RHEOLOGY OF PARTICULATE DISPERSIONS AND COMPOSITESDANIEL BLANKSCHTEINDepartment of ChemicalEngineeringMassachusetts Institute of TechnologyCambridge, MassachusettsS. KARABORNIShell International PetroleumCompany LimitedLondon, EnglandLISA B. QUENCERThe Dow Chemical CompanyMidland, MichiganJOHN F. SCAMEHORNInstitute for Applied SurfactantResearchUniversity of OklahomaNorman, OklahomaP. SOMASUNDARANHenry Krumb School of MinesColumbia UniversityNew York, New YorkERIC W. KALERDepartment of ChemicalEngineeringUniversity of DelawareNewark, DelawareCLARENCE MILLERChemical and Biomolecular Engineering DepartmentRice UniversityHouston, TexasDON RUBINGHThe Procter & Gamble CompanyCincinnati, OhioBEREND SMITShell International Oil Products B.V.Amsterdam, The NetherlandsJOHN TEXTERStrider Research CorporationRochester, New YorkSURFACTANT SCIENCE SERIESFOUNDING EDITORMARTIN J. SCHICK19181998SERIES EDITORARTHUR T. HUBBARDSanta Barbara Science ProjectSanta Barbara, CaliforniaADVISORY BOARD1. Nonionic Surfactants, edited by Martin J. Schick (see alsoVolumes 19, 23, and 60)2. Solvent Properties of Surfactant Solutions, edited by Kozo Shinoda (see Volume 55)3. Surfactant Biodegradation, R. D. Swisher (see Volume 18)4. Cationic Surfactants, edited by Eric Jungermann (see alsoVolumes 34, 37, and 53)5. Detergency: Theory and Test Methods (in three parts), edited byW. G. Cutler and R. C. Davis (see also Volume 20)6. Emulsions and Emulsion Technology (in three parts), edited byKenneth J. Lissant7. Anionic Surfactants (in two parts), edited by Warner M. Linfield(see Volume 56)8. Anionic Surfactants: Chemical Analysis, edited by John Cross9. Stabilization of Colloidal Dispersions by Polymer Adsorption,Tatsuo Sato and Richard Ruch 10. Anionic Surfactants: Biochemistry, Toxicology, Dermatology,edited by Christian Gloxhuber (see Volume 43)11. Anionic Surfactants: Physical Chemistry of Surfactant Action,edited by E. H. Lucassen-Reynders 12. Amphoteric Surfactants, edited by B. R. Bluestein and Clifford L. Hilton (see Volume 59)13. Demulsification: Industrial Applications, Kenneth J. Lissant 14. Surfactants in Textile Processing, Arved Datyner15. Electrical Phenomena at Interfaces: Fundamentals,Measurements, and Applications, edited by Ayao Kitahara and Akira Watanabe16. Surfactants in Cosmetics, edited by Martin M. Rieger (seeVolume 68)17. Interfacial Phenomena: Equilibrium and Dynamic Effects,Clarence A. Miller and P. Neogi18. Surfactant Biodegradation: Second Edition, Revised and Expanded, R. D. Swisher19. Nonionic Surfactants: Chemical Analysis, edited by John Cross20. Detergency: Theory and Technology, edited by W. Gale Cutlerand Erik Kissa21. Interfacial Phenomena in Apolar Media, edited by Hans-FriedrichEicke and Geoffrey D. Parfitt22. Surfactant Solutions: New Methods of Investigation, edited byRaoul Zana23. Nonionic Surfactants: Physical Chemistry, edited by Martin J. Schick24. Microemulsion Systems, edited by Henri L. Rosano and Marc Clausse25. Biosurfactants and Biotechnology, edited by Naim Kosaric, W. L. Cairns, and Neil C. C. Gray26. Surfactants in Emerging Technologies, edited by Milton J. Rosen27. Reagents in Mineral Technology, edited by P. Somasundaran and Brij M. Moudgil28. Surfactants in Chemical/Process Engineering, edited by Darsh T. Wasan, Martin E. Ginn, and Dinesh O. Shah29. Thin Liquid Films, edited by I. B. Ivanov30. Microemulsions and Related Systems: Formulation, Solvency,and Physical Properties, edited by Maurice Bourrel and Robert S. Schechter 31. Crystallization and Polymorphism of Fats and Fatty Acids, edited by Nissim Garti and Kiyotaka Sato32. Interfacial Phenomena in Coal Technology, edited by Gregory D. Botsaris and Yuli M. Glazman33. Surfactant-Based Separation Processes, edited by John F. Scamehorn and Jeffrey H. Harwell34. Cationic Surfactants: Organic Chemistry, edited by James M. Richmond35. Alkylene Oxides and Their Polymers, F. E. Bailey, Jr., and Joseph V. Koleske36. Interfacial Phenomena in Petroleum Recovery, edited by Norman R. Morrow37. Cationic Surfactants: Physical Chemistry, edited by Donn N. Rubingh and Paul M. Holland38. Kinetics and Catalysis in Microheterogeneous Systems, edited by M. Grtzel and K. Kalyanasundaram39. Interfacial Phenomena in Biological Systems, edited by Max Bender40. Analysis of Surfactants, Thomas M. Schmitt (see Volume 96)41. Light Scattering by Liquid Surfaces and ComplementaryTechniques, edited by Dominique Langevin42. Polymeric Surfactants, Irja Piirma43. Anionic Surfactants: Biochemistry, Toxicology, Dermatology.Second Edition, Revised and Expanded, edited by Christian Gloxhuber and Klaus Knstler44. Organized Solutions: Surfactants in Science and Technology,edited by Stig E. Friberg and Bjrn Lindman45. Defoaming: Theory and Industrial Applications, edited by P. R. Garrett46. Mixed Surfactant Systems, edited by Keizo Ogino and Masahiko Abe47. Coagulation and Flocculation: Theory and Applications, edited byBohuslav Dobis48. Biosurfactants: Production Properties Applications, edited byNaim Kosaric49. Wettability, edited by John C. Berg50. Fluorinated Surfactants: Synthesis Properties Applications, Erik Kissa51. Surface and Colloid Chemistry in Advanced CeramicsProcessing, edited by Robert J. Pugh and Lennart Bergstrm52. Technological Applications of Dispersions, edited by Robert B. McKay53. Cationic Surfactants: Analytical and Biological Evaluation, edited by John Cross and Edward J. Singer54. Surfactants in Agrochemicals, Tharwat F. Tadros55. Solubilization in Surfactant Aggregates, edited by Sherril D. Christian and John F. Scamehorn56. Anionic Surfactants: Organic Chemistry, edited by Helmut W. Stache57. Foams: Theory, Measurements, and Applications, edited byRobert K. Prudhomme and Saad A. Khan58. The Preparation of Dispersions in Liquids, H. N. Stein59. Amphoteric Surfactants: Second Edition, edited by Eric G. Lomax60. Nonionic Surfactants: Polyoxyalkylene Block Copolymers, edited by Vaughn M. Nace61. Emulsions and Emulsion Stability, edited by Johan Sjblom62. Vesicles, edited by Morton Rosoff63. Applied Surface Thermodynamics, edited by A. W. Neumann and Jan K. Spelt64. Surfactants in Solution, edited by Arun K. Chattopadhyay and K. L. Mittal65. Detergents in the Environment, edited by Milan Johann Schwuger66. Industrial Applications of Microemulsions, edited by Conxita Solans and Hironobu Kunieda67. Liquid Detergents, edited by Kuo-Yann Lai68. Surfactants in Cosmetics: Second Edition, Revised and Expanded, edited by Martin M. Rieger and Linda D. Rhein69. Enzymes in Detergency, edited by Jan H. van Ee, Onno Misset,and Erik J. Baas70. Structure-Performance Relationships in Surfactants, edited byKunio Esumi and Minoru Ueno71. Powdered Detergents, edited by Michael S. Showell72. Nonionic Surfactants: Organic Chemistry, edited by Nico M. van Os73. Anionic Surfactants: Analytical Chemistry, Second Edition,Revised and Expanded, edited by John Cross74. Novel Surfactants: Preparation, Applications, and Biodegradability, edited by Krister Holmberg75. Biopolymers at Interfaces, edited by Martin Malmsten76. Electrical Phenomena at Interfaces: Fundamentals,Measurements, and Applications, Second Edition, Revised and Expanded, edited by Hiroyuki Ohshima and Kunio Furusawa77. Polymer-Surfactant Systems, edited by Jan C. T. Kwak78. Surfaces of Nanoparticles and Porous Materials, edited byJames A. Schwarz and Cristian I. Contescu79. Surface Chemistry and Electrochemistry of Membranes, edited by Torben Smith Srensen80. Interfacial Phenomena in Chromatography, edited by Emile Pefferkorn81. SolidLiquid Dispersions, Bohuslav Dobis, Xueping Qiu, and Wolfgang von Rybinski82. Handbook of Detergents, editor in chief: Uri Zoller Part A:Properties, edited by Guy Broze83. Modern Characterization Methods of Surfactant Systems, edited by Bernard P. Binks84. Dispersions: Characterization, Testing, and Measurement, Erik Kissa85. Interfacial Forces and Fields: Theory and Applications, edited byJyh-Ping Hsu86. Silicone Surfactants, edited by Randal M. Hill87. Surface Characterization Methods: Principles, Techniques, and Applications, edited by Andrew J. Milling88. Interfacial Dynamics, edited by Nikola Kallay89. Computational Methods in Surface and Colloid Science, edited by Malgorzata Borwko90. Adsorption on Silica Surfaces, edited by Eugne Papirer91. Nonionic Surfactants: Alkyl Polyglucosides, edited by DieterBalzer and Harald Lders92. Fine Particles: Synthesis, Characterization, and Mechanisms of Growth, edited by Tadao Sugimoto93. Thermal Behavior of Dispersed Systems, edited by Nissim Garti94. Surface Characteristics of Fibers and Textiles, edited byChristopher M. Pastore and Paul Kiekens 95. Liquid Interfaces in Chemical, Biological, and PharmaceuticalApplications, edited by Alexander G. Volkov96. Analysis of Surfactants: Second Edition, Revised and Expanded, Thomas M. Schmitt97. Fluorinated Surfactants and Repellents: Second Edition, Revised and Expanded, Erik Kissa98. Detergency of Specialty Surfactants, edited by Floyd E. Friedli99. Physical Chemistry of Polyelectrolytes, edited by Tsetska Radeva100. Reactions and Synthesis in Surfactant Systems, edited by John Texter101. Protein-Based Surfactants: Synthesis, PhysicochemicalProperties, and Applications, edited by Ifendu A. Nnanna and Jiding Xia102. Chemical Properties of Material Surfaces, Marek Kosmulski103. Oxide Surfaces, edited by James A. Wingrave104. Polymers in Particulate Systems: Properties and Applications,edited by Vincent A. Hackley, P. Somasundaran, and Jennifer A. Lewis105. Colloid and Surface Properties of Clays and Related Minerals,Rossman F. Giese and Carel J. van Oss106. Interfacial Electrokinetics and Electrophoresis, edited by ngel V. Delgado107. Adsorption: Theory, Modeling, and Analysis, edited by Jzsef Tth108. Interfacial Applications in Environmental Engineering, edited byMark A. Keane109. Adsorption and Aggregation of Surfactants in Solution, edited byK. L. Mittal and Dinesh O. Shah110. Biopolymers at Interfaces: Second Edition, Revised and Expanded, edited by Martin Malmsten111. Biomolecular Films: Design, Function, and Applications, edited by James F. Rusling112. StructurePerformance Relationships in Surfactants:Second Edition, Revised and Expanded, edited by Kunio Esumiand Minoru Ueno113. Liquid Interfacial Systems: Oscillations and Instability, Rudolph V. Birikh,Vladimir A. Briskman, Manuel G. Velarde, and Jean-Claude Legros114. Novel Surfactants: Preparation, Applications, andBiodegradability: Second Edition, Revised and Expanded, edited by Krister Holmberg115. Colloidal Polymers: Synthesis and Characterization, edited by Abdelhamid Elaissari116. Colloidal Biomolecules, Biomaterials, and BiomedicalApplications, edited by Abdelhamid Elaissari117. Gemini Surfactants: Synthesis, Interfacial and Solution-PhaseBehavior, and Applications, edited by Raoul Zana and Jiding Xia118. Colloidal Science of Flotation, Anh V. Nguyen and Hans Joachim Schulze119. Surface and Interfacial Tension: Measurement, Theory, and Applications, edited by Stanley Hartland120. Microporous Media: Synthesis, Properties, and Modeling, Freddy Romm121. Handbook of Detergents, editor in chief: Uri Zoller Part B:Environmental Impact, edited by Uri Zoller122. Luminous Chemical Vapor Deposition and Interface Engineering,Hirotsugu Yasuda123. Handbook of Detergents, editor in chief: Uri Zoller Part C:Analysis, edited by Heinrich Waldhoff and Rdiger Spilker124. Mixed Surfactant Systems: Second Edition, Revised and Expanded, edited by Masahiko Abe and John F. Scamehorn125. Dynamics of Surfactant Self-Assemblies: Micelles,Microemulsions, Vesicles and Lyotropic Phases, edited by Raoul Zana126. Coagulation and Flocculation: Second Edition, edited by Hansjoachim Stechemesser and Bohulav Dobis127. Bicontinuous Liquid Crystals, edited by Matthew L. Lynch and Patrick T. Spicer128. Handbook of Detergents, editor in chief: Uri Zoller Part D:Formulation, edited by Michael S. Showell129. Liquid Detergents: Second Edition, edited by Kuo-Yann Lai130. Finely Dispersed Particles: Micro-, Nano-, and Atto-Engineering,edited by Aleksandar M. Spasic and Jyh-Ping Hsu131. Colloidal Silica: Fundamentals and Applications, edited byHoracio E. Bergna and William O. Roberts132. Emulsions and Emulsion Stability, Second Edition, edited byJohan Sjblom133. Micellar Catalysis, Mohammad Niyaz Khan134. Molecular and Colloidal Electro-Optics, Stoyl P. Stoylov and Maria V. Stoimenova135. Surfactants in Personal Care Products and DecorativeCosmetics, Third Edition, edited by Linda D. Rhein, Mitchell Schlossman, Anthony O'Lenick, and P. Somasundaran136. Rheology of Particulate Dispersions and Composites, Rajinder PalRHEOLOGY OF PARTICULATEDISPERSIONS AND COMPOSITESRajinder PalUniversity of WaterlooOntario, CanadaCRC Press is an imprint of theTaylor & Francis Group, an informa businessBoca Raton London New YorkCRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number-10: 1-57444-520-0 (Hardcover)International Standard Book Number-13: 978-1-57444-520-6 (Hardcover)This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.Library of Congress Cataloging-in-Publication DataPal, Rajinder.Rheology of particulate dispersions and composites / Rajinder Pal.p. cm. -- (Surfactant science series ; v. 136)Includes bibliographical references and index.ISBN 1-57444-520-0 (alk. paper)1. Granular materials--Fluid dynamics. 2. Inhomogeneous materials--Fluid dynam-ics. I. Title. II. Series.TA418.78.P324 2006660.294514--dc22 2006045549Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.comDK3354_Prelims.fm Page x Tuesday, October 24, 2006 8:56 AMDedicationTo the memory of my mother, Smt Karma-Bhari, and to my father, Shri Khushal ChandDK3354_C000.fm Page xi Tuesday, October 24, 2006 9:00 AMDK3354_C000.fm Page xii Tuesday, October 24, 2006 9:00 AMPrefaceParticulate dispersion (or simply dispersion) consists of fine insoluble particlesdistributed throughout a continuous liquid phase. The particulate phase of thedispersion may be solid, liquid, or gas. When the particulate phase is solid, thedispersions are referred to as suspensions. When the particulate phase is liquid(liquid droplets), the dispersion is called an emulsion. The dispersion with gaseousparticulate phase (bubbles) is referred to as bubbly liquid or bubbly suspensionwhen the volume fraction of bubbles in the dispersion is less than , themaximum packing concentration of undeformed bubbles; the dispersion is calledfoam when the volume fraction of bubbles exceeds is 0.637 for randomclose packing of uniform spheres). The particles of the dispersion are not always composed of a single phase(solid, liquid, or gas). For instance, the particles may consist of a liquid coreencapsulated with a uniform layer of solid material. Such types of complexparticles are referred to as capsules. Examples of other types of complex particlesare solid coreliquid shell particles, which consist of a solid inner core encapsu-lated with a uniform layer of liquid that is immiscible in the continuous phase,and liquid coreliquid shell particles (also referred to as double-emulsion drop-lets), which consist of a liquid inner core completely engulfed by a second liquidthat is immiscible in both the inner liquid and the continuous phase. Particulate dispersions form a large group of materials of industrial impor-tance. Both aqueous and nonaqueous dispersions are encountered in industrialapplications. Some of the fields in which dispersions play a vital role are ceramics;computers and particulate recording media; nanotechnology; biomedicine; bio-technology; paints; environment (marine oil spills); food; pipeline transportationof materials; petroleum production; cosmetics and toiletries; and geology (vol-canic eruptions).In the formulation, handling, mixing, processing, storage, and pumping ofparticulate dispersions, knowledge of the rheological properties is required forthe design, selection, and operation of the equipment involved.Unlike particulate dispersions, which are generally fluidic in nature, compos-ites are solid heterogeneous materials composed of two or more phases. Manycomposites of practical interest are composed of just two phases: the dispersedphase and the matrix (continuous phase). Composite materials can be classifiedinto two broad groups: particle-reinforced (particulate) composites and fiber-reinforced composites. Particulate composites usually consist of isometric (samedimension in all directions) particles. Fiber-reinforced composites, as the nameimplies, consist of fibers of high aspect ratio as the dispersed phase. The com-mercial and industrial applications of composite materials are many. For example,m m m(DK3354_C000.fm Page xiii Tuesday, October 24, 2006 9:00 AMxiv Prefacethey are used widely as dental restorative materials, as tool materials for high-speed cutting of difficult-to-machine materials, and as solid propellants in aero-space propulsion. Composite materials also play an important role in aircraft,automotive, sport, marine, plastics, and electronics industries. Knowledge of the rheological properties of composites is required in theanalysis and design of structures made from composite materials. Rheology alsoplays a vital role in the development of new composite materials that meet specificstrength or stiffness requirements. In order to develop tailor-made compositeswith specific mechanical properties, rheological models are needed to predict themechanical properties of composites from the properties and volume fractions ofthe individual components. A number of excellent books are available on the rheology of materials. Butnone of them provide a systematic and comprehensive coverage of the funda-mental rheology of particulate dispersions and two-phase solid composites. Thisbook covers a wide variety of dispersed systems with major emphasis on theexact rheological constitutive equations based on the fundamental laws ofmechanics. Empirical results are generally avoided. The book is divided into six parts. Part I, titled Introduction, consists ofthree chapters. Chapter 1 discusses the applications of particulate dispersionsand composites. Chapter 2 reviews the fundamental aspects of fluid mechanics,solid mechanics, and interfacial mechanics. Chapter 3 introduces concepts suchas bulk stress in dispersions and composites, dipole strength of a particle, andconstitutive equations for particulate dispersions and composites. Part II, titledRheology of Dispersions of Rigid Particles, consists of Chapter 4 to Chapter6. Both spherical and nonspherical particles are considered. The rheology ofdispersions of rigid dipolar (magnetic) particles, spherical and nonspherical, inthe presence of an external magnetic field is also described. Part III, titledRheology of Dispersions of Nonrigid Particles, consists of Chapter 7 to Chapter11. Chapter 7 deals with dispersions of soft (deformable) solid particles. Therheology of emulsions (dispersions of liquid droplets) in the absence and pres-ence of surfactant is discussed in Chapter 8. Chapter 9 describes the rheologyof bubbly suspensions. The dispersion of capsules is dealt with in Chapter 10.The rheology of dispersions of coreshell particles is described in Chapter 11.The types of core-shell particles considered are solid coreporous shell, solidcoreliquid shell, and liquid coreliquid shell. Part IV, titled Rheology ofComposites, consists of two chapters (Chapter 12 and Chapter 13) dealing withthe elastic properties of solid composite materials. Chapter 12 describes partic-ulate composites in this respect and Chapter 13 deals with fiber-reinforcedcomposites. Part V, titled Linear Viscoelasticity of Particulate Dispersions andComposites, consists of Chapter 14 to Chapter 16. Chapter 14 covers some ofthe basic aspects of linear viscoelasticity. The dynamic viscoelastic behavior ofparticulate dispersions and composites are dealt with in Chapter 15 and Chapter 16,respectively. Part VI, titled Appendices, consists of four useful appendices.This book provides both an introduction to the subject for newcomers andsufficient in-depth coverage for those involved with the rheology of dispersedDK3354_C000.fm Page xiv Tuesday, October 24, 2006 9:00 AMPreface xvsystems. Scientists and engineers from a broad range of fields will find the bookan attractive and comprehensive source of information on the fundamental rhe-ology of a wide variety of particulate dispersed systems. It could also serve as atextbook for a graduate-level course on rheology.I wish to thank the late consulting editor of the Surfactant Science Series,Dr. Martin Schick, for inviting me to write a book in my area of specialization,that is, the rheology of dispersed systems. For their love and support, I am gratefulto my wife, Archana, and my children, Anuva and Arnav. Rajinder PalDK3354_C000.fm Page xv Tuesday, October 24, 2006 9:00 AMDK3354_C000.fm Page xvi Tuesday, October 24, 2006 9:00 AMAbout the AuthorRajinder Pal is a professor of chemical engineering at the University of Waterloo,Ontario, Canada. He received his B.Tech degree (1981) in chemical engineeringfrom the Indian Institute of Technology, Kanpur, and a Ph.D. degree (1987) inchemical engineering from the University of Waterloo. The author of more than100 refereed journal publications in the areas of rheology of dispersed systems(emulsions, suspensions, foams, and particulate composites), pipeline flow behav-ior of particulate dispersions, and emulsion liquid membranes, Dr. Pal is a fellowof the Chemical Institute of Canada. In recognition of his distinguished contri-butions in chemical engineering before the age of 40, he received the SyncrudeCanada Innovation Award in 1998 from the Canadian Society for ChemicalEngineering. In 2001, he received the Teaching Excellence Award of the Facultyof Engineering, University of Waterloo. Dr. Pal served as associate editor of theCanadian Journal of Chemical Engineering from 1992 to 2004. He is a registeredprofessional engineer in the province of Ontario.DK3354_C000.fm Page xvii Tuesday, October 24, 2006 9:00 AMDK3354_C000.fm Page xviii Tuesday, October 24, 2006 9:00 AMTable of ContentsPART I IntroductionChapter 1Applications of Particulate Dispersions and Composites .................................... 31.1 Particulate Dispersions................................................................................... 31.1.1 Ceramics .............................................................................................31.1.2 Particulate Recording Media ............................................................. 41.1.3 Nanotechnological Applications .......................................................51.1.4 Biomedical Applications ................................................................... 51.1.5 Biotechnological Applications ..........................................................71.1.6 Paints.................................................................................................. 81.1.7 Marine Oil Spills ............................................................................... 81.1.8 Food Applications ............................................................................. 91.1.9 Pipeline Transportation of Materials ................................................ 91.1.10 Petroleum Production ......................................................................101.1.11 Cosmetics and Toiletries ................................................................. 121.1.12 Geological Applications .................................................................. 121.2 Composites ..................................................................................................131.2.1 Particulate Composites and Their Applications ............................... 141.2.1.1 Coarse-Particle Composites ............................................ 141.2.1.2 Fine-Particle Composites.................................................. 151.2.2 Fiber-Reinforced Composites and Their Applications......................16References ...........................................................................................................17Chapter 2Brief Review of Mechanics of Fluids, Solids, and Interfaces .......................... 212.1 Basic Concepts of Continuum Mechanics ................................................. 212.1.1 Continuum Model of Matter .............................................................. 212.1.2 Kinematics ......................................................................................... 212.1.2.1 Lagrangian and Eulerian Descriptions of Deformation and Flow................................................... 212.1.2.2 Displacement Gradient Tensors ...................................... 252.1.2.3 Deformation Gradient Tensors ........................................ 262.1.2.4 Finite Strain Tensors ....................................................... 262.1.2.5 Material Time Derivative of a Spatial Function ............. 28DK3354_bookTOC.fm Page xix Tuesday, October 24, 2006 5:41 PMxx Table of Contents2.1.2.6 Material Time Derivative of a Volume Integral (Reynolds Transport Theorem) ...................................... 292.1.2.7 Velocity Gradient Tensor ................................................ 302.1.2.8 Rate of Deformation Tensor and Vorticity Tensor ......... 302.1.2.9 Shear Rate Tensor ........................................................... 322.1.3 Stress Vector and Stress Tensor ........................................................322.1.3.1 Stress Vector .....................................................................322.1.3.2 Stress Tensor..................................................................... 332.1.4 Constitutive Equation ......................................................................... 342.2 Mechanics of Fluids.....................................................................................352.2.1 The Continuity Equation.................................................................... 352.2.2 The Equation of Motion ................................................................... 372.2.3 The NavierStokes Equation ............................................................ 382.2.4 CreepingFlow Equations .................................................................392.3 Mechanics of Solids ...................................................................................402.4 Mechanics of Interfaces .............................................................................. 402.4.1 Definitions of Important Terms ........................................................412.4.1.1 Surface Unit Tensor and Surface Gradient Operator .....412.4.1.2 Surface Deformation Gradient Tensor ............................ 412.4.1.3 Surface Strain Tensor ...................................................... 412.4.1.4 Surface Rate of Strain Tensor ......................................... 422.4.1.5 Surface Stress Vector ...................................................... 422.4.1.6 Surface Stress Tensor ...................................................... 432.4.2 Surface Divergence Theorem ............................................................ 432.4.3 Force Balance on Interfacial Film .................................................... 442.4.4 Interfacial Rheology .......................................................................... 45Notation............................................................................................................... 46Supplemental Reading ........................................................................................48Chapter 3Bulk Stress in Particulate Dispersions and Composites ....................................513.1 Dispersed System as a Continuum ............................................................. 513.2 Ensemble vs. Volume Averaging ................................................................513.3 Bulk Stress in Dispersions and Composites ..............................................523.3.1 Dispersions ........................................................................................533.3.1.1 Dipole Strength of Rigid Particles .................................. 573.3.1.2 Dipole Strength of Droplets with Interfacial Film ...............................................................583.3.2 Composites ........................................................................................613.4 Constitutive Equations for Dispersed Systems .......................................... 623.4.1 Dilute System of Nonspherical Particles .......................................... 633.4.2 Dilute System of Spherical Particles ................................................ 63DK3354_bookTOC.fm Page xx Tuesday, October 24, 2006 5:41 PMTable of Contents xxi3.5 Nonhydrodynamic Effects in Dispersions .................................................. 63Notation............................................................................................................... 67References ...........................................................................................................69PART II Rheology of Dispersions of Rigid Particles Chapter 4 Dispersions of Rigid Spherical Particles ........................................................... 734.1 Introduction .................................................................................................734.2 Dispersions of Solid Spherical Particles ....................................................734.3 Dispersion of Porous Rigid Particles ......................................................... 774.4 Dispersions of Electrically Charged Solid Particles .................................. 814.4.1 Fundamental Equations ................................................................... 834.4.2 The Bulk Stress ...............................................................................874.4.3 Constitutive Equation ......................................................................89Notation............................................................................................................... 94References ...........................................................................................................96Chapter 5 Dispersions of Rigid Nonspherical Particles .................................................... 975.1 Introduction .................................................................................................975.2 Motion of a Single Isolated Spheroidal Particle in Shear Flow ................ 985.3 Rheology of Suspension of Non-Brownian Axisymmetric Particles ......1025.4 Effects of Brownian Motion on the Rheology of Axisymmetric Particles .........................................................................111Notation.............................................................................................................122References .........................................................................................................124Chapter 6 Dispersions of Rigid (Spherical and Nonspherical) Magnetic Particles ........1276.1 Introduction ...............................................................................................1276.2 Suspensions of Spherical Dipolar Particles .............................................1296.2.1 Motion of a Single Isolated Dipolar Particle in Shear Flow .........1296.2.2 Rheology of Suspensions of Spherical Dipolar Particles ..............1316.2.2.1 Effect of Rotary Brownian Motion ..................................1376.3 Suspensions of Nonspherical Dipolar Particles........................................ 139Notation.............................................................................................................146References .........................................................................................................148DK3354_bookTOC.fm Page xxi Tuesday, October 24, 2006 5:41 PMxxii Table of ContentsPART III Rheology of Dispersions of Nonrigid Particles Chapter 7 Dispersions of Soft (Deformable) Solid Particles ...........................................1517.1 Introduction ...............................................................................................1517.2 Fundamental Equations .............................................................................1527.2.1 Constitutive Equation of the Particle Material ...............................1537.3 Rheology of Dispersions of Soft, Solid-Like Elastic Particles ...............1547.4 Rheology of Dispersions of Soft Solid-Like Viscoelastic Particles ........159Notation.............................................................................................................159References .........................................................................................................161Chapter 8 Dispersions of Liquid Droplets .......................................................................1638.1 Introduction ...............................................................................................1638.2 Deformation and Breakup of Droplets .....................................................1658.3 Fundamental Equations .............................................................................1688.4 Rheology of Emulsions ............................................................................1708.4.1 Zero-Order Deformation Solution ..................................................1708.4.2 First-Order Deformation Solution ..................................................1748.4.3 Second-Order Deformation Solution ..............................................1818.5 Effect of Surfactants on Emulsion Rheology ...........................................185Notation.............................................................................................................190References .........................................................................................................193Chapter 9 Dispersions of Bubbles ....................................................................................1979.1 Introduction ...............................................................................................1979.2 Dilational Viscosity of Bubbly Suspensions ............................................1979.2.1 Normal Force at the Cell Boundary ...............................................1989.2.2 Normal Force at the Boundary of the Equivalent Homogeneous Fluid ........................................................................2009.2.3 Equation for Dilational Viscosity ...................................................2019.3 Constitutive Equation for Bubbly Suspensions ........................................2029.4 Effect of Surfactants on the Rheology of Bubbly Suspensions .............................................................................206Notation.............................................................................................................208References .........................................................................................................209DK3354_bookTOC.fm Page xxii Tuesday, October 24, 2006 5:41 PMTable of Contents xxiiiChapter 10 Dispersions of Capsules ..................................................................................21110.1 Introduction .............................................................................................21110.2 Fundamental Equations ...........................................................................21310.3 Membrane Mechanics .............................................................................21510.3.1 Strain Energy Function of Membrane Material .........................21610.3.1.1 MooneyRivlin (MR) Type Membrane ......................21710.3.1.2 RBC-Type Membrane .................................................21710.4 Instantaneous Shape of Initially Spherical Capsule ...................................................................................21710.4.1 Deformation of a Capsule in Steady Irrotational Flow .........................................................................22010.4.2 Deformation of a Capsule in Steady Simple Shear Flow ..................................................................................22110.4.2.1 Capsule with a MooneyRivlin-Type Membrane ....................................................................22110.4.2.2 Capsule with an RBC-Type Membrane ......................22210.5 Rheological Constitutive Equation for Dispersion of Capsules ..........................................................................22310.5.1 Steady Irrotational Flow .............................................................22310.5.2 Steady Simple Shear Flow .........................................................22410.5.2.1 Capsule with a MooneyRivlin-Type Membrane ....................................................................22410.5.2.2 Capsule with an RBC-Type Membrane ...................... 226Notation.............................................................................................................227References .........................................................................................................229Chapter 11Dispersions of CoreShell Particles ................................................................23111.1 Introduction .............................................................................................23111.2 Rheology of Dispersions of Coreshell Particles ..................................23411.2.1 Dispersions of Solid CoreHairy Shell Particles .......................23411.2.2 Dispersions of Solid CoreLiquid Shell Particles .....................23911.2.3 Dispersions of Liquid CoreLiquid Shell (Double-Emulsion) Droplets ......................................................242Notation.............................................................................................................249References .........................................................................................................251DK3354_bookTOC.fm Page xxiii Tuesday, October 24, 2006 5:41 PMxxiv Table of ContentsPART IV Rheology of Composites Chapter 12Particulate Composites ....................................................................................25512.1 Introduction .............................................................................................25512.2 Constitutive Equation for Particulate Composites .................................25612.3 Dipole Strength of Spherical Particles ...................................................25712.4 Effective Elastic Moduli of Particulate Composites with Spherical Particles .....................................................25912.4.1 Composites with Rigid Spherical Particles ................................26412.4.2 Composites with Incompressible Matrix ...................................26512.4.3 Composites with Pores ...............................................................26512.5 Effective Elastic Moduli of Particulate Composites with Disk-shaped Particles .................................................26612.6 Bounds for the Effective Elastic Properties of Particulate Composites ......................................................................269Notation.............................................................................................................276References .........................................................................................................277Chapter 13Fiber-Reinforced Composites ..........................................................................27913.1 Introduction .............................................................................................27913.2 Elastic Behavior of Continuous-Fiber Composites ................................27913.2.1 Unidirectional Continuous-Fiber Composites ............................27913.2.1.1 Elementary Models ......................................................28213.2.1.2 Improved Models .........................................................28713.2.1.3 Bounds on the Elastic Properties of Unidirectional Continuous-Fiber Composites .....................................29013.2.2 Randomly Oriented Continuous-Fiber Composites ...................29113.3 Elastic Behavior of Discontinuous Short-fiber Composites ..................29213.3.1 Unidirectional Short-Fiber Composites...................................... 29213.3.2 Randomly Oriented Short-Fiber Composites .............................298Notation.............................................................................................................299References .........................................................................................................301PART V Linear Viscoelasticity of Particulate Dispersions and Composites Chapter 14 Introduction to Linear Viscoelasticity .............................................................30514.1 Linear Viscoelasticity .............................................................................30514.2 Oscillatory Shear .....................................................................................306DK3354_bookTOC.fm Page xxiv Tuesday, October 24, 2006 5:41 PMTable of Contents xxv14.3 Maxwell Model .......................................................................................309Notation.............................................................................................................311References .........................................................................................................312Chapter 15 Dynamic Viscoelastic Behavior of Particulate Dispersions ............................31315.1 Dispersions of Soft Rubberlike Solid Particles ......................................31315.1.1 Generalization of Frohlich and Sack Model ..............................31815.2 Dispersions of Deformable Liquid Droplets with Pure Interface .................................................................................31915.2.1 Generalization of Oldroyd Model ..............................................32415.3 Dispersions Of Deformable Liquid Droplets Coated With Additive .............................................................................32915.3.1 Droplets Coated with Purely Viscous Films ..............................32915.3.2 Droplets Coated with Purely Elastic Films ................................33215.3.3 Droplets Coated with Viscoelastic Films ...................................33615.3.3.1 Palierne Model .............................................................34115.3.4 Droplets Coated with Films Possessing Bending Rigidity ........34215.3.5 Droplets Coated with Liquid Films ............................................347Notation.............................................................................................................351References .........................................................................................................354Chapter 16 Dynamic Viscoelastic Behavior of Composites ..............................................35516.1 Introduction .............................................................................................35516.2 Elastic-Viscoelastic Correspondence Principle ..................................................................................................35516.3 Complex Moduli of Viscoelastic Particulate Composites .....................35516.4 Complex Moduli of Viscoelastic Fiber-Reinforced Composites ...........364Notation.............................................................................................................371References .........................................................................................................372PART VI AppendicesAppendix AEquations Related to Mechanics of Fluids and Solids in Different Coordinate Systems .....................................................................375A.1 Equations Related to Fluid Mechanics ....................................................375A.1.1 Continuity Equation in Different Coordinate Systems .....................................................................375A.1.2 Equations of Motion in Different Coordinate Systems .....................................................................376DK3354_bookTOC.fm Page xxv Tuesday, October 24, 2006 5:41 PMxxvi Table of ContentsA.1.3 Rate of Strain Tensor (E__) in Different Coordinate Systems .....................................................................378A.1.4 Shear Rate Tensor in Different Coordinate Systems .....................................................................379A.1.5 Vorticity Tensor in Different Coordinate Systems .....................................................................380A.1.6 Viscous Stress Tensor for Newtonian Fluids in Different Coordinate Systems ......................................380A.1.7 NavierStokes Equations in DifferentCoordinate Systems .....................................................................382A.2 Equations Related to Mechanics of Solids ......................................................................................................384A.2.1 Infinitesimal Strain Tensor in Different Coordinate Systems .....................................................................384A.2.2 Equilibrium Equation in Different Coordinate Systems .....................................................................385A.2.3 Hookes Law in Different Coordinate Systems .....................................................................387A.2.4 NavierCauchy Equations in DifferentCoordinate Systems .....................................................................388Appendix BVector and Tensor Operations in Index Notation ...........................................391B.1 Vector Operations ...................................................................................391B.2 Tensor Operations ..................................................................................393B.3 Some Useful Relations ...........................................................................395Appendix CGauss Divergence Theorem .............................................................................397Appendix D Symmetric Deviator of Fourth-Order Tensor ..................................................399Index..................................................................................................................401( )

( ) ( ) ( ) eDK3354_bookTOC.fm Page xxvi Tuesday, October 24, 2006 5:41 PMPart IIntroductionChapter 1 deals with the industrial and commercial applications of particulatedispersions and composites. Although the applications of such dispersed sys-tems are numerous, only some important ones are highlighted in this chapter.Industries in which dispersed systems are of importance include ceramics,particulate recording media, nanotechnology, biomedicine, biotechnology,paints, environment, food, pipeline transportation, petroleum, cosmetics andtoiletries, geology, cutting tools, aerospace, plastics, dentistry, metals and metalalloys, automobile, electronics, polymers, aircraft, sports, and marine.Chapter 2 presents a brief review of the mechanics of fluids, solids, andinterfaces. The basic concepts of continuum mechanics such as the continuumhypothesis, kinematics, stress vector, stress tensor, and constitutive equation areintroduced. Using the principles of conservation of mass and momentum, thecontinuity equation and equation of motion are derived. In the special case ofNewtonian fluids of constant viscosity and density, the equation of motion isshown to reduce to the celebrated NavierStokes equation. The section on themechanics of fluids concludes with creeping flow and creeping flow equations.The mechanics of solids is introduced with the equilibrium equation valid at everypoint of a solid material subjected to surface and body forces. The constitutiveequation for a Hookean solid is discussed. Using the Hookean constitutive equa-tion together with the equilibrium equation, the well-known NavierCauchyequation is derived. The last section of the chapter is devoted to the mechanicsof interfaces. After introducing some important definitions and the surface diver-gence theorem, the force balance on interfacial film is carried out. The sectionconcludes with a discussion on interfacial rheology.DK3354_S001.fm Page 1 Tuesday, October 3, 2006 9:35 PM2 Rheology of Particulate Dispersions and CompositesChapter 3 defines the bulk or average fields (stress, velocity, rate of strain,etc.) in dispersions and composites. The expressions for bulk stress in disper-sions and composites, in terms of the dipole strength of particles, are derived.The equations for the dipole strength of rigid (spherical and nonspherical)particles and nonrigid droplets with interfacial film are derived. The chapterconcludes with a section on the effects of nonhydrodynamic forces (such asBrownian, electrostatic, steric, and van der Waals forces) on the bulk stress ofdispersions.DK3354_S001.fm Page 2 Tuesday, October 3, 2006 9:35 PM31Applications of Particulate Dispersions and Composites1.1 PARTICULATE DISPERSIONSIn this book, particulate dispersions are defined as systems consisting of fineinsoluble particles (solid, liquid, or gas) distributed throughout a continuous liquidphase. The particles distributed within the continuous liquid phase are collectivelyreferred to as the particulate or dispersed phase. The continuous phase of thedispersion is sometimes referred to as the dispersion medium, external phase, ormatrix. Dispersions with a solid particulate phase are called suspensions, thosewith a liquid particulate phase are termed emulsions, and those with a gaseousparticulate phase are referred to as bubbly liquids or bubbly suspensions. Particulatedispersions have so many commercial and industrial applications that it is notpossible to list them all. Only some important ones are highlighted here.1.1.1 CERAMICSCeramics are a class of materials different from plastics (organics) and metals.They are inorganic nonmetal materials with unique properties such as high hard-ness (harder than steel), high heat and corrosion resistance (higher than polymersor metals), and low density (lower than most metals). Traditional ceramics arecomposed of materials such as clays and silica. Modern or advanced ceramicsare composed of materials such as pure metallic oxides (Al2O3) and nonoxidemetallic compounds such as carbides, nitrides, borides, and silicides [13].Ceramic materials have a great diversity of applications. They are used in bricks,glassware, dinnerware, home electronics, watches, automobiles, space shuttles,airplanes, cutting tools, filters, electrical resistors and insulators, bearings, fuelcells, dental restoration products, bone implants, orthopedic joint replacement, etc.The steps involved in the manufacture of ceramics are: (1) preparation ofparticulate dispersion (suspension) by mixing raw ceramic powder homogeneouslyin a liquid dispersion medium (water), (2) compactation of particulate dispersionto a high-volume fraction of particles by removing most of the liquid, (3) a shape-forming process, and (4) a heat-treatment process called firing or sintering toproduce a rigid, final product. A good understanding of the rheology of particulatedispersion is vital for the successful completion of steps (1) to (3). Furthermore,DK3354_C001.fm Page 3 Wednesday, October 25, 2006 2:02 PM4 Rheology of Particulate Dispersions and Compositesonline measurement of the rheological properties of particulate dispersion can beused for quality control purposes so as to minimize batch-to-batch variations [4,5].1.1.2 PARTICULATE RECORDING MEDIAFloppy disks, audio and video tapes, and magnetic stripes are all referred to asparticulate recording media as they are manufactured using a suspension ofmagnetic particles [68]. Figure 1.1 shows a schematic diagram of the processused for the production of particulate recording media (magnetic tapes). A sus-pension of single-domain rodlike ferromagnetic particles (length of the order of0.5 m or less, aspect ratio about 8 to 10) is prepared by dispersing the particlesin a liquid dispersion medium consisting of solvent, polymeric binder, surfactant,and other additives in trace amounts. The volume fraction of the magnetic particles(iron oxide, chromium oxide, or barium ferrite) in the suspension is usually 1 to5%. The suspension is allowed to spread onto the moving polymeric film substrate,also referred to as a web, which is usually made from polyester (polyethylenetetraphthalate) and is about 25 m thick. In the next stage of the process, themagnetic particles in the film are aligned in the direction of the length of the tapeusing a magnetic field while the film is still in liquid dispersion form. Followingthe alignment of the magnetic particles, the web is heated to drive off the volatilesolvent and to cross-link the polymeric binder. The cross-linked binder holds themagnetic particles together and attaches them to the supporting substrate. Thestructure of the magnetic film or layer formed on the substrate is similar to thatof grapes-filled Jell-O, with Jell-O representing the binder and grapes representingthe magnetic particles. The tape is then rolled to reduce the surface roughness.The thickness of the top magnetic layer of the tape in the finished product is about3 to 5 m.The magnetic particles of the suspension are prone to flocculation as strongattractive forces exist between them. Flocculation of the particles adversely affectsthe coating and particle-alignment processes. A poor-quality suspension with a highFIGURE 1.1 Production of particulate recording media (magnetic tapes). (From AppliedAlloy Chemistry Group, Magnetic Recording, University of Birmingham, http://www.aacg.bham.ac.uk/magnetic_materials/magnetic_recording.htm.)PET substrateAligning eldMagnetic particles+ Solvent + Binder+ Lubricant + AbrasivesHeatSolventDirection of moving substrateDK3354_C001.fm Page 4 Wednesday, October 25, 2006 2:02 PMApplications of Particulate Dispersions and Composites 5degree of flocculation of particles results in increased surface roughness andrecording noise in the final product. As the rheological properties of magneticsuspension are strongly affected by the degree of aggregation of particles, sus-pension rheology can be used as a tool to monitor the quality of the suspension [6].1.1.3 NANOTECHNOLOGICAL APPLICATIONSNanotechnology can be defined as a branch of engineering in which dimensionsin the range of nanometers (usually 0.1 to 100 nm) play a critical role. Thenanomaterials subdivision of nanotechnology includes dry powder of nanoparti-cles as well as dispersion of nanoparticles in liquid. According to a recent marketanalysis of nanotechnology, the total world market for nanoparticulate materialswas $492.5 million in 2000 and $900.1 million in 2005 [9].Nanomaterials in the form of dispersions of nanoparticles in liquids, alsoreferred to as nanodispersions, have many practical applications. One importantapplication of such systems is in the area of drug delivery [10,11]. Most drugs,especially those that are poorly soluble, perform better in nanoparticulate form.A significant number of the new drugs discovered today by the pharmaceuticalcompanies are poorly soluble. The bioavailability of the poorly soluble drugs canbe enhanced significantly by reducing the size of the drug particles to the nano-meter size range and thus increasing the specific surface area of the drug.Nanoparticulate drugs can be formulated either in the dry tablet (capsule) formor in the form of a nanodispersion. However, most production techniques currentlyutilized to manufacture drug nanoparticles generally yield nanodispersion as thefinal product. In one production technique, the coarse drug powder is dispersedin a surfactant solution and the dispersion is subjected to high-pressure homog-enization. The forces in the homogenizer are so strong that the coarse drugparticles disintegrate into drug nanoparticles (nanocrystals) [11]. In another pro-duction technique, the drug is first dissolved in some appropriate lipid at atemperature above the melting point of the lipid. The druglipid solution isdispersed in a hot aqueous surfactant solution by a stirrer. The coarse emulsionthus formed is homogenized in a high-pressure homogenizer while the tempera-ture is maintained above the melting point of the lipid. The resulting dispersionof nanodroplets is finally cooled down to room temperature. The cooling processleads to crystallization of the lipid, and the final product is a nanodispersion ofdrug-loaded solid lipid nanoparticles (also referred to as SLN) [10].The applications of nanodispersions are not restricted to drug delivery alone.Some other areas in which nanodispersions are significant are cosmetics, bio-medicine, inks, and paints.1.1.4 BIOMEDICAL APPLICATIONSThe biomedical applications of particulate dispersions are many. However, themost promising ones involve the use of so-called ferrofluids [1216]. Ferro-fluids are stable dispersions of single-domain magnetic nanoparticles, typicallyDK3354_C001.fm Page 5 Wednesday, October 25, 2006 2:02 PM6 Rheology of Particulate Dispersions and Composites10 nm in diameter. In the absence of an external magnetic field, the ferrofluidhas no net magnetization, as the magnetic moments of the particles are randomlydistributed owing to thermal agitation (Brownian motion). In the presence ofan external magnetic field, however, the magnetic moments of the particlesalign with the field and the dispersion acts as a magnet. As the single-domainmagnetic particles contain several thousand atomic magnetic moments, ferro-fluids often behave like a superparamagnetic material magnetizing stronglyunder the application of an external field but retaining no permanent magneti-zation upon the removal of the field. The nanoparticles of ferrofluids (usuallyiron oxide) are stabilized with a layer of surfactant molecules attached to thesurface of the particles. The surfactant layer provides steric repulsion betweenthe particles and, consequently, agglomeration or flocculation of particles isprevented.Ferrofluids have many potential applications in biomedical as well as non-biomedical areas [1218]. In the biomedical area, ferrofluids are gainingsignificance in applications involving targeted drug delivery and hyperthermia.They are also being considered as possible contrast agents for magnetic resonanceimaging (MRI).In targeted drug delivery applications, drug molecules are first adsorbed ontothe surface of the magnetic nanoparticles by mixing the particles with the drugsolution. The drug-loaded nanoparticles are then released at the intended treat-ment site. Figure 1.2 shows schematically how the particles can be delivered tothe intended site [14]. The dispersion of drug-loaded magnetic nanoparticles isinjected into an arterial feed to the intended tissue or organ with the help of acatheter. A powerful magnetic field is then applied near the target site. The magneticFIGURE 1.2 Delivery of drug-loaded magnetic nanoparticles to the intended tissueor organ. (From Z.M. Saiyed, S.D. Telang, C.N. Ramchand, Application of magnetictechniques in the field of drug discovery and biomedicine, Biomagn. Res. Technol.1: 2, 2003.)Body surfaceMagnetic eldTissue/organArterial feed totissue/organsMTCCatheterDK3354_C001.fm Page 6 Wednesday, October 25, 2006 2:02 PMApplications of Particulate Dispersions and Composites 7field causes the magnetic particles (MTCmagnetic targeted carriers) to extrava-sate through the capillary bed into the targeted organ or tissue where the drug isreleased. Targeted drug delivery is particularly important in cancer treatment.Chemotherapy is known to have many unpleasant side effects; the drugs used tokill cancerous cells also damage healthy cells. These side effects can be preventedby targeting the drug directly at the cancerous cells.Hyperthermia is used for the treatment of cancer. It involves heating thecancerous tissue to a temperature of about 45C so as to reduce the viability ofcancerous cells and enhance their sensitivity to chemotherapy. Ferrofluids arebeing studied as potential hyperthermia-causing agents. The magnetic nanoparticlesof ferrofluids are first concentrated in the cancerous tissue. Then an external ACmagnetic field is applied near the targeted tissue. The magnetic nanoparticlesoscillate with the external magnetic field and produce heat.1.1.5 BIOTECHNOLOGICAL APPLICATIONSBiotechnology involves the manipulation of microorganisms (bacteria, molds,yeast, etc.), mammalian cells, or plant cells to produce industrial chemicals andpharmaceuticals. Dispersions of microbial organisms or cells in a liquid medium,also referred to as broths, are grown inside a bioreactor. As the organisms or cellsgrow, they also produce the desired chemical. Table 1.1 gives the morphologicalcharacteristics (shape, size, etc.) of various microbial organisms and cells [19].The table indicates that the particulate phase of the broth often consists ofaggregates of organisms or cells.Broth rheology is an active area of research [1925]. Most broths exhibitnon-Newtonian behavior, especially at high biomass concentrations. The designand operation of bioreactor- and downstream-processing equipment require agood understanding of the rheology of broths.TABLE 1.1Morphological Characteristics of Microbial Organisms and CellsType Shape Size (m) Cell Wall AggregatesPlant cells Spherical 100500 (dia) Yes YesCylindrical 2050 (length)Animal cells Spherical 1020 (dia) No NoBacteria Spherical < 1 (dia) Yes Yes/NoCylindrical < 5 (length)Yeasts Spherical 510 (dia) Yes Yes/NoMoulds Mycelial 510 (dia)< 100 (length)Yes Yes/NoSource: From P.M. Kieran, P.F. MacLoughlin, D.M. Malone, J. Biotechnol. 59: 3952, 1997.DK3354_C001.fm Page 7 Wednesday, October 25, 2006 2:02 PM8 Rheology of Particulate Dispersions and Composites1.1.6 PAINTSPaint is a particulate dispersion composed of pigments and extenders as theparticulate phase and binder solution or latex (referred to as the vehicle) as thecontinuous phase. Pigments are fine insoluble solid particles that give the desiredcolor to paint. Titanium dioxide is probably the most widely used pigment in thepaint industry. Extenders are also fine insoluble solid particles, but they provideno color to paint; they are basically used as inexpensive fillers to help controlthe paint rheology and to improve the properties of paint film. Some commonextenders are calcium carbonate (whitewash), aluminum silicate (clay), magnesiumsilicate (talc), and silica [2629].The continuous phase or vehicle of paint is either a true liquid solution offilm-forming polymeric binder in some appropriate solvent or latex (emulsion)of nanosize binder particles and water. The latex is used in water-based paintsand the binder or solvent solution is used in oil-based paints. The solvents usedin oil-based paints are low molecular weight organic liquids such as aromatic andaliphatic hydrocarbons, alcohols, esters, and ketones. The most widely usedpolymeric binders in oil paints are alkyds; they are highly branched, oil-modifiedpolyesters [26]. The function of the binder is to cement (bind) the pigment andextender particles into a uniform continuous film and to make the pigment andextender particles adhere to the surface. In the case of water-based paints,the binder consists of nanosize polymer particles usually made of vinyl acetate(polyvinyl acetate) or 100% acrylic. When the water-based paint is applied on asurface, the water evaporates, forcing the pigment, extender, and binder particlesto come closer together; the latex particles eventually coalesce and bind thepigment and extender particles in a continuous film. The film-forming ability ofthe polymeric latex particles, as well as their ability to bind the pigment andextender particles together, is dependent on factors such as the size of the latexparticles and the glass transition temperature (Tg) of the polymer. Small particlesize and low Tg (the lower the Tg, the softer the polymer) are better for film forming.1.1.7 MARINE OIL SPILLSMarine oil spills are often caused by oil tanker accidents (collisions, hull failure,and groundings) [30,31]. In the well-known Exxon Valdez oil spill that occurredin March 1989, the Exxon Valdez struck the rocks of Bligh Reef in Prince WilliamSound [32]. Nearly 11 million gallons of crude oil were spilled within 5 h of theaccident. Oil tanker accidents are not the only cause of marine oil spills; theycan occur owing to accidents on the offshore oil and gas production facilities (oilrigs) as well. Oil spills can have a major effect on sea animals and humans. Thediving and surface-dwelling populations of seabirds are known to be sensitive tooiling; severe oiling almost always results in death. There is some evidence tosuggest that oil spills can have long-term effects on sea animals [30].The oil starts to spread rapidly over the sea surface as soon as it is spilled.At the same time, it starts to lose the lighter components due to evaporation and,consequently, the viscosity of the remaining oil tends to rise. A significant degreeDK3354_C001.fm Page 8 Wednesday, October 25, 2006 2:02 PMApplications of Particulate Dispersions and Composites 9of emulsification also occurs simultaneously because of wave action and windagitation [31,3335]. Emulsification is a process by which one liquid is dispersedin the form of small droplets in a continuum of another immiscible liquid. In thepresent situation, water is dispersed in the form of small droplets in the continuousoil phase. Such particulate dispersions are referred to as water-in-oil (W/O)emulsions. With certain types of crude oils, highly stable W/ O emulsions con-taining up to 80% by volume sea water can form. Highly concentrated W/Oemulsions are generally reddish-brown in color and look like a gel. They areoften nicknamed chocolate mousse as they resemble this dessert.The formation of a W/O emulsion makes cleanup operations more difficult.With the addition of a large amount of water droplets to the oil, there occurs adramatic increase in the viscosity. In fact, the emulsion at high-volume fractionsof water droplets is highly non-Newtonian. It often exhibits a large value of yieldstress. Furthermore, the formation of an emulsion substantially increases thevolume of the spill.There are a number of different methods proposed to deal with oil floatingon the sea [35,36], such as: (1) mechanical cleanup, (2) burning, (3) bioremediation,and (4) treatment with chemical dispersants. Among these, mechanical cleanupis probably the most commonly used method for mitigation of oil spills. Usually,the first step is to limit the spread of oil (the W/ O emulsion) on the water surfacewith the help of so-called booms. Skimmers, which are floating mechanicaldevices, are then used to remove oil from the water surface. A wide variety ofskimmers are available [33], and they seem to function best when the oil or water-in-oil emulsion layer is thick. Pumps are used to transfer oil or the emulsion fromskimmers to storage tanks of the recovery vessel. The rheological properties ofthe oil or W/ O emulsion play an important role in the selection and successfuloperation of the skimmers and pumps.1.1.8 FOOD APPLICATIONSMany natural and processed food products are particulate dispersions. A vastmajority of them are emulsions of oil and water with additives such as sugar,salts, vitamins, minerals, food-grade surfactants, proteins, gums, colors, flavors,etc. Examples of food emulsions are milk, butter, margarine, mayonnaise, coffeewhiteners, and salad dressings [3739]. A brief description of the compositionof these products is given in Table 1.2.Emulsion rheology plays a critical role not only in the processing of emulsion-based foods, but also in the acceptance of these products by the consumer [39].Therefore, it is not surprising to note that it is a very active area of research atpresent.1.1.9 PIPELINE TRANSPORTATION OF MATERIALSPipeline transportation of solids and highly viscous liquids in the form ofparticulate dispersions [40,41] is not only feasible but has many advantages overother modes of material transportation such as trucks, trains, or sea vessels.DK3354_C001.fm Page 9 Wednesday, October 25, 2006 2:02 PM10 Rheology of Particulate Dispersions and CompositesIn addition to long-term economic benefits, pipelines have an aesthetic advantageover other transport options in that they are buried underground and are out ofsight for the most part. As they do not cause noise and air pollution, they arealso environmentally friendly. A wide variety of industrial materials (solids andliquids) have been transported in particulate dispersion form through pipelinesacross a range of distances. Examples of solid materials transported in the formof solids-in-water suspensions are: coal, kaolin, limestone, and various metallicores (copper, iron, zinc, nickel, etc.). Examples of liquids transported in the formof oil-in-water (O/W) emulsions are waxy crude oils, bitumen, and highlyviscous heavy oils [41,42].For economically successful pipeline transport, it is important that a highlevel of particulate loading is achieved without a substantial increase in theviscosity of the particulate dispersion. One possible method of achieving this isto optimize the particle size distribution (PSD). Many studies have been conductedon the effects of PSD on the rheology of particulate dispersions [4346]. It isgenerally concluded that at high levels of particulate loading, a particulate dis-persion with bimodal or multimodal PSD has a much lower viscosity than aparticulate dispersion with uniform-size particles, when compared at the samevolume fraction of the dispersed phase.1.1.10 PETROLEUM PRODUCTIONA significant portion of the worlds crude oil is produced in the form of emulsions,that is, dispersions of oil and water [47]. Emulsions can be classified into twobroad groups, namely, W/O emulsions and O/W emulsions. W/O emulsionsconsist of water droplets dispersed in a continuum of oil phase, whereas O/Wemulsions have a reverse arrangement, that is, oil droplets are dispersed in acontinuum of water phase. In the petroleum industry, W/O emulsions are morecommonly encountered.In primary oil production where the reservoirs natural energy (pressure) isused to produce the oil, the source of water is the connate water [48] that isTABLE 1.2Composition of Emulsion-Based Food ProductsFood Product Particulate Phase Matrix PhaseVolume Percentage of Particulate PhaseMilk Oil droplets Water 3 to 4Butter Water droplets Liquid oil and fat crystalsAbout 16Margarine Water droplets Liquid oil and fat crystals16 to 50Mayonnaise Oil droplets Water 65Coffee whiteners Oil droplets Water 10 to 15Salad dressings Oil droplets Water 30DK3354_C001.fm Page 10 Wednesday, October 25, 2006 2:02 PMApplications of Particulate Dispersions and Composites 11naturally present along with the oil in the formation. It is believed that theemulsification of oil and water occurs in the formation near the well bore,where the velocity gradients are very high. The high shear in the productionfacilities such as pumps, valves, chokes, and turns also favors the formation ofthe emulsion [48,49]. The source of emulsifying agents in these emulsions isthe crude oil itself, which may contain a variety of surface-active chemicalssuch as long-chain fatty acids and polycyclics [47,48]. Although W/O emulsionsare more commonly encountered in primary oil production operations, O/Wemulsions are also produced from some oil fields; O/W emulsions frequentlyoccur when a given oil field becomes old and produces an increased amountof water [50].When the reservoirs natural energy is no longer capable of pushing the oilfrom the formation into the oil well, a fluid is often injected into the formationthrough injection wells. A variety of fluids are used for this purpose, such aswater, aqueous polymer solution, caustic solution, aqueous surfactant solutions,microemulsion, and steam. Most of these fluids not only push the oil from theformation into the producing well but also help to recover oil that adheres to thewalls of the pores (because of strong capillary forces). Very often, however,channeling and breakthrough of fluid into the producing well occurs, causingemulsions to be formed [48].In some situations where the crude oil or W/O emulsion being produced froma given oil well is highly viscous, an aqueous solution of surface-active chemicalsis often injected into the production well bore to convert the high-viscosity oil(or W/O emulsion) to a low-viscosity O/W emulsion [51,52]. This increases theoil production rate substantially by increasing the rod-dropping rate and bylowering the flow line pressure drop. This process, whereby aqueous solutionsof surface-active chemicals are pumped down into the producing well to enhancethe oil production rate, is referred to as downhole emulsification.Oil-well drilling is another important application in which particulate disper-sions (emulsions as well as solids-in-liquid suspensions) are used [53,54]. Duringthe drilling process, particulate dispersions called drilling muds are pumped downthe drill pipe and out of the nozzles of the drill bit. The mud acts as a coolantand lubricant for the drill bit. When the drilling mud returns to the surface throughthe annular region between the rotating drill pipe and the borehole wall, it alsobrings cuttings such as rocks and sand from the hole with it. Drilling muds areeither water-based or oil-based. The water-based drilling muds are solids-in-liquidsuspensions with clay (usually bentonite) and a weighting agent (usually bariumsulfate) as the particulate phase and freshwater or seawater as the liquid phase.The weighting agent is added to increase the density of the mud to overcomeformation pressures and to keep oil and other reservoir fluids in place. To controlthe rheological, fluid-loss, and shale-stabilizing properties of the drilling muds,a wide variety of water-soluble polymers are also used. Although water-baseddrilling muds are used more often, some situations require the use of oil-baseddrilling muds. The oil-based drilling muds are basically W/O emulsions withsome solids, such as weighting agents and organophilic clay.DK3354_C001.fm Page 11 Wednesday, October 25, 2006 2:02 PM12 Rheology of Particulate Dispersions and Composites1.1.11 COSMETICS AND TOILETRIESToothpaste is a particulate dispersion [5557]. The dispersed phase of a toothpasteconsists of solid particles of some mildly abrasive agent (usually dicalciumphosphate) to help remove stains and polish teeth. The weight percentage ofsolids in the dispersion is about 10 to 50. The continuous phase is an aqueoussolution consisting of water, humectant (moisture controller to prevent the tooth-paste from becoming dry and firm) such as glycerol, a binder or thickener suchas sodium carboxymethylcellulose to prevent the solid particles of the polishingagent from settling out, detergent or surfactant such as lauryl sulphate to providefoaming action and to enhance the cleaning ability of the toothpaste, therapeuticagents such as sodium monofluorophosphate to prevent tooth decay, and minoramounts of flavors, preservatives, and coloring agents.Most roll-on antiperspirants currently sold in the market are suspensions ofsolid particles of some active ingredient (such as aluminum chlorohydrates) involatile silicone liquid such as cyclomethicone [58]. To prevent the solid particlesof the active ingredient from settling out, additives such as organophilic clay areadded to the continuous phase to thicken the product. Rheology plays a key rolein the success of roll-on antiperspirants. A properly formulated product shouldhave the right consistency. It should be thick enough so that it is not runny orspillable and the solid particles of the active ingredient do not settle out at thebottom of the container. At the same time, the product should thin down enoughduring the application to allow a uniform coating to be applied on the skin.Sunscreen lotions are particulate dispersions available commercially either inthe form of an emulsion or in the form of a solids-in-liquid suspension [5964].Emulsion-based sunscreen lotions are usually chemical absorbers of ultravioletradiation (UVR); the chemical ingredient (aromatic compound conjugated witha carbonyl group) that absorbs UVR is incorporated into the oil phase of theemulsion. Suspension-based sunscreen lotions are generally physical blockers ofUVR; the particulate phase of the suspension (usually unagglomerated nanosizeparticles of zinc oxide or titanium dioxide) reflects or scatters UVR.A large number of skincare and makeup creams marketed today are in theform of an emulsion [56,57,6569]. Both O/W and W/O emulsion creams aremanufactured commercially, although a majority of the cosmetic creams availablein the market are O/W type with oil droplets as the dispersed phase and aqueoussolution as the continuous phase. The W/O-type emulsion creams are often usedas barrier creams to lock moisture in the skin over a period of time by forminga protective hydrophobic film on the skin. Although the O/W-type emulsioncreams are used for various reasons, one important function of these creams isto prevent dryness of the skin by replacing lost moisture and by keeping the skinhydrated over a period of time.1.1.12 GEOLOGICAL APPLICATIONSDispersions of gas bubbles in magma (molten matter of silicate composition),also referred to as magmatic emulsions in the literature, play an important roleDK3354_C001.fm Page 12 Wednesday, October 25, 2006 2:02 PMApplications of Particulate Dispersions and Composites 13in volcanic eruptions [7079]. During an eruption, as the magma rises througha volcanic conduit toward the earths surface, gas bubbles are formed due to ex-solution of volatiles (mainly water and carbon dioxide) that were initiallydissolved in magma at high pressures. The bubbles also tend to grow in size asthe magma rises toward the surface. The growth of bubbles is governed bydecompression and diffusional processes.The vesiculation of the rising magma drastically changes the physicochemicalproperties and rheology of magma within the conduit and, thus, the ascent rateof magma. The changes in magma rheology occur partly because of a change inthe melt rheology (owing to loss of volatiles) and partly owing to the introductionof bubbles in the melt.Figure 1.3 summarizes the main processes occurring in a volcanic conduit.A major portion of the conduit consists of a two-phase bubbly flow region inwhich bubbles nucleate and grow. At the end of the bubbly section, the magmaticemulsion fragments and turns into a gas consisting of small particles (ash), whichmay be liquid or partially solid.Rheology of magmas and magmatic emulsions is an active area of research.A good understanding of the rheology of bubble-bearing magmas, over a widerange of bubble volume fractions, is important in the analysis of ascent, eruption,and emplacement of magmas [7077].1.2 COMPOSITESComposites are solid heterogeneous materials composed of at least two phases:the continuous phase is termed the matrix, and the phase that is dispersed in thematrix as discrete units is called the dispersed phase. The mechanical propertiesof composites depend on factors such as: (1) the volume fraction of the dispersedphase, (2) the geometry of the dispersed phase (shape, size and size distribution,FIGURE 1.3 Processes occurring in a volcanic conduit.VentHost rock FragmentationlevelExsolutionlevelMagma chamberBubbly owDK3354_C001.fm Page 13 Wednesday, October 25, 2006 2:02 PM14 Rheology of Particulate Dispersions and Compositesand orientation of the dispersed units), and (3) the properties of the constituentphases. Composite materials can be roughly classified into two broad groups,namely particle-reinforced (particulate) composites and fiber-reinforced compos-ites. Particulate composites generally consist of nearly isometric (same dimen-sions in all directions) particles, whereas fiber-reinforced composites consist offibers of high aspect ratio as the dispersed phase.1.2.1 PARTICULATE COMPOSITES AND THEIR APPLICATIONSParticulate composites can be subdivided into two groups: coarse-particle com-posites and fine-particle composites. Coarse-particle composites consist of par-ticles significantly larger than 1 m, and the volume fraction of the dispersedphase in these composites is often high. Examples of coarse-particle compositesare ceramic-metal composites, solid propellants, wood-plastic composites, andtraditional dental composites. Fine-particle composites consist of particles in thesubmicron or nanometer range and the volume fraction of the dispersed phase isusually small. Examples of fine-particle composites are dispersion-hardened metalalloys, carbon blackfilled rubbers and plastics, and clay-polymer nanocomposites.1.2.1.1 Coarse-Particle CompositesCeramic-metal particulate composites, also called cermets, are widely used as atool material for high-speed cutting of materials that are difficult to machine,such as hardened steels [80,81]. The ceramic material alone, although hard enoughto provide the cutting surface, is extremely brittle whereas the metal alone,although tough, does not possess the requisite hardness. The combination of thesetwo materials (ceramic and metal) in the form of a particulate composite over-comes the limitations of the individual materials. In cermets used for cuttingtools, the particles of ceramic (tungsten carbide, titanium carbide, Al2O3, etc.)are embedded in a matrix of a ductile metal (cobalt, nickel, etc.). A large volumefraction of the dispersed particulate phase is generally used to maximize theabrasive action of the composite. Cermets are used in many other applicationssuch as: (1) thermocouple protection tubes, (2) mechanical seals, (3) valve andvalve seats, and (4) turbine wheels.The solid propellants commonly used in aerospace propulsion are particu-late composites consisting of particles of solid oxidizer (usually ammoniumperchlorate NH4ClO4) and metal fuel (usually aluminum) dispersed in a poly-meric binder (usually polybutadiene). The fuel combines with oxygen providedby the oxidizer to produce gas for propulsion. The volume fraction of particlesin solid propellants is typically high [82]. The composite is a rubberlike materialwith the consistency of a rubber eraser.The plastics industry employs a number of different types of particulatefillers to improve the mechanical properties of the plastic. In several applica-tions, less expensive particulate fillers are added to expensive plastic materials,mainly to lower the cost. Wood-derived fillers are receiving a lot of attentionthese days. According to some estimates, wood-plastic composites (WPCs) areDK3354_C001.fm Page 14 Wednesday, October 25, 2006 2:02 PMApplications of Particulate Dispersions and Composites 15the fastest growing construction materials today [8387]. Wood filler, most oftenused in a particulate form referred to as wood flour, has several advantages overthe traditional inorganic fillers. It is derived from a renewable resource, is lighter,and is less expensive. Also, it is less abrasive to processing equipment ascompared to traditional fillers. Commercially produced wood-flour filler gener-ally consists of large-size particles (>100 m). The weight fraction of wood inWPCs is typically 0.5, although some WPCs contain a much larger amount ofwood (as high as 70% by weight), and others contain only a small amount ofwood (as low as 10% by weight). Both thermoset plastics and thermoplasticsare used as matrix materials for WPCs, although most WPCs are currentlymanufactured with thermoplastics such as polyethylene, polypropylene, andpolyvinylchloride as the matrix.Dental composites consist of a polymerizable resin matrix, usually urethanedimethacrylate (UDMA) or ethylene glycol dimethacrylate (Bis-GMA), glassparticulate fillers, and a silane coupling agent [88,89]. Polymerization of the resinmatrix is either light activated or chemically initiated. The silane coupling agent(usually 3-methacryloxypropyltrimethoxy silane) coats the surface of the hydro-philic filler particles, allowing them to couple with the hydrophobic resin matrix.The purpose of fillers in dental composites is to reduce shrinkage (the resin tendsto shrink while it sets) and to improve mechanical properties (wear resistance,fracture resistanc