in the manufacture of tablets or capsules that
`does not contain dryers. Unfortunately, the op-
`eration of drying is so taken for granted that ef-
`forts for achieving increased efficiency in the
`production of tablets do not include a study of
`drying. This chapter introduces the industrial
`pharmacist to the theory and fundamental con-
`cepts of drying.
`Definition. For the purpose of this discus-
`sion, drying is defined as the removal of a liquid
`from a material by the application of heat, and is
`accomplished by the transfer of a liquid from a
`surface into an unsaturated vapor phase. This
`definition applies to the removal of a small
`amount of water from moisture-bearing table
`salt as well as to the recovery of salt from the sea
`by evaporation. Drying and evaporation are dis-
`tinguishable merely by the relative quantities of
`liquid removed from the solid.
`There are, however, many nonthermal meth-
`ods of drying, for example, the expression of a
`solid to remove liquid (the squeezing of a Wetted
`sponge), the extraction of liquid from a solid by
`use of a solvent, the adsorption of water from a
`solvent by the use of desiccants (such as anhy-
`drous calcium chloride), the absorption of mois-
`ture from gases by passage through a sulfuric
`acid column, and the desiccation of moisture
`from a solid by placing it in a sealed container
`with a moisture-removing material (silica gel in
`a bottle).
`Purpose. Drying is most commonly used in
`pharmaceutical manufacturing as a unit process
`in the preparation of granules, which can be dis-
`pensed in bulk or converted into tablets or cap-
`sules. Another application is found in the proc-
`essing of materials, e.g., the preparation of dried
`aluminum hydroxide,
`the spray drying of lac-
`tose, and the preparation of powdered extracts.
`Drying also can be used to reduce bulk and
`
`weight, thereby lowering the cost of transporta-
`tion and storage. Other uses include aiding in
`the preservation of animal and vegetable drugs
`by minimizing mold and bacterial growth in
`moisture-laden material and facilitating commi-
`nution by making the dried substance far more
`friable than the original, water—containing drug.
`Dried products often are more stable than
`moist ones, as is the case in such diverse sub-
`stances as effervescent salts, aspirin, hygro-
`scopic powders, ascorbic acid, and penicillin.
`The drying reduces the chemical reactivity of
`the remaining water, which is expressed as a '
`reduction in the water activity of the product.
`Various processes for the removal of moisture
`are used in the production of these materials.
`After the moisture is removed, the product is
`maintained at low water levels by the use of
`desiccants and/or low moisture transmission
`
`packaging materials. The proper application of
`drying
`techniques
`and moisture-protective
`packaging requires a knowledge of the theory of
`drying, with particular reference to the concept
`of equilibrium moisture content.
`
`Psychrometry
`A critical factor in drying operations is the
`vapor-carrying capacity of the air, nitrogen, or
`other gas stream passing over the drying mate-
`rial. This carrying capacity determines not only
`the rate of drying but also the extent of drying,
`i.e.,
`the lowest moisture content to which a
`given material can be dried. The determination
`of the vapor concentration and carrying capacity
`of the gas is tenned psychrometry. The air—-
`water vapor system is the system most com-
`monly employed in pharmaceutical drying oper-
`ations
`and is
`therefore
`included in this
`discussion.
`
`The concentration of water vapor in a gas is
`
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`
`called the humidity of the gas. Humidity may be
`expressed in various ways, depending on the
`information required. A knowledge of humidity
`is necessary, therefore, to understand the basic
`principles of drying. g
`Psychrometric Chart. The humidity char—
`acteristics of air are best shown graphically in a
`psychrometric or humidity chart. Such charts
`can be found in various handbooks.” The psy-
`Chrometric chart has a formidable look because
`
`of the wealth of information presented in a small
`area. If the different curves in the chart are sep~
`arated and analyzed individually, however, their
`utility and ease of use becomes apparent.
`The basic curves of the psychrometric chart
`are shown in a simplified version in Figure 3-1.
`These curves are graphic representations of the
`relationship between the temperature and hu-
`' midity of the a.ir~water vapor system at constant
`pressure. The temperature is shown in the hori-
`
`'§
`
`.:
`Vt:
`>5L
`c:
`'3
`
`E36 n
`
`.\L Sa
`
`. EW
`
`.5
`
`3I
`
`n u£
`
`-
`
`>«
`5.
`IN
`Q‘*4
`
`ED I i
`
`n:
`5-.
`
`D»
`
`-2
`
`aC
`
`I}
`in
`V:
`
`I 05067
`
`8185
`
`DR Y-BULB TEMPERATURE (°F)
`
`FIG. 3-1. Diagram of psychrometric chart showing the relationship of air temperature to humidity.
`
`48 ~ The Theory and Practice of Industrial Pharmacy
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`
`dW/d9 = k’A(HS ~ Hg)
`
`(2)
`
`where dW/d0 is the rate of diffusion expressed
`as pounds of water per hour; k’ is the coefficient
`of mass transfer [pounds of water/(hour) (square
`foot) (absolute humidity difference)]; A is the
`area of the evaporating surface in square feet; H3
`is the absolute humidity at the evaporating sur-
`face (pounds of water per pound of dry air); and
`Hg is the absolute humidity in the passing air
`stream (pounds of water per pound of dry air).
`The coefficient of mass transfer, .k’, is not a
`constant, but Varies with the velocity of the air
`stream passing over the evaporating surface.
`The relationship is in the form:
`
`k’ = cc"
`
`(3)
`
`where c is a proportionality constant, G is the
`rate of flow of air [pounds of dry air/(hour)
`(square foot)], and n is a fractional exponent,
`usually about 0.8.2
`After an initial period of adjustment, the rate
`of evaporation is equal to the rate of diffusion of
`vapor, and the rate of heat transfer [equation
`(1)] can be equated with the rate of mass trans-
`fer [equation (2)], or:
`
`dW/d0 = q/A = k’A(H5 — Hg).
`
`(4)
`
`If the overall rate of heat transfer, q, is ex-
`pressed as the sum of the rates of heat transfer
`by convection, radiation, and conduction, equa-
`tion (4) is expanded to the form:
`
`dW/d6 = (qc -I- q,. + qk)/A
`
`= k’/\(Hs — Hg)
`
`(5)
`
`where qc, q,, and qk are the rates of heat transfer
`by convection, radiation, and conduction, re-
`spectively.
`The rate of drying may be accelerated by in-
`creasing any of the individual terms in equation
`(5). The rate of convection heat transfer, qc, can
`be increased by increasing the air flow rate and
`by raising the inlet air temperature. The rate of
`radiation heat transfer, q,, can be speeded up by
`introducing a high-temperature radiatingdheat
`source into the drying chamber. The rate of con-
`duction heattransfer, qk, can he stepped up by
`reducing the thickness of the material being
`dried and by allowing it to come in contact with
`raised-temperature surfaces. Increasing the air
`velocity also speeds up the rate of drying by in-
`creasing the coefficient of mass transfer, k’, as
`
`shown in equation (3). Dehumidifying the inlet
`air, thus increasing the humidity differential,
`(HS — Hg), is still another means of speeding up
`the rate of drying.
`Rapid drying may also be accomplished
`through the application of a microwave or die-
`lectric field. In this case, heat is generated inter-
`nally by the interaction of the applied electro-
`magnetic field with the solvent. Mass transfer
`results from an internal pressure gradient estab-
`lished by the internal heat generation, while the
`mass concentration remains relatively uniform.
`The drying rate, then, primarily depends on the
`strength of the field applied to the material.
`The utility of equation (5) in actual practice
`can be demonstrated by the following analysis:
`What is the effect of heating the air in a dryer to
`150°F if the outside air is 81°F with 50% relative
`humidity? From the psychrometric chart (Fig.
`3-1), it can be seen that for ambient air at this
`condition (point A), the absolute humidity is 78
`grains water/pound dry air. Following the wet-
`bulb temperature line from this point to the sat-
`uration curve (point D) yields an absolute hu-
`midity of 99 grains water/pound dry air.
`For the ambient air, the humidity differential
`(HS e H is (99 — 78), which is equal to 21
`grains 0003 pounds) water/pound dry air.
`When this air is heated to 150°F, the absolute
`humidity remains the same, but the relative ‘
`humidity is now reduced to 7%, and following
`the new wet—bulb temperature line (85°F) to the
`saturation curve yields a saturation humidity of
`185 grains water/pound dry air. The humidity
`gradient is now 185 — 78, which is equal to 107
`grains (00153 pounds) water/pound dry air, an
`increase of fivefold, indicating an increase in
`drying rate of 500% produced by a 69°F rise in
`temperature. In actual practice, the increase in
`drying rate would be even higher because in~
`creasing the inlet air temperature would in-
`crease k’ as well as the humidity gradient. It
`should be noted that this increase in the drying
`rate does not produce a serious increase in the
`temperature of the material being dried, because
`the wet—bulb temperature of the l50°F air is only
`85°F.
`
`The foregoing discussion holds true as long as
`there is a film of moisture on the surface of the
`material being dried. When the surface becomes
`partially or completely dry, the heat and mass
`transfer equations become more complex. In
`this case, the rate of drying is controlled by the
`rate of diffusion of moisture from the interior of
`the material. This diffusion is greatly influenced
`by the molecular and capillary structure of the
`solid. The process becomes further complicated
`when the drying surface causes a shrinkage of
`
`DRYING - 51
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`FIG. _3-6. Tray dryer.
`Schwartz Company.)
`
`(Courtesy of the Proctor and
`
`formed in a moving belt dryer. Batch drying is
`used extensively in the manufacture of pharma—
`ceuticals for several reasons: (1) Each batch of
`material can be handled as a separate entity. (2)
`The batch sizes of the pharmaceutical industry
`are relatively small (500 or less pounds per
`batch) compared with the chemical
`industry
`(2000 or more pounds per hour). (3) The same
`equipment is readily adjusted for use in drying a
`wide variety of materials.
`Tray dryers may be classified as direct or indi-
`rect. Most tray dryers used in the pharmaceuti-
`cal industry are of the direct type, in which heat—
`ing is accomplished by the forced circulation of
`large volumes of heated air. Indirect tray dryers
`utilize heated shelves or radiant heat sources
`
`inside the drying chamber to evaporate the
`moisture, which is then removed by either a vac-
`uum pump or a small amount of circulated gas.
`Further discussion in this section is confined to
`the direct (convection—type) dryer. Vacuum dry—
`ers are described separately later in the chapter.
`The trays used have solid, perforated, or Wire
`mesh bottoms. The circulation of drying air in
`trays with a solid base is limited to the top and
`bottom of the pan, whereas in trays with a perfo-
`rated screen, the circulation can be controlled to .
`pass through each tray and the solids on it. The
`screen trays used in most pharmaceutical drying
`operations are lined with paper, and the air thus
`circulates across rather than through the drying
`material. The paper is used as a disposable tray
`liner to reduce cleaning time and prevent prod—
`uct contamination.
`
`To achieve xuniform drying, there must be a
`constant temperature and a uniform airflow over
`the material being dried. This is accomplished
`in modern dryers by the use of a well-insulated
`cabinet with strategically placed fans and heat
`ing coils as integral parts of the unit. The air
`circulates through the dryer at 200 to 2000 feet
`per minute. The use of adjustable louvers helps
`to eliminate nonuniform airflow and stagnant
`pockets.
`The preferred energy sources for heating the
`
`drying air used on pharmaceutical products are
`steam or electricity. Units fired with coal, oil,
`and gas produce higher temperatures at lower
`cost, but are avoided because of possible product
`contamination with fuel combustion products,
`and explosion hazards when flammable solvents
`are being evaporated. Steam is preferred over
`electricity, because steam energy is usually
`cheaper. If steam is not readily available, and
`drying loads are small, electric heat is used.
`Tunnel and Conveyor Dryers. Tunnel dry-
`ers are adaptations of the truck dryer for contin-
`uous drying. The trucks are moved progressively
`through the drying tunnel by a moving chain.
`These trucks are loaded on one side of the dryer,
`allowed to reside in the heating chamber for a
`time sufficiently long to effect the desired dry~
`ing, and then discharged at the exit. The op-
`eration may be more accurately described as
`semicontinuous, because each truck requires
`individual loading and unloading before and
`after the drying cycle. Heat is usually supplied
`by direct convection, but radiant energy also
`may be used.
`Conveyor dryers are an improvement over
`tunnel dryers because they are truly continuous.
`The individual trucks of the tunnel are replaced
`with an endless belt or screen that carries the
`
`wet material through the drying tunnel. Con-
`veyor dryers provide for uninterrupted loading
`and unloading and are thus more suitable for
`handling large Volumes of materials.
`The drying curve characteristic of the mate-
`rial in batch drying is altered considerably when
`continuous type dryers are used. As the mass is
`moved along its drying path in a continuous op-
`eration, this mass is subjected to drying air, the
`temperature and humidity of which are continu-
`ally changing. As a consequence, the “constant
`rate” period is not constant, but decreases as the
`air temperature decreases, although the surface
`temperature of the wetted mass remains con-
`stant. Thus, drying rate curves for batch drying
`are not equally applicable to continuous drying
`procedures.
`
`Moving-Bed Systems
`Turbo-Tray Dryers. The turbo—tray dryer,
`illustrated in Figure 3-7, is a continuous shelf,
`n1oving—bed dryer. It consists of a series of rotat-
`ing annular trays arranged in a vertical stack, all
`of which rotate slowly at 0.1 to 1.0 rpm. Heated
`air is circulated over the trays by turbo-type fans
`mounted in the center of the stack. Wet mass
`
`fed through the roof of the dryer is leveled by a
`stationary wiper. After about seven—eighths of a
`revolution, the material being dried is pushed
`
`4
`
`DRYING - 57
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`I
`
`ployed: condensers, desiccants, and pumps. The
`water vapor is removed from the drying chamber
`and condensed in the form of a thin layer of ice
`on a heat-transfer surface in the condenser. The
`ice is removed intermittently by melting it with a
`heated fluid that is circulated through the con-
`denser, or in the case of a continuous operation,
`by means of scraper blades. Liquid or solid
`desiecants are often employed in the initial
`vapor removal to enhance the efficiency of the
`pumps removing the water vapor. In general,
`scraper blades and desiccants are used for freeze
`drying large-volume biologicals (e.g., serum,
`penicillin), and usually are not used for prepar-
`ing pharmaceutical dosage forms.
`Microwave Drying. The application of mi-
`crowave energy to the drying of solids represents
`a radical departure from conventional means of
`drying. Instead of applying heat externally to a
`material, energy in the form of microwaves is
`converted into internal heat by interaction with
`the material itself. This permits extremely rapid
`heat transfer throughout the material, which in
`turn can lead to rapid drying.
`The-heating effect is produced by the interac-
`tion of a rapidly oscillating electric field (915 or
`2450 megahertz) with the polarized molecules
`and ions in the material. The field imposes order
`on otherwise randomly oriented molecules. As
`the field reverses polarity, it relaxes and allows
`the molecules to return to their random orienta-
`tion, giving up stored potential energy as ran-
`dom kinetic energy, or heat. The interaction of
`the alternating field with ions causes billiard-
`ball—like collisions with un-ionized molecules,
`and the impact energy is converted into heat.
`A given material’s molecular
`and ionic
`makeup intimately affects its ability to be dried,
`as is shown in the power conversion equation for
`microwave heating:9
`
`2
`P = ME 6' tan 5 = kfE2€"
`
`<9)
`
`where: P = the power developed,
`(watts/unit volume)
`k = a constant
`f = the frequency
`E = the electric field strength,
`(volts/unit distance)
`as’ = the relative dielectric constant
`of the material being heated
`tan 6 = the loss tangent, or dissipation
`factor of the material
`e” = the loss factor of the material,
`equal to the product e’ tan 6
`
`64 ° The Theory and Practice of Industrial Phamiacy
`
`In microwave drying, the mass transfer is pri-
`marily the result of a pressure gradient due to
`rapid vapor generation inside the material, that
`is, most of the internal moisture is vaporized be-
`fore leaving the sample. Thus, the moisture is
`mobilized as a vapor rather than a liquid, and its
`movement to the‘ surface can be extremely rapid
`because it does not depend on mass concentra-
`tion gradients or on slow liquid diffusion rates.
`Industrial microwave dryers are usually of the
`static bed continuous type. Materials to be dried
`are placed on conveyor belts and conveyed
`through the microwave applicator. Generally, a
`stream of hot air is used simultaneously with the
`microwaves to sweep away the moisture evolv-
`ingpfrom the surface of the material being dried.
`Often, the microwave treatment is used in the
`last stages of hot air drying (the second falling
`rate period of Fig. 3-3) to remove the last re-
`maining portion of the solvent, reducing total
`drying time by 50% or more.
`Microwave drying can be used for the drying
`of pharmaceutical materials at low ambient tem-
`peratures, avoiding high surface temperatures,
`case hardening, and solute migration. Micro-
`wave vacuum drying at
`low pressure (1 to
`20 mm Hg) and moderate temperature (30 to
`40°C) can be used for drying thermolabile mate-
`rials such as vitamins, enzymes, proteins, and
`flavors.
`
`The rising cost of energy has generated a great
`deal of interest in microwave drying. The micro-
`waves couple directly into the solvent, and no
`energy is used to heat the air, the walls of the
`dryer, the conveyor, or the trays. This results in
`extremely efficient energy utilization, and en-
`ergy savings of as much as 70% have been real-
`ized in industrial installations.
`
`References
`
`I.: Psychrometric
`1. Zimmerman, O. T., and Lavine,
`Charts and Tables. Industrial Research Service, Dover,
`NH, 1945.
`. Perry, R. H., and Green, D. W.: Perry’s Chemical Engi-
`neers’ Handbook. 6th Ed. McGraw-Hill, New York,
`1984.
`. Bone, D. P.: Food Prod. Devel., 3:81, 1969.
`. Callahan, J. C., et al.: Drug Devel. and Industrial Phar-
`macy, 8:355, 1982.
`,
`. Rockland, L. B., and Nishi, S. K.: Food Technol.,
`34:42, 1980.
`. Scott, M. W., et al.: J. Pharm Sei., 52284, 1963.
`. Kuelling, W., and Simon, E. J .: Pharm. Technol. lnt.,
`3:29, 1980.
`. Nuernberg, E.: Acta Pharm. Technol., 26:39, 1980.
`. Lyons, D. W., and Hatcher, J. D.: J. Heat Mass Trans-
`fer, 15:897, 1972.
`
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`Pharmaceutical Rheology
`
`JOHN H. WOOD
`
`Pharmaceutical fluid preparations are recog-
`nized as materials that pour and flow, having no
`ability to retain their original shape when not
`confined. The semisolids are a more nebulous
`grouping. They essentially retain their shape
`when unconfined bug flow or deform when an
`external force is applied. Those materials that
`readily pour from bottles and form a puddle are
`clearly fluids. Ointments or pastes that clearly
`retain their shape after extrusion from a tube
`characteristically are associated with pharma-
`ceutical semisolids. Obviously a continuum of
`properties exists between these limits.
`Rheology (from the Greek rheos meaning flow
`and logos meaning science) is the study of the
`flow or deformation under stress. In pharmaceu-
`tical and allied research and technology, rheo-
`logic measurements are utilized to characterize
`the easeof pouring from a bottle, squeezing from
`a tube or other deformable container, maintain-
`ing product shape in a jar or after extrusion, rub-
`bing the product onto and into the skin, and
`even pumping the product from mixing and
`storage to filling equipment. Of extreme impor-
`tance in both product development and quality
`assurance is the determination that the desired
`
`attributes of body and flow are retained for the
`required shelf—life of the product.
`
`Definitions and Fundamental
`
`Concepts
`'l‘he tangential application of a force to a body
`and the resultant deformation of that body are
`the essential components for a rheologic obser-
`vation. If this force is applied for only a short
`time and then withdrawn, the deformation is
`defined as elastic if the shape is restored, but as
`flow if the deformation remains. A fluid or liquid
`then becomes a body that flows under the action
`
`of an infinitesimal force. In practice, gravity is
`generally regarded as the criterion of such a
`minimal force.
`To best understand the fundamental compo-
`nents of viscous flow, consider Figure 6-1. Two
`parallel planes are a distance x apart; between
`the planes, the viscous body is confined. The
`top, plane A, moves horizontally with Velocity v
`because of the action of force F. The lower
`plane B is motionless. As a consequence, there
`exists a velocity gradient V/X between the planes.
`This gradient is given the definition of rate of
`shear, D. The shear stress, S, is the force per unit
`area creating the deformation.
`Example 1. If some oil is rubbed into the skin
`with a relative rate of motion between the two
`surfaces of 15 cm/sec, and the film thickness is
`0.01 cm, then the shear rate is as follows:
`
`cm/sec
`15
`D “ 35:71?
`
`= 1500 see”
`
`This shear stress may be applied either mo-
`mentarily or continuously. Elastic deformation
`occurs if, as the force is applied, the upper plate
`moves in the direction of the force only momen-
`tarily and then stops but returns to its original
`position when the deforming force is removed.
`On the other hand, pure viscous flow occurs if
`there is continuous movement during the ap-
`plied force, and no restorative motion follows
`removal of the deforming force.
`Between the limits of elastic deformation and
`pure viscous flow, there exists a continuum of
`combinations of these limits. Such behavior is
`called viscoelastic flow. The elastic component
`of viscosity is considered in a later section.
`Newtonian fluid is a fluid in which a direct
`
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`Velocity = v
`,T:‘::"
`
`However, the dyne is the force acting for 1 sec to
`produce a velocity in a 1—g mass of 1 cm/sec.
`Hence,
`this dimensional analysis for viscosity
`reduces to:
`‘
`
`x-———>
`
`""'[""_"'l""'Y\.I
`
`K B (Stationary)
`
`Velocity = 0
`FIG. 6-]. Model to demonstrate components of classic vis-
`cous flow.
`
`proportionality exists, for all values of shear, be-
`tween shear stress and shear rate.
`Viscosity or coefficient of viscosity is the pro—
`portionality constant between shear rate and
`shear stress. Conventionally, viscosity is repre—
`sented by n. Then:
`
`77 = S/D
`
`(1)
`
`sys—
`The centimeter~gram-second (C.G.S.)
`tern uses grams per centimeter per second
`(g cm” see”) as the dimensional units of vis-
`cosity. In these units, viscosity is expressed in
`poises, a term used in recognition of the pioneer~
`ing work in the 1840s of the French scientist
`J. L. M. Poiseuille. For dilute aqueous solutions,
`the common unit becomes the centipoise (10‘2
`poise), op. The viscosity of water is about 1 cp.
`In the newly adopted International System of
`Units (SI), the unit corresponding to the centi-
`poise is the millipascal~second (mPas).
`A perspective of these units may be obtained
`by considering the case of Figure 6-1 when a
`force of 1 dyne acts to produce a velocity of
`1 em/sec for plate A when the distance between
`plates is lcni, and both plates are 1cm2 in
`' cross—sectional area. Under these terms, viscos—
`ity is calculated as:
`
`” ”“ D
`
`force/area
`
`velocity differenceldistance
`
`:
`
`dyne/cmz
`(em/sec)/cm
`
`= dyne sec cm”
`
`124 - The Theory and Practice of Industrial Pharmacy
`
`17 = g - cm” sec”
`= poise
`
`In the International System of Units, which is
`not yet used routinely in viscosity references,
`the pascal (Pa) is the unit of stress and has the
`dimensions of newton/meter2, where the new-
`ton is a kilogram meter/secondg. Hence, equiva-
`lence occurs for the centipoise with millipasca1~
`seconds.
`
`Example 2. If in example 1, the oil had the
`same viscosity as water, then the force used to
`create the shear can be determined as follows:
`
`"“D
`
`1 X 1O‘Z poise =
`
`3
`1500 33°
`
`-1
`
`Then S = (1500)(1 >< 1O‘2)(sec“1)(poise)
`= 15 (sec1)(dyne sec em”)
`= 15 dyne crn‘2
`
`Example 8.
`would become:
`
`In S.l. units,
`
`the above terms
`
`Fluidity is the reciprocal of the viscosity, usu-
`ally designated by the symbol q5. This is an occa-
`sional unit of convenience but not an essential
`one.
`
`Kinematic viscosity (v) is the Newtonian vis~
`cosity divided by density (n/d). The unit is now
`the stake, in honor of the English scientist who
`studied problems of gravitational settlement in
`fluids. As discussed later in this chapter, certain
`fluid flow viscometers give values in this kind?’
`matic scale.
`Example 4. If the oil from examples 1 and 2
`had a density of 0.82, then the kinematic viscos—
`ity would be:
`
`I/=31
`1 X 10”2
`0.82
`
`= 1.22 X 10‘2 stokes
`1.22 centistokes
`
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`
`Nonmewtonian fluids are those in which there
`is no direct linear relationship between shear
`stress and shear rate. Most systems of pharma~
`ceutical
`interest fall
`into this category. The
`shear stress necessary to achieve a given shear
`rate may increase more rapidly or less rapidly
`than is required by the linear direct proportion-
`ality (Fig. 62).
`A pseudoplastic material is one in which the
`stress increases at less than a linear rate with
`increasing shear rate, while a dilatant material
`is one in which the increase is more rapid. Thus,
`if viscosity is calculated at each of a series of
`shear rate points by use of equation (1), then the
`resultant values decrease with increasing shear
`rate for pseudoplastic materials and increase for
`dilatant ones. Measurements at such single
`points are frequently referred to as apparent vis-
`cosity to recognize clearly that
`the number
`quoted refers only to the condition of measure-
`
`
`
`SIIEARSTRESS
`
`ment. Although frequently, reference is care—
`lessly made to a lotion having a viscosity of
`300 cp or to a paste or ointment having a viscos~
`ity of 1200 poises, these are meaningless terms
`unless the shear rate at which the measurement
`was made becomes a clear part of the statement.
`The fact that one number cannot characterize
`the viscous behavior, however, requires the use
`of some equation of state. One such empiric one
`is the Power Law Equation:
`
`S =AD“
`
`(2)
`
`where S and D are the shear stress and shear
`
`rate respectively, A is an appropriate proportion-
`ality constant, and n is the Power Index. In this
`form, n is less than 1 for pseudoplastic materials
`and greater than 1 for dilatant materials. The
`Power Law Equation is also used with the index
`n associated with stress rather than shear rate.
`Obviously, the magnitude of the values of n are
`then interchanged. Unfortunately, there is no
`clear convention for such equations.
`When the logarithm of both sides of equation
`(2) is taken, the result is:
`
`logS=1ogA+nlogD
`
`(3)
`
`Compared with the equation of a straight line,
`y = b + mx, a plot of log S against log D results
`in a straight line of slope n and intercept log A.
`Figure 6-3 shows such plots on logarithmic scale
`for one gum system as a function of gum con-
`centration.
`
`Example 5. Calculate the parameters of the
`Power Law Equation for 0.01%, 0.02%, 0.04%,
`and 0.