The Theory
`
`and Practice of Industrial
`
`Pharmacy
`
`LEON LACHMAN. PhD.
`Lanhman Cumulinnl Sal-vim, Inc.
`Garden City. New York
`
`HERBERT A. LIEEERMAN. Ph.D.
`H. H. Lieberman Associates. Inc.
`Cmmltanl. Services
`
`Livingslun. New Jersey
`
`JOSEPH L- KANIG. Ph.D.
`Rania Cansuking and flmmh Ami-ates. Inc.
`Ridgufiefld, Conmcflcui
`
`THIRD EDITION
`
`LEA. 31 FEBIGEFI1
`
`' PHILADELPHIA
`
`
`
`Mylan V. MonoSol
`IPR2017-00200
`MonoSol Ex. 2014
`
`Page 1
`
`Mylan v. MonoSol
`IPR2017-00200
`MonoSol Ex. 2014
`
`Page 1
`
`

`

`Lea 8: Febiger
`600 Vlbskmgttm Square
`Philadelphia, PA 19106-4198
`USA.
`(215) 922-1330
`
`Library of Congress Cataloging in Publication Data
`Main entry under title:
`
`The Theory and practice of industrial pharmacy.
`
`Includes bibliographies and index.
`I. Lachman, been,
`1. Pharmacy.
`2. Drug trade.
`1929—
`II. Lieberman, Herbert A., 1920—
`III. Kanig. Joseph-L, 1921 —
`[DNLMZ 1. Drug
`Industry.
`QV 704 T396]
`RSI92.L33 1985
`ISBN 0-8121-0977-5
`
`84-27806
`
`615’.19
`
`First Edition, 1970
`Second Edition, 1976
`
`Copyright © 1986 by Lea & Febiger. Copyright under the
`International Copyright Union. All Rights Reserved. This book is
`protected by copyright. No part of it may be reproduced in any
`manner or by any means without written permission from the
`publisher.
`
`FIRST INDIAN REPRINT, 1987
`SECOND INDIAN REPRINI‘, 1989
`THIRD INDIAN REPRINT. 1990
`FOUR'I'II INDIAN REPRINT, 1991
`
`Reprinted in India by special arrangement with LEA & FEBIGER
`Philadelphia U S A.
`Indian Edition published by
`Varghese Publishing House, Hind Rajasthan Building, Dadar,
`Bombay 400 014.
`Reprinted by Akshar Pratiroop Pvt Ltd, Bombay 400 031.
`
`34.70;;,.,._..4hg..
`
`
`
`Page 2
`
`Page 2
`
`

`

`
`
`Preface
`
`Fifteen years have elapsed since the publication
`of the first edition of this book, and a decade has
`gone by since the second edition was published
`in 1976. The intervening years have witnessed
`many important changes in the field of indus-
`trial pharmacy—probably more so than at any
`other period of time in its history. Therefore, the
`editors were challenged to select the most quali-
`fied contributors to this third edition of the text—
`book.
`
`As before, the major objective of this edition is
`to serve as a textbook for graduate and under—
`graduate students in the pharmaceutical sci-
`ences. In addition, it is intended to provide a
`comprehensive reference source on modern in—
`dustrial pharmacy. As such, this book'should be
`useful
`to practitioners in the pharmaceutical
`and allied health sciences; hospital pharmacists,
`drug patent attorneys, government scientists
`and regulatory personnel, and others seeking
`information concerning the design, manufac-
`ture, and control of pharmaceutical dosage
`forms.
`
`Despite the fact that the preface to a book ap-
`pears, as its title implies, at the beginning of a
`volume, it is common practice for editors and
`authors to delay its writing as one of their last
`tasks. This is done in order to reflect on the
`changes or modifications that have been insti—
`tuted in the content and arrangement of the
`chapters in the new edition. In so doing, the edi-
`tors are provided with an opportunity to high-
`light such major changes.
`Writing this preface has provided us with the
`opportunity to note the enormous changes in
`pharmaceutical
`technology since the appear—
`ance of the first edition. This book was created to
`fill a need that existed during the 1960s and
`early 1970s, when many undergraduate and
`graduate programs in colleges of pharmacy in-
`cluded courses in industrial pharmacy to teach
`the unique factors involved in the production of
`commercially prepared drug dosage forms. It
`was a period during which the young disciplines
`
`of pharmacokinetics and biopharmaceutics were
`beginning to solve new problems associated with
`the burgeoning array of increasingly sophisti-
`cated new drug entities, and with the growing
`concerns about bioavailability of these com-
`pounds fiom various dosage delivery systems. At
`that time, graduate programs offered many op—
`portunities for aspiring pharmaceutical scien-
`tists to deal with these exciting and innovative
`technologic advances. Thus,
`there existed an
`obvious need for a textbook that could bring to-
`gether in one volume the emerging concepts,
`new theories, and their practical applications in
`the development and production of what were
`then termed “dosage forms,” and what are now
`more appropriately referred to as “drug delivery
`systems.”
`Along with the development of new drug de-
`livery systems and new drugs came new produc-
`tion processes and machines for manufacture,
`new control methods for accurate definition of
`drug delivery, and new and improved quality
`control procedures. All of these innovations and
`improvements contributed to superior quality
`drug dosage forms, and in many cases,
`to en-
`hanced concomitant production economics. For
`example,
`the advent of microprocessors and
`small computers has begun to revolutionize the
`capabilities inherent in modern drug production
`to an extent not foreseeable when the second
`
`edition of this book was published.
`Since the first edition of this textbook ap-
`peared in 1970, we have been most gratified to
`learn from comments received from all parts of
`the world that this book has been well-received
`
`and utilized as a basic teaching and reference
`text in colleges, research institutions, govern-
`ment agencies, and pharmaceutical and related
`industries. These comments have also provided
`us with useful suggestions and ideas for this
`third edition.
`The multi-author approach, used in all three
`editions, has resulted in a uniquely prepared
`textbook in industrial pharmacy. This editorial
`Page 3
`
`Page 3
`
`

`

`method so common to the writing of modern
`technical books permits the use of a wide range
`of expertise that is necessary in dealing with the
`manifold aspects of modern industrial phar-
`macy,
`It also, however, poses
`the problem
`unique to all editors, namely, the necessity of
`gently coercing some very busy people to com-
`plete, revise, and polish their chapters In spite
`of these pressures, we are grateful for the pa—
`tience and forbearance of our contributors in
`
`helping us to complete this edition. Without the
`skillful sharing of their knowledge in the pages
`of this book, the enormous task of compiling this
`third edition of the textbook would have been
`impossible to consider.
`We and our contributing authors will be ex-
`tremely pleased if our efforts have results in an
`improved book to serve as a teaching and refer-
`ence source in industrial pharmacy.
`
`Garden City, New York
`Livingston, New Jersey
`Ridgefield, Connecticut
`
`LEON LACHMAN, PHD.
`HERBERT A. LIEBERMAN, PHD.
`JOSEPH L, KANIG, PHD.
`
`iv 0 Preface
`
`Page 4
`
`Page 4
`
`

`

`Contributors
`
`MICHAEL]. AKEHS, PHD.
`Head
`Dry Products Development Department
`Eli Lilly Er Company
`Indianapolis, IN
`‘
`
`NEIL R. ANDERSON, PHD. ~
`Director
`Solid Dosage Form Design
`Merrell Dow Pharmaceutical Company
`Indianapolis, IN ~
`
`KENNETH E. AvIs, D.Sc.
`Goodman Professor and Chairman
`Department of Pharmaceutics
`College of Pharmacy
`University of Tennessee
`Memphis, TN
`
`JOSEPH A. BAKAN
`Director
`Research and Development Division
`Eurand America Inc.
`Vandalia, OH
`
`GILBERT S. BANKER, PHD.
`Dean and Professor of Pharmaceutics
`College of Pharmacy
`University of Minnesota
`Minneapolis, MN
`
`J .V. BATTISTA
`Formerly Management Consultant
`Lakehurst, N]
`
`SANFORD BOLTON, PHD.
`Professor and Chairman
`Department of Pharmacy and Administrative
`Sciences
`St. John’s University
`Jamaica, NY
`
`JAMES C. BOYLAN, PHD.
`Adjunct Professor
`School of Pharmacy and Pharmaceutical Sciences
`Purdue University
`W. Lafayette, IN
`Director
`Scientific Services
`Hospital Products Division
`Abbott Laboratories
`N. Chicago, IL
`
`SUGGY CHRAI, PHD.
`E.R. Squibb 8' Sons, Inc.
`New Brunswick, NJ
`
`CARLO P. CROCE, M.B.A.
`Manager
`Package Development
`Warner-Lambert Company
`Morris Plains, NJ
`
`LARRYJ. COBEN, PHD.
`Director of Manufacturing
`Alcon Laboratories, Inc.
`Ft. Worth, TX
`
`ANTHONY J. CUTIE, PHD.
`Associate Professor of Pharmaceutics
`Arnold and Marie Schwartz College of Pharmacy
`and Health Sciences
`Long Island University
`Brooklyn, NY
`
`PATRICK DELUCA, PHD.
`Professor and Associate Dean
`College of Pharmacy
`University of Kentucky
`Lexington, KY
`
`MR. DOBRINSKA, PHD.
`.
`Research Fellow
`Merck Sharp Er Dohme Research Laboratories
`West Point, PA
`
`Page 5
`
`Page 5
`
`

`

`JOSEPH R. FELDKAMP
`Research Engineering Specialist
`Monsanto Company
`St. Louis, MO
`
`EUGENE F. FIESE, PHD.
`Pfizer Central Research
`Groton, CT
`
`ARTHUR FISCHER
`DuPont Pharmaceuticals
`Garden City, NY
`
`TIMOTHY A. HAGEN, PHD.
`Pfizer Central Research
`Groton, CT
`
`SAMIR A. HANNA, PHD.
`Vice President
`Quality Assurance
`Industrial Division
`Bristol—Myers Company
`Syracuse, NY
`
`SAMUEL HARDER, PHD.
`Laboratory Manager
`Pharmaceutical Research and Development
`Riker Laboratories, Inc.
`St. Paul, MN
`
`STANLEY L. HEM, PHD.
`Professor of Physical Pharmacy
`School of Pharmacy and Pharmaceutical Sciences
`Associate Dean
`Graduate School
`Purdue University
`W. Lafayette, IN
`
`VAN E. HOSTETLER
`Manager
`Equipment Development
`Lilly Corporation Center
`Eli Lilly 8 Company
`Indianapolis, IN
`
`BERNARD IDSON, PHD.
`American Cyanamid Company
`Clifton, NJ
`
`JOSEPH L. KANIG, PHD.
`Kanig Consulting and Research Associates, Inc.
`Ridgefield, CT
`
`vi 0 Contributors
`
`LLOYD KENNON, PH.D.*
`Formerly Associate Professor and Program Director
`Division of Industrial Pharmacy
`Arnold and Marie Schwartz College of Pharmacy
`and Health Sciences
`Long Island University
`Brooklyn, NY
`
`K.C. KWAN, PHD.
`Executive Director
`Drug Metabolism
`Merck Sharp 8 Dohrne Research Laboratories
`West Point, PA
`
`LEON LACHMAN, PHD.
`Lachrnan Consultant Services, Inc.
`Garden City. NY
`
`JACK H. LAZARUS, M.S.*
`Formerly Senior Scientist
`Pharmacy Research and Development
`Hoffman-LaRoche, Inc.
`Nutley, N]
`R, SAUL LEVINSON
`Manager
`Exploratory Research
`Abbott Laboratories
`N. Chicago, IL
`
`HERBERT A. LIEBERMAN, PHD.
`President, Consultant Services
`H. H. Lieberman Associates, Inc.
`Livingston, NJ
`
`KARL LIN, PH.D.
`Vice President of Science and Technology
`United Laboratories
`Manila, Philippines
`
`NICHOLAS C—. LORD], PHD.
`Professor of Pharmacy
`Graduate Director of Pharmaceutical Science
`College of Pharmacy
`Rutgers University
`Piscataway, NJ
`
`KEITH MARSHALL, PH.D.
`Adjunct Professor
`School of Pharmacy
`University of Rhode Island
`Kingston, RI
`Associate Director
`Department of Pharmaceutical Research and
`Technologies
`Smith Kline 8 French Laboratories
`Philadelphia, PA
`
`*Deceased.
`
`Page 6
`
`Page 6
`
`

`

`RAYMOND D. MCMURRAY, J.D.*
`Formerly of McMurray and Pendergast
`Washington, DC
`
`ROBERT F. SCHIEEMANN, M.S.
`R.F. Schiffmann Associates, Inc.
`New York, NY
`
`SHASHI P. MEHTA, PH.D.
`Section Head
`Tablet Products, Research and Development
`Abbott Laboratories
`N. Chicagoy IL
`
`EUGENE L. PARROTT, PH.D.
`Professor of Industrial Pharmacy
`College of Pharmacy
`University of Iowa
`Iowa City, IA
`
`NAGIN K. PATEL, PH.D.
`Associate Professor of Industrial Pharmacy
`Arnold and Marie Schwartz College- of Pharmacy
`and Health Sciences
`Long Island University
`Brooklyn, NY
`
`WILLIAM R. PENDERGAST, J .D.
`Arent, Fox, Kintner, Plotkin, g. Kahn
`Washington, DC
`
`ALBERT S. RANKELL, PH.D.
`Vicks Research Center
`Health Care Products Division
`Richardson-Vicks Inc.
`Shelton, CT
`
`MARTIN M. RIEGER, PH.D.
`M. f} A. Rieger Associates
`Morris Plains, NJ
`
`EDWARD G. RIPPIE, PH.D.
`Professor
`Department of Pharmaceutics
`College of Pharmacy
`University of Minnesota
`Minneapolis, MN
`
`JOHN J. SCIARRA, PH.D.
`Professor of Industrial Pharmacy
`Arnold and Marie Schwartz College of Pharmacy
`and Health Sciences
`Long Island University
`President
`Retail Drug Institute
`Brooklyn, NY
`
`JAMES A. SEITZ, PH.D.
`Manager
`Tablet Products, Research and Development
`Pharmaceutical Products Division
`Abbott Laboratories
`N. Chicago, IL
`
`J.P. STANLEY, PH.D.
`Formerly Technical Director
`R.P. Scherer Corporation
`Grosse Pointe Park, MI
`
`RALPH H. THOMAS
`Thomas Packaging Consultants, Inc.
`Union, NJ
`
`A.E. TILL, PH.D.
`Research Fellow
`Merck Sharp {a Dohme Research Laboratories
`West Point, PA
`
`GLENN VAN BUSKIRK
`Director of Formulations
`Ortho Pharmaceutical Corporation
`Raritan, N]
`
`JOE L. WHITE, PH.D.
`Professor of Soil Mineralogy
`Department of Agronomy
`Purdue University
`W. Lafayette, IN
`
`J.D. ROGERS, PH.D.
`Research Fellow
`Merck Sharp Er Dohme Research Laboratories
`West Point, PA
`
`’Deceased.
`
`JOHN H. WOOD, PH.D.
`Professor
`Coordinator of Research and Graduate Program
`Department of Pharmacy and Pharmaceutics
`School of Pharmacy
`Medical College of Virginia Campus
`Virginia Commonwealth University
`Richmond, VA
`
`Contributors 0 vii
`
`Page 7
`
`Page 7
`
`

`

`JAMES L. YEAGER, PHD.
`Project Manager
`Scientific Affairs
`Abbott International, Ltd.
`N. Chicago, IL
`
`K.C. YEH, PHD.
`Senior Research Fellow
`Merck Sharp 8r Dohme Research Laboratories
`West Point, PA
`
`[W1
`
`viii 0 Contributors
`
`Page 8
`
`Page 8
`
`

`

`Contents
`
`Section 1.
`
`Principles of Pharmaceutical Processing
`1.
`
`3
`Mixing
`EDWARD G. RIPPIE
`
`2.
`
`21
`Milling
`EUGENE L. PARROT
`
`47
`. Drying
`ALBERT s. RANKELL, HERBERT A. LIEBERMAN, ROBERT F. SCHIFFMANN
`. Compression and Consolidation of Powdered Solids
`66
`KEITH MARSHALL
`
`. 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
`
`7
`
`123
`
`'
`
`146
`
`Section II. Pharmaceutical Dosage Form Design
`. Prefonnulation
`171
`EUGENE F. FIESE, TIMOTHY A. HAGEN
`
`8 9
`
`197
`. Biophannaceutics
`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
`11
`. Tablets
`293
`GILBERT s. BANKER, NEIL R. ANDERSON
`
`12
`
`346
`. Tablet Coating
`JAMEs A. SEITZ, SHASHI P. MEHTA, JAMES L. YEAGER
`
`ix
`
`Page 9
`
`Page 9
`
`

`

`374
`13. Capsules
`Part One Hard Capsules
`VAN B. HOSTETLER
`
`374
`
`Part Two Soft Gelatin Capsules
`JP. STANLEY
`
`Part Three *Microencapsulation
`J.A. BAKAN
`
`398
`
`412
`
`‘14. Sustained Release Dosage Forms
`NICHOLAS G. LORD1
`
`430
`
`15. Liquids
`J.C. BOYLAN
`
`457
`
`479
`16. Pharmaceutical Suspensions
`NAGIN K. PATEL, LLOYD KENNON*, R. SAUL LEVINSON
`17. Emulsions
`502
`MARTIN M. RIEGER
`
`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
`
`33. Pilot Plant Scale—Up Techniques
`SAMUEL HARDER, GLENN VAN BUSKIRK
`
`681
`
`711
`24. Packaging Materials Science
`CARLO P. CROCE, ARTHUR FISCHER, RALPH H. THOMAS
`
`25. Production Management
`J.V. BATTISTA
`.
`
`733
`
`760
`26. Kinetic Principles and Stability Testing
`LEON LACHMAN, PATRICK DELUCA, MICHAEL J. AKERS
`
`804
`27. Quality Control and Assurance
`LEON LACHMAN, SAMIR A. HANNA, KARL LIN
`
`856
`28. Drug Regulatory Affairs
`WILLIAM R. PENDERGAST, RAYMOND D. MCMURRAY*
`
`INDEX
`
`883
`
`“ Deceased.
`
`x 0 Contents
`
`Page 10
`
`Page 10
`
`

`

`SECTION I
`
`Principles of
`Pharmaceutical
`
`Processing
`
`Page 1 1
`
`Page 11
`
`

`

`vi
`
`Page 12
`
`Page 12
`
`

`

`
`
`Mixing
`
`EDWARD G. RIPPIE
`
`The process of mixing is one of the most com—
`monly employed operations in everyday life.
`Owing in part to the almost limitless variety of
`materials that can be mixed, much remains to
`be learned regarding the mechanisms by which
`mixing occurs.
`For our purposes, mixing is defined as a proc-
`ess that tends to result in a, randomization of dis-
`similar particles vvithin a system. This is to be
`distinguished from an ordered system in which
`the particles are arranged according to some it-
`erative rule and thus follow a repetitive pattern.
`It is possible to consider the mixing of particles
`differing only by some vector quantity, such as
`spatial orientation or translational velocity. In
`this chapter, however, we will deal solely with
`particles distinguishable by means of scalar
`quantities,
`e.g.,
`composition,
`size, density,
`shape, or a combination of these. The following
`text is intended as an introduction to the funda-
`mental concepts that lead to an understanding
`of the techniques employed in the chemical and
`pharmaceutical industries to obtain satisfactory '
`mixing. A list of general references is included
`at the end of the chapter for those who desire
`further reading on this subject.
`
`Fluids Mixing
`
`Fundamentals
`
`Flow Characteristics. Fluids may generally
`be classified as Newtonian or non-Newtonian,
`depending on the relationship between their
`
`shear rates and the applied stress. Forces of
`shear are generated by interactions between
`moving fluids and the surfaces over which they
`flow during mixing. The rate of shear may be
`defined as the derivative of velocity with respect
`to distance measured normal to the direction of
`flow (dv/dx). The viscosity (dynamic) is the ratio
`of shear stress to the shear rate. For Newtonian
`fluids, the rate of shear is proportional to the
`applied stress, and such fluids have a dynamic
`viscosity that is independent of flow rate. In con-
`trast, non-Newtonian fluids exhibit apparent
`dynamic viscosities that are a function of the
`shear stress.
`The flow characteristics and mixing behavior
`of fluids are governed by three primary laws or
`principles: conservation of mass, conservation of
`energy, and the classic laws of motion. The
`equations that result from the application of
`these simple laws of conservation and motion to
`systems used for mixing are often complex and
`are beyond the scope of this discussion. An un-
`derstanding LE‘ the fundamental principles of ,
`fluid dynamics, however, will help the reader to
`visualize the overall process of fluids mixing.
`Mixing Mechanisms. Mixing mechanisms
`for fluids fall essentially into four categories:
`bulk transport, turbulent flow, laminar flow, and
`molecular diffusion. Usually, more than one of
`these processes is operative in practical mixing
`situations.
`1. Bulk transport. The movement of a rela-
`tively large portion of the material being mixed
`from one location in the system to another con-
`
`Page 13
`
`Page 13
`
`

`

`
`
`stitutes bulk transport. A simple circulation of
`material in a mixer, however, does not necessar»
`ily result in efficient mixing. For bulk transport
`to be effective it must result in a rearrangement
`or permutation of the various portions of the
`material to be mixed. This is usually accom-
`plished by means of paddles, revolving blades, or
`other devices within the mixer arranged so as to
`move adjacent volumes of the fluid in different
`directions, thereby shuffling the system in three
`dimensions.
`2. Turbulent mixing. The phenomenon of tur-
`bulent mixing is a direct result of turbulent fluid
`flow, which is characterized by a random fluctu-
`ation of the fluid velocity at any given point
`Within the system. The fluid velocity at a given
`instant may be expressed as the vector sum of its
`components in the x, y, and 1 directions. With
`turbulence, these directional components fluc-
`tuate randomly about their individual mean val-
`ues, as does the Velocity itself.
`In the case of turbulent flow in a pipe, the
`mean velocity in the direction of flow through
`the pipe is positive, of course, and varies some—
`what depending on the distance from the pipe
`wall, in contrast, the mean velocity perpendicu-
`lar to the wall is zero, The churning flow charac-
`teristic of
`turbulence results
`in constantly
`changing velocities in these directions. This is
`in contrast to laminar flow in which the velocity
`components at a given point in the flow field
`remain constant, at their mean value.
`In general, with turbulence, the fluid has dif-
`ferent instantaneous velocities at different loca-
`tions at the same instant in time. This observa—
`tion is
`true of both the direction and the
`magnitude of the velocity. if the instantaneous
`velocities at two points in a turbulent flow field
`are measured simultaneously, they show a de—
`gree of similarity provided that the points se-
`lected are not too far apart. There is no velocity
`correlation between the points, however, if they
`are separated by a sufficient distance.
`Turbulent flow can be conveniently visualized
`as a composite of eddies of various sizes. An
`eddy is defined as a portion of fluid moving as a
`unit in a direction often contrary to that of the
`general flow. Large eddies tend to break up,
`forming eddies of smaller and smaller size until
`they are no longer distinguishable. The size dis-
`tribution of eddies within a turbulent region is
`referred to as the scale of turbulence.
`It is readily apparent that such temporal and
`spatial velocity differences as result from turbu—
`lence within a body of fluid produce a randomi-
`zation of the fluid particles. For this reason, tur-
`bulence is a highly effective mechanism for
`
`4 - The Theory and Practice of industrial Pharmacy
`
`mixing. Thus, when small eddies are predomi-
`nant, the scale of turbulence is low.
`An additional characteristic of turbulent flow
`is its intensity, which is related to the velocities
`with which the eddies move. A composite pic—
`ture of eddy size versus the velocity distribution
`of each size eddy may be described as a complex
`spectrum. Such spectra are characteristic of the
`turbulent flow and are used in its analysis.
`3. Laminar mixing. Streamline or laminar
`flow is frequently encountered when highly vis—
`cous fluids are being processed. It can also occur
`if stirring is relatively gentle and may exist adja-
`cent to stationary surfaces in vessels in which
`the flow is predominantly turbulent. When two
`dissimilar liquids are mixed through laminar
`flow, the shear that is generated stretches the
`interface between them. If the mixer employed
`folds the layers back upon themselves, the num—
`ber of layers, and hence the interfacial area be—
`tween them, increase exponentially with time.
`This relationship is observed because the rate of
`increase in interfacial area with time is propor—
`tional to the instantaneous interfacial area.
`Example. Consider
`the case wherein the
`mixer produces a folding effect and generates a
`complete fold every 10 seconds. Given an initial
`fluid layer thickness of 10 cm, a thickness re—
`duction by a factor of 10’s is necessary to attain
`layers 1 nm thick, which approximate molecular
`dimensions. Since a single fold results in a layer
`thickness reduction of one half, 11 folds are re—
`quired Where:
`
`(1/2)n = we8
`
`log [(1/2)“l = n log 1/2 =
`or in logarithmic form,
`log 10’8 = 78. Therefore?
`
`11 = —8/log 1/2 = 26.6
`
`Thus, the time required for mixing is equal to n
`times 10 seconds (266 sec), or 4.43 min.
`Mixers may also operate by simply stretching
`the fluid layers without any significant folding
`action. This mechanism does not have the
`stretch compounding effect produced by folding,
`but may be satisfactory for some purposes in
`which only a moderate reduction in mixing scale
`(to be defined in detail
`later) is required.
`It
`should be pointed out, however,
`that by this
`process alone, an exceedingly long time is re-
`quired for the layers of the different fluids to
`reach molecular dimensions. Therefore, good
`mixing at the molecular level requires a signifi—
`cant contribution by molecular diffusion after
`the layers have been reduced to a reasonable
`
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`
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`

`thickness (several hundred molecules) by lami-
`nar flow.
`4. Molecular diffusion. The primary mecha-
`nism responsible for mixing at the molecular
`level
`is diffusion resulting from the thermal
`motion of the molecules. When it occurs in con
`junction with laminar flow, molecular diffusion
`tends to reduce the sharp discontinuities at the
`interfaces between the fluid layers, and if al-
`lowed to proceed for sufficient time, results in
`complete mixing.
`The process is described quantitatively in
`terms of Fick’s first law of diffusion:
`
`dc
`dm
`a — ‘DAE
`
`<1)
`
`where the rate of transport of mass, dm/dt,
`across an interface of area A is proportional to
`the concentration gradient, dc/dx, across the in
`terface. The rate of intermingling is governed
`also by the diffusion coefficient, D, which is a
`function of variables including fluid viscosity
`and the size of the diffusing molecules. The
`sharp interface between dissimilar fluids, which
`has been generated by laminar flow, may be
`rather quickly obliterated by the ensuing diffu-
`sion. Considerable time may be required, how,
`ever, for the entire system to become homogene—
`ous.
`
`the original
`The concentration gradient at
`boundary is a decreasing function of time, ap-
`proaching zero as mixing approaches comple—
`tion. Since the amount of material passing a
`boundary plane in a given time depends on the
`concentration gradient, the time required to at-
`tain complete uniformity may be considerable
`unless the fluid layers are very thin.
`5. Scale and intensity of segregation. The
`quality of mixtures must ultimately be judged
`upon the basis of some measure of the random
`distribution of their components. Such an evalu-
`ation depends on the selection of a quantitative
`method of expressing the quality of randomness
`or “goodness of mixing.” Danckwerts has sug—
`gested two criteria that are statistically defined
`and may be applied to mixtures of mutually sol—
`uble liquids, fine powders, or gases. Perhaps the
`greatest value of these concepts lies in the in-
`sight they give the pharmacist or chemical engi-
`neer regarding the physical nature of the mix-
`tures produced.
`Bulk transport, turbulent flow, and laminar
`flow all result in the intermingling of “lumps” of
`the liquids to be mixed. The shape and size of
`these lumps largely depend on the relative con-
`tribution of each of these mechanisms to the
`
`overall process and on the time over which mix-
`ing is carried out. Unless molecular diffusion
`occurs, however, the composition of the lumps
`varies discontinuously from one to the next. In
`other words, each lump retains a constant and
`uniform internal composition. This can be al-
`tered only if molecular diffusion in the case of
`liquids and gases, or interparticulate motion in
`the case of powders, tends to eliminate concen-
`tration gradients between adjacent lumps. On
`this basis, Danckwerts defined “two quantities
`to describe the degree of mixing—mamely the
`scale of segregation and the intensity of segrega—
`tion.”
`
`The scale of segregation is defined in a man-
`ner analogous to the scale of turbulence dis—
`cussed earlier, and may be expressed in two
`ways: as a linear scale or as a volume scale. The
`linear scale may be considered to represent an
`average value of the diameter of the lumps pres—
`ent, whereas the volume scale roughly corre-
`sponds to the average lump volume.
`The intensity of segregation is a measure of
`the variation in composition among the various
`portions of the mixture. When mixing is com—
`plete, the intentsity of segregation is zero.
`6. Time. dependence. In any given case, the
`mechanisms that are active in bringing about
`mixing are time-dependent in their relative im-
`portance as the process of mixing proceeds. For
`example, consider the mixing of two miscible
`liquids of different densities contained in a verti-
`cal tank of cylindric form, The denser liquid is
`placed in the bottom of the tank, and an approxi—
`mately equal volume of the less dense fluid is
`layered on top. Mixing is to be done with a
`down-draft propeller mounted on a vertical shaft
`midway between the tank bottom and the inter-
`face between the liquids.
`If the propeller is operated at a speed suffi-
`cient to produce turbulent flow in its discharge
`region, mixing occurs initially, to any significant
`degree, only by mechanisms that reduce the
`scale of segregation. Until such time as both
`fluids are present in the region of turbulence,
`created by the impeller, only bulk transport is
`effective in the mixing process, The convection
`results from the flow generated by the pumping
`action of the propeller. When the scale of segre—
`gation has been reduced to the point at which
`both fluids are present in the turbulent zone,
`turbulent mixing becomes an important means
`of further reduction in scale. Convection is still
`of importance here, however, largely because it
`serves to bring the entire tank contents to the
`turbulent zone in a comparatively short time.
`As the scale of segregation is reduced, with a
`
`MIXING - 5
`Page 15
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`

`

`resulting increase in interfacial area, moleClllélr
`diffusion becomes significant. As pointed Ollt
`earlier, diffusion is necessary for the effective
`reduction of the intensity of segregation to zero,
`at which time mixing is complete.
`The increase in scale observed in the latter
`part of the mixing process, as shown in Figure
`1-1, results from molecular diffusion, which
`equalizes the composition of adjacent portions of
`fluid, resulting in large regions with an interme-
`diate composition. At the completion of mjxing,
`the composition becomes. uniform throughOUI
`the fluid, and the linear scale of segregation in-
`creases in value to a number equal in magnitude
`to the dimension of the mixing tank.
`
`Equipment
`to be
`Batch Mixing. When the material
`mixed is limited in volume to that which may be
`conveniently contained in a suitable mixer,
`batch mixing is usually most feasible. A system
`for batch mixing commonly consists of two Pfi-
`mary components: (1) a tank or other container
`suitable to hold the material being mixed, and
`(2) a means of supplying energy to the system SO
`as to bring about reasonably rapid mixing. Power
`may be supplied to the fluid mass by means Of
`an impeller, air stream, or liquid jet. Besides
`Supplying power, these also serve to direct the
`flow of material within the vessel. Baffles, vanes.
`or ducts also are used to direct the bulk move-
`ment of material in such mixers,
`thereby in—
`creasing their efficiency.
`1. Impellers. The distinction between 11111361-
`ler types is often made on the basis of type 0f
`flow pattern they produce, or on the basis of the
`
`
`
`TIME OF MIXING
`FIG. 1-1. The intensity of segregation, 1, and the scale of
`segregation, S, as a function of time. Bulk transport, tur-
`bulent mixing, and molecular diffusion are predominant
`over the time periods A, B, and C, respectively. The linear
`scale of segregation may be seen to increase at the end of
`the mixing operation. The final mixture will be uniform in
`composition and may be considered a single lump with ll
`linear scale equal to the linear dimensions of the mix”.
`
`6 - The Theory and Practice of Industrial Pharmacy
`
`A
`
`q
`
`B
`
`11
`
`I.
`
`C
`
`FIG. 1-2. A and B, Diagrammatic representation of
`cylindric tanks in which tangential and radial flow occur,
`respectively. C, Side view of a similar tank in which axial
`flow occurs. These diagrams represent systems in which
`only one type of flow occurs, in contrast to the usual situa-
`tion in which two or more of these flow patterns occur
`simultaneously.
`
`shape and pitch of the blades. Three basic types
`of flow may be produced: radial, axial, and tan—
`gential. These may occur singly or in various
`combinations. Figure 1—2 illustrates these pat-
`terns as they occur in vertical cylindric tanks.
`Propellers characteristically produce flow paral-
`lel to their axes of rotation, whereas turbines
`may produce either axial or tangential flow, or a
`combination of these.
`Propellers of various types and form are used
`but all are essentially a segment of a multi-
`threaded screw, that is, a screw with as many
`threads as the propeller has blades. Also, in com—
`mon with machine screws, propellers may be
`either right-or left-handed depending on the di-
`rection of slant of their blades. As with screws,
`propeller pitch is defined as the distance of axial
`movement per revolution if no slippage occurs.
`Although any number of blades may be used,
`the three—blade design is most common for use
`with fluids. The blades may be set at any angle
`or pitch, but for most applications, the pitch is
`approximately equal to the propeller diameter.
`Propellers are most efficient when they can be
`run at high speed in liquids of relatively low vis—
`cosity.
`Although some tangential‘flow occurs, the pri-
`mary effect of a propeller is to induce axial flow.
`Also, intense turbulence usually occurs in the
`immediate vicinity of the propeller. Consider, for
`example,
`a down-draft propeller vertically
`
`Page 16
`
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`
`

`

`all
`
`7"
`
`071‘
`
`FIG. 1-3. Impellerblade types (only one bladeshown?top
`
`and side views. A and B, Radial flow design: C and D,
`mixed radial-axial flow design. For axial pumping,
`the
`blade must be set at an incline to the axis of the shaft.
`
`mounted midway to the bottom of a tank Mod-
`erate radial and tangential flow occurring above
`and below the blades acting in conjunction with
`the axial flow near the shaft, brings portions of
`fluid together from all regions of the tank and
`passes them through the intense turbulence
`near the blades.
`Turbines are usually distinguished from pro—
`pellers in that the blades of the latter do not have
`a constant pitch throughout their length. When
`radial—tangential flow is desired