dk3417fm.pdf

WETTING AND SPREADING DYNAMICS

© 2007 by Taylor & Francis Group, LLC

DANIEL BLANKSCHTEIN

Department of ChemicalEngineeringMassachusetts Institute of TechnologyCambridge, Massachusetts

S. KARABORNI

Shell International PetroleumCompany LimitedLondon, England

LISA B. QUENCER

The Dow Chemical CompanyMidland, Michigan

JOHN F. SCAMEHORN

Institute for Applied SurfactantResearchUniversity of OklahomaNorman, Oklahoma

P. SOMASUNDARAN

Henry Krumb School of MinesColumbia UniversityNew York, New York

ERIC W. KALER

Department of ChemicalEngineeringUniversity of DelawareNewark, Delaware

CLARENCE MILLER

Chemical and Biomolecular Engineering DepartmentRice UniversityHouston, Texas

DON RUBINGH

The Procter & Gamble CompanyCincinnati, Ohio

BEREND SMIT

Shell International Oil Products B.V.Amsterdam, The Netherlands

JOHN TEXTER

Strider Research CorporationRochester, New York

SURFACTANT SCIENCE SERIES

FOUNDING EDITOR

MARTIN J. SCHICK

1918–1998

SERIES EDITOR

ARTHUR T. HUBBARD

Santa Barbara Science ProjectSanta Barbara, California

ADVISORY BOARD


1. 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 also

Volumes 34, 37, and 53)5. Detergency: Theory and Test Methods (in three parts), edited by

W. G. Cutler and R. C. Davis (see also Volume 20)6. Emulsions and Emulsion Technology (in three parts), edited by

Kenneth 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 Watanabe

16. Surfactants in Cosmetics, edited by Martin M. Rieger (seeVolume 68)

17. Interfacial Phenomena: Equilibrium and Dynamic Effects,Clarence A. Miller and P. Neogi

18. Surfactant Biodegradation: Second Edition, Revised and Expanded, R. D. Swisher

19. Nonionic Surfactants: Chemical Analysis, edited by John Cross20. Detergency: Theory and Technology, edited by W. Gale Cutler

and Erik Kissa21. Interfacial Phenomena in Apolar Media, edited by Hans-

Friedrich Eicke and Geoffrey D. Parfitt22. Surfactant Solutions: New Methods of Investigation, edited by

Raoul Zana23. Nonionic Surfactants: Physical Chemistry, edited by

Martin J. Schick24. Microemulsion Systems, edited by Henri L. Rosano

and Marc Clausse


25. Biosurfactants and Biotechnology, edited by Naim Kosaric, W. L. Cairns, and Neil C. C. Gray

26. 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 Sato

32. Interfacial Phenomena in Coal Technology, edited by Gregory D. Botsaris and Yuli M. Glazman

33. Surfactant-Based Separation Processes, edited by John F. Scamehorn and Jeffrey H. Harwell

34. Cationic Surfactants: Organic Chemistry, edited by James M. Richmond

35. Alkylene Oxides and Their Polymers, F. E. Bailey, Jr., and Joseph V. Koleske

36. Interfacial Phenomena in Petroleum Recovery, edited by Norman R. Morrow

37. Cationic Surfactants: Physical Chemistry, edited by Donn N. Rubingh and Paul M. Holland

38. Kinetics and Catalysis in Microheterogeneous Systems, edited by M. Grätzel and K. Kalyanasundaram

39. Interfacial Phenomena in Biological Systems, edited by Max Bender

40. Analysis of Surfactants, Thomas M. Schmitt (see Volume 96)41. Light Scattering by Liquid Surfaces and Complementary

Techniques, edited by Dominique Langevin42. Polymeric Surfactants, Irja Piirma43. Anionic Surfactants: Biochemistry, Toxicology, Dermatology.

Second Edition, Revised and Expanded, edited by Christian Gloxhuber and Klaus Künstler

44. Organized Solutions: Surfactants in Science and Technology,edited by Stig E. Friberg and Björn Lindman

45. Defoaming: Theory and Industrial Applications, edited by P. R. Garrett

46. Mixed Surfactant Systems, edited by Keizo Ogino and Masahiko Abe

47. Coagulation and Flocculation: Theory and Applications, editedby Bohuslav Dobiás


48. Biosurfactants: Production Properties Applications, edited byNaim Kosaric

49. Wettability, edited by John C. Berg50. Fluorinated Surfactants: Synthesis Properties Applications,

Erik Kissa51. Surface and Colloid Chemistry in Advanced Ceramics

Processing, edited by Robert J. Pugh and Lennart Bergström52. 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 by

Robert K. Prud’homme 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 Sjöblom62. 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 by

Kunio 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 Cross


74. Novel Surfactants: Preparation, Applications, and Biodegradability, edited by Krister Holmberg

75. 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 Furusawa

77. Polymer-Surfactant Systems, edited by Jan C. T. Kwak78. Surfaces of Nanoparticles and Porous Materials, edited by

James A. Schwarz and Cristian I. Contescu79. Surface Chemistry and Electrochemistry of Membranes,

edited by Torben Smith Sørensen80. Interfacial Phenomena in Chromatography, edited by

Emile Pefferkorn81. Solid–Liquid Dispersions, Bohuslav Dobiás, 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 by

Jyh-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 Borówko90. Adsorption on Silica Surfaces, edited by Eugène Papirer91. Nonionic Surfactants: Alkyl Polyglucosides, edited by Dieter

Balzer and Harald Lüders92. 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 by

Christopher M. Pastore and Paul Kiekens 95. Liquid Interfaces in Chemical, Biological, and Pharmaceutical

Applications, edited by Alexander G. Volkov96. Analysis of Surfactants: Second Edition, Revised and

Expanded,Thomas M. Schmitt

97. Fluorinated Surfactants and Repellents: Second Edition, Revised and Expanded, Erik Kissa

98. Detergency of Specialty Surfactants, edited by Floyd E. Friedli


99. Physical Chemistry of Polyelectrolytes, edited by Tsetska Radeva

100. Reactions and Synthesis in Surfactant Systems, edited by John Texter

101. Protein-Based Surfactants: Synthesis, PhysicochemicalProperties, and Applications, edited by Ifendu A. Nnanna and Jiding Xia

102. 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. Lewis

105. Colloid and Surface Properties of Clays and Related Minerals,Rossman F. Giese and Carel J. van Oss

106. Interfacial Electrokinetics and Electrophoresis, edited by Ángel V. Delgado

107. Adsorption: Theory, Modeling, and Analysis, edited by József Tóth

108. Interfacial Applications in Environmental Engineering, edited byMark A. Keane

109. Adsorption and Aggregation of Surfactants in Solution, editedby K. L. Mittal and Dinesh O. Shah

110. Biopolymers at Interfaces: Second Edition, Revised and Expanded, edited by Martin Malmsten

111. Biomolecular Films: Design, Function, and Applications, edited by James F. Rusling

112. Structure–Performance Relationships in Surfactants: Second Edition, Revised and Expanded, edited by Kunio Esumiand Minoru Ueno

113. Liquid Interfacial Systems: Oscillations and Instability, Rudolph V. Birikh,Vladimir A. Briskman, Manuel G. Velarde, and Jean-Claude Legros

114. Novel Surfactants: Preparation, Applications, andBiodegradability: Second Edition, Revised and Expanded, edited by Krister Holmberg

115. Colloidal Polymers: Synthesis and Characterization, edited by Abdelhamid Elaissari

116. Colloidal Biomolecules, Biomaterials, and BiomedicalApplications, edited by Abdelhamid Elaissari

117. Gemini Surfactants: Synthesis, Interfacial and Solution-PhaseBehavior, and Applications, edited by Raoul Zana and Jiding Xia

118. Colloidal Science of Flotation, Anh V. Nguyen and Hans Joachim Schulze

119. Surface and Interfacial Tension: Measurement, Theory, and Applications, edited by Stanley Hartland


120. Microporous Media: Synthesis, Properties, and Modeling, Freddy Romm

121. Handbook of Detergents, editor in chief: Uri Zoller Part B:Environmental Impact, edited by Uri Zoller

122. Luminous Chemical Vapor Deposition and Interface Engineering,HirotsuguYasuda

123. Handbook of Detergents, editor in chief: Uri Zoller Part C:Analysis, edited by Heinrich Waldhoff and Rüdiger Spilker

124. Mixed Surfactant Systems: Second Edition, Revised and Expanded, edited by Masahiko Abe and John F. Scamehorn

125. Dynamics of Surfactant Self-Assemblies: Micelles,Microemulsions, Vesicles and Lyotropic Phases, edited by Raoul Zana

126. Coagulation and Flocculation: Second Edition, edited by Hansjoachim Stechemesser and Bohulav Dobiás

127. Bicontinuous Liquid Crystals, edited by Matthew L. Lynch and Patrick T. Spicer

128. Handbook of Detergents, editor in chief: Uri Zoller Part D:Formulation, edited by Michael S. Showell

129. 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 by

Horacio E. Bergna and William O. Roberts132. Emulsions and Emulsion Stability, Second Edition, edited by

Johan Sjöblom133. Micellar Catalysis, Mohammad Niyaz Khan134. Molecular and Colloidal Electro-Optics, Stoyl P. Stoylov

and Maria V. Stoimenova135. Surfactants in Personal Care Products and Decorative

Cosmetics, Third Edition, edited by Linda D. Rhein, Mitchell Schlossman, Anthony O'Lenick, and P. Somasundaran

136. Rheology of Particulate Dispersions and Composites, Rajinder Pal

137. Powders and Fibers: Interfacial Science and Applications, edited by Michel Nardin and Eugène Papirer

138. Wetting and Spreading Dynamics, Victor M. Starov, Manuel G. Velarde, and Clayton J. Radke


WETTING ANDSPREADING DYNAMICS

Victor M. StarovLoughborough University

Loughborough, U.K.

Manuel G. VelardeInstituto Pluridisciplinar

Madrid, Spain

Clayton J. RadkeUniversity of California at Berkeley

Berkeley, California, U.S.A.

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Starov, V. M.Wetting and spreading dynamics / Victor Starov, Manuel Velarde, and Clayton

Radke.p. cm. -- (Surfactant science ; 138)

Includes bibliographical references and index.ISBN-13: 978-1-57444-540-4 (alk. paper) 1. Wetting. 2. Surface (Chemistry) I. Velarde, Manuel G. (Manuel García) II. Radke, Clayton. III. Title. IV. Series.

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Contents

Preface .............................................................................................................. xviiAcknowledgments ..............................................................................................xxi

Chapter 1 Surface Forces and the Equilibrium of Liquids on Solid Substrates.........................................................................................1

Introduction ...........................................................................................................11.1 Wetting and Young’s Equation ....................................................................21.2 Surface Forces and Disjoining Pressure ...................................................11

Components of the Disjoining Pressure ...................................................13Molecular or Dispersion Component............................................13The Electrostatic Component of the Disjoining Pressure ............19Structural Component of the Disjoining Pressure ........................21

1.3 Static Hysteresis of Contact Angle ...........................................................23Static Hysteresis of Contact Angles from Microscopic Point of View: Surface Forces ................................................................28

References ...........................................................................................................30

Chapter 2 Equilibrium Wetting Phenomena ..................................................31

Introduction .........................................................................................................312.1 Thin Liquid Films on Flat Solid Substrates .............................................31

Equilibrium Droplets on the Solid Substrate under Oversaturation (Pe < 0) ..........................................................................................36

Flat Films at the Equilibrium with Menisci (Pe > 0) ...............................38S-Shaped Isotherms of Disjoining Pressure in the Special Case S– < S+.... 40

2.2 Nonflat Equilibrium Liquid Shapes on Flat Surfaces...............................41General Consideration ...............................................................................42Microdrops: The Case Pe > 0....................................................................47Microscopic Equilibrium Periodic Films..................................................49Microscopic Equilibrium Depressions on β-Films...................................54

2.3 Equilibrium Contact Angle of Menisci and Drops: Liquid Shape in the Transition Zone from the Bulk Liquid to the Flat Films in Front.....56Equilibrium of Liquid in a Flat Capillary: Partial Wetting Case .............57Meniscus in a Flat Capillary .....................................................................60Meniscus in a Flat Capillary: Profile of the Transition Zone ..................63Partial Wetting: Macroscopic Liquid Drops .............................................65Profile of the Transition Zone in the Case of Droplets............................71Axisymmetric Drops .................................................................................71


Meniscus in a Cylindrical Capillary .........................................................72Appendix 1 ................................................................................................73

2.4 Profile of the Transition Zone between a Wetting Film and the Meniscus of the Bulk Liquid in the Case of Complete Wetting..............74

2.5 Thickness of Wetting Films on Rough Solid Substrates ..........................812.6 Wetting Films on Locally Heterogeneous Surfaces: Hydrophilic

Surface with Hydrophobic Inclusions.......................................................902.7 Thickness and Stability of Liquid Films on Nonplanar Surfaces ..........1002.8 Pressure on Wetting Perimeter and Deformation of Soft Solids............1062.9 Deformation of Fluid Particles in the Contact Zone ..............................113

Two Identical Cylindrical Drops or Bubbles..........................................115Interaction of Cylindrical Droplets of Different Radii...........................119Shape of a Liquid Interlayer between Interacting Droplets: Critical

Radius ..........................................................................................1232.10 Line Tension ............................................................................................130

Comparison with Experimental Data and Discussion ............................1422.11 Capillary Interaction between Solid Bodies ...........................................144

Appendix 2 ..............................................................................................152Equilibrium Liquid Shape Close to a Vertical Plate...................152

2.12 Liquid Profiles on Curved Interfaces, Effective Disjoining Pressure. Equilibrium Contact Angles of Droplets on Outer/Inner Cylindrical Surfaces and Menisci inside Cylindrical Capillary ................................154Liquid Profiles on Curved Surface: Derivation of Governing

Equations .....................................................................................154Equilibrium Contact Angle of a Droplet on an Outer Surface of

Cylindrical Capillaries.................................................................159Equilibrium Contact Angle of a Meniscus inside Cylindrical

Capillaries ....................................................................................161References .........................................................................................................163

Chapter 3 Kinetics of Wetting......................................................................165

Introduction .......................................................................................................1653.1 Spreading of Droplets of Nonvolatile Liquids over Flat Solid

Substrates: Qualitative Consideration .....................................................174Capillary Regime of Spreading...............................................................179Similarity Solution of Equation 3.18 and Equation 3.19 .......................181Gravitational Spreading...........................................................................186Similarity Solution ..................................................................................187Spreading of Very Thin Droplets ............................................................190

3.2 The Spreading of Liquid Drops over Dry Surfaces: Influence of Surface Forces.....................................................................197Case n = 2 ...............................................................................................205Case n = 3 ...............................................................................................205


Comparison with Experiments ................................................................209Conclusions..............................................................................................211Appendix 1 ..............................................................................................211Appendix 2 ..............................................................................................213Appendix 3 ..............................................................................................214Appendix 4 ..............................................................................................216

3.3 Spreading of Drops over a Surface Covered with a Thin Layer of the Same Liquid ............................................................................................217

3.4 Quasi-Steady-State Approach to the Kinetics of Spreading...................2253.5 Dynamic Advancing Contact Angle and the Form of the Moving

Meniscus in Flat Capillaries in the Case of Complete Wetting .............235Appendix 5 ..............................................................................................242

3.6 Motion of Long Drops in Thin Capillaries in the Case of Complete Wetting.....................................................................................................245Appendix 6 ..............................................................................................255

3.7 Coating of a Liquid Film on a Moving Thin Cylindrical Fiber.............259Statement of the Problem........................................................................260Derivation of the Equation for the Liquid–Liquid Interface Profile ......262Immobile Meniscus .................................................................................264Matching of Asymptotic Solutions in Zones I and II (Figure 3.17)......265Equilibrium Case (Ca = 0)......................................................................267Numerical Results ...................................................................................269

3.8 Blow-Off Method for Investigation of Boundary Viscosity of Volatile Liquids .....................................................................................................270Boundary Viscosity..................................................................................270Theory of the Method .............................................................................271

Experimental Part ........................................................................284Conclusions..............................................................................................287

3.9 Combined Heat and Mass Transfer in Tapered Capillaries with Bubbles under the Action of a Temperature Gradient............................287Cylindrical Capillaries.............................................................................292Tapered Capillaries ..................................................................................293

3.10 Static Hysteresis of Contact Angle .........................................................296Equilibrium Contact Angles ....................................................................297Static Hysteresis of the Contact Angle of Menisci ................................301Static Hysteresis Contact Angles of Drops.............................................308Conclusions..............................................................................................312

References .........................................................................................................312

Chapter 4 Spreading over Porous Substrates...............................................315

Introduction .......................................................................................................3154.1 Spreading of Liquid Drops over Saturated Porous Layers ....................315

Theory......................................................................................................316


Liquid inside the Drop (0 < z < h(t,r)) .......................................316Inside the Porous Layer beneath the Drop (–D < z < 0, 0 < r < L) ...............................................................318Materials and Methods ................................................................325Results and Discussion. Experimental Determination of Effective Lubrication Coefficient ω........................................327

4.2 Spreading of Liquid Drops over Dry Porous Layers: Complete Wetting Case............................................................................................331Theory......................................................................................................332

Inside the Porous Layer outside the Drop (–D < z < 0, L < r < l) ................................................................338Experimental Part ........................................................................343Independent Determination of Kppc ............................................344Results and Discussion................................................................345

Appendix 1 ..............................................................................................3514.3 Spreading of Liquid Drops over Thick Porous Substrates: Complete

Wetting Case............................................................................................354Theory......................................................................................................355

Inside the Porous Substrate .........................................................358Experimental Part ........................................................................358Results and Discussion................................................................360Spreading of Silicone Oil Drops of Different Viscosity over Identical Glass Filters..................................................................363Spreading of Silicone Oil Drops over Filters with Similar Properties but Made of Different Materials................................364Spreading of Silicone Oil Drops with the Same Viscosity (η = 5P) over Glass Filters with Different Porosity and Average Pore Size .......................................................................366Conclusions..................................................................................368

4.4 Spreading of Liquid Drops from a Liquid Source .................................369Theory......................................................................................................370Experimental Set-Up and Results ...........................................................374

Materials and Methods ................................................................374Results and Discussion................................................................376Conclusions..................................................................................379

Appendix 2 ..............................................................................................379Capillary Regime, Complete Wetting .........................................380Gravitational Regime, Complete Wetting ...................................384Partial Wetting .............................................................................387

References .........................................................................................................388

Chapter 5 Dynamics of Wetting or Spreading in the Presence of Surfactants ...................................................................................389

Introduction .......................................................................................................390


5.1 Spreading of Aqueous Surfactant Solutions over Porous Layers...........390Experimental Methods and Materials [1] ...............................................391

Spreading on Porous Substrates (Figure 4.4) .............................391Measurement of Static Advancing and Receding Contact Angles on Nonporous Substrates ................................................391Results and Discussion................................................................393Advancing and Hydrodynamic Receding Contact Angles on Porous Nitrocellulose Membranes.........................................398Static Hysteresis of the Contact Angle of SDS Solution Drops on Smooth Nonporous Nitrocellulose Substrate.........................400Conclusions..................................................................................403

5.2 Spontaneous Capillary Imbibition of Surfactant Solutions into Hydrophobic Capillaries..........................................................................403Theory......................................................................................................406

Concentration below CMC..........................................................410Concentration above CMC..........................................................413Spontaneous Capillary Rise in Hydrophobic Capillaries ...........417

Appendix 1 ..............................................................................................4195.3 Capillary Imbibition of Surfactant Solutions in Porous Media and

Thin Capillaries: Partial Wetting Case....................................................421Theory......................................................................................................422

Concentration below CMC..........................................................424Concentration above CMC..........................................................432Experimental Part ........................................................................434Results and Discussions ..............................................................435

5.4 Spreading of Surfactant Solutions over Hydrophobic Substrates ..........436Theory......................................................................................................437

Experiment: Materials .................................................................442Monitoring Method .....................................................................442Results and Discussion................................................................443

5.5 Spreading of Non-Newtonian Liquids over Solid Substrates ................445Governing Equation for the Evolution of the Profile of the Spreading

Drop .............................................................................................446Gravitational Regime of Spreading.........................................................452Capillary Regime of Spreading...............................................................455Discussion................................................................................................459

5.6 Spreading of an Insoluble Surfactant over Thin Viscose Liquid Layers ......................................................................................................460Theory and Relation to Experiment........................................................462

The First Spreading Stage...........................................................465The Second Spreading Stage ......................................................470Experimental Results...................................................................473

Appendix 2 ..............................................................................................475Derivation of Governing Equations for Time Evolution of Both Film Thickness and Surfactant Surface Concentration .....475


Appendix 3 ..............................................................................................476Influence of Capillary Forces during Initial Stage of Spreading .....................................................................................476

Appendix 4 ..............................................................................................478Derivation of Boundary Condition at the Moving Shock Front.............................................................................................478

Appendix 5 ..............................................................................................479Matching of Asymptotic Solutions at the Moving Shock Front.............................................................................................479

Appendix 6 ..............................................................................................480Solution of the Governing Equations for the Second Stage of Spreading.................................................................................480

5.7 Spreading of Aqueous Droplets Induced by Overturning of Amphiphilic Molecules or Their Fragments in the Surface Layer of an Initially Hydrophobic Substrate.....................................................481Theory and Derivation of Basic Equations.............................................482Boundary Conditions...............................................................................487

Solution of the Problem ..............................................................493Comparison between Theory and Experimental Data............................497

References .........................................................................................................499

Conclusions .......................................................................................................501Frequently Used Equations...............................................................................502

Navier–Stokes Equations.........................................................................502Navier-Stokes Equations in the Case of Two-Dimensional Flow..........504Capillary Pressure....................................................................................505

List of Main Symbols Used..............................................................................505Greek........................................................................................................505Latin.........................................................................................................506Subscripts.................................................................................................506


Preface

This book is for anyone who has recently started to be interested in, or is alreadyinvolved in, research or applications of wetting and spreading, i.e., for newcomersand practitioners alike. Its contents are not a comprehensive and critical reviewof the existing research literature. Needless to say, it rather reflects the authors’recent scientific interests and understanding. The authors presume that the readerusing this book has some knowledge in thermodynamics, fluid mechanics, andtransport phenomena. Yet the book has been written in an almost self-containedmanner, and it should be possible for a graduate student, scientist, or engineerwith a reasonable background in differential equations to follow it. Although invarious parts we have used the phrase “it can be shown …” or the like, the authorshave tried to go as deep into the details of derivation of results as required tomake the book useful.

The term wetting commonly refers to the displacement of air from a solidsurface. Throughout this book we shall be discussing wetting and spreadingfeatures of liquids, which partially (the most important example being water andaqueous solutions) or completely (oils) wet the solids or other liquids.

Wetting water films occur everywhere, even in the driest deserts or in thesauna and bathtub, although you might not see them with the naked eye becausethey are too thin or because they seem to disappear too quickly. Water is essentialfor life. It may very well be that without water, life would have not have startedon Earth. In fact no life seems possible without fluids! Life, as we know it startedin a little “pond,” the “primordial soup” leading to the first replicating bio-relatedamino acids.

In the processes of wetting or spreading, three phases — air, liquid, andsolids — meet along a line, which is referred to as a three-phase contact line.Recall the spreading drop and the drop edge, which is the three-phase contactline. In the vicinity of a three-phase contact line, the thickness of the dropletbecomes very thin and, even more, virtually tends to zero. In a thin water layer,new very special surface forces come into play. These forces are well known incolloid science: forces in thin layers between interfaces of neighbor particles,droplets, and bubbles in suspensions and emulsions. Understanding of the impor-tance of surface forces in colloid science has resulted in substantial progress inthis area. In fact, it is the reason why colloid science is referred to nowadays ascolloid and interface science.

Surface forces of the same nature act in thin liquid layers in the vicinity ofthe three-phase contact lines in the course of wetting and spreading. Surprisingly,the importance of surface forces has been much less recognized in wetting andspreading than it deserves. In Chapter 1 through Chapter 3 we will try to convince


the reader that virtually all wetting and spreading phenomena are determined bythe surface forces acting in a tiny vicinity of the three-phase contact line.

Water is, indeed, a strange liquid. For example, if you place a glass bottlefull of pure water (H2O) in the deep freezer, the bottle will break as water increasesin volume while solidifying as ice, an anomalous property relative to other liquids.Life (fish) in frozen lakes would not be possible without the anomalous behaviorof water around 4˚C.

We shall see that a property of water relative to “surface” forces is key tounderstanding its wetting and spreading features. We will also find that surfaceforces (frequently also referred to as disjoining pressure) have a very peculiarshape, in the case of water and aqueous solutions. This fact is critical for theexistence of our life in a way which is yet to be understood.

Wetting and spreading are dramatically affected by SURFace ACTtiveAgeNTS (in short, surfactants). Their molecules have a hydrophilic head (ionicor nonionic) with affinity for water and a hydrophobic tail (a hydrocarbon group),which is repelled by an aqueous phase. Fatty acids, alcohols, and some proteins(natural polymers), and washing liquids, powders, and detergents all act as sur-factants. It is the reason why the kinetics of wetting and spreading of surfactantsolutions is under investigation in this book.

On the other hand a number of solid substrates — printing materials, textiles,hairs — when in contact with liquids are porous in different degrees. In spite ofmuch experimental and practical experience in the area, only a limited number ofpublications are available in the literature that deals with fundamental aspects of thephenomenon. We show in this book that spreading kinetics over porous substratesdiffers substantially as compared with spreading over nonporous substrates.

Aiming at a logical progression in the problems treated with discussion ateach level, building albeit not rigidly, upon the material that came earlier, thebook can be divided into two parts: Chapter 1 to Chapter 3 form one part, andChapter 4 and Chapter 5 constitute the other. Chapter 1 is key to the former inthat its reading is a must for the understanding of Chapter 2 and Chapter 3. Toa large extent Chapter 4 and Chapter 5 can be read independently from thepreceding chapters, yet they are tied to each other and to the previous three.

Chapter 1 introduces surface forces and a detailed critical analysis of thecurrent understanding of Young’s equation, the building block in most wettingand spreading research and in a number of publications. The surface forces arealso frequently referred to in the literature as colloidal forces and disjoiningpressure. All these terms are used as equivalents in this book, following appro-priate clarification of concepts, terminology, and origins. Colloidal forces act inthin liquid films and layers when thickness goes down to about 10–5 cm = 0.1μm = 102 nm. Below this thickness the surface forces or disjoining pressurebecome so increasingly powerful that they dominate all other forces (for example,capillary forces and gravity). Accordingly, surface forces determine the wettingproperties of liquids in contact with solid substrates. One purpose of Chapter 1through Chapter 3 is to show that progress in the area of equilibrium and dynamicsof wetting demands due consideration of surface forces action in the vicinity of


the three-phase contact line. Chapter 2 and Chapter 3 look sequentially at theequilibrium and kinetics or dynamics of wetting, showing that the action ofsurface forces determines all equilibrium and kinetics features of liquids in contactwith solids. Note that Chapter 3 cannot be read and understood without readingthe introduction to the chapter.

Colloidal forces or disjoining pressure are well known and widely used incolloid science to account for equilibrium and dynamics of colloidal suspensionsand emulsions. The current theory behind colloidal forces between colloidalparticles, drops, and bubbles is the DLVO theory, an acronym made after thenames of Derjaguin (B.V.), Landau (L.D.), Verwey (E.J.W.) and Overbeek(J.Th.G.). The same forces act in the vicinity of the three-phase contact line, andtheir action is as important in this case as it is in the case of colloids. Unfortu-nately, most authors currently ignore the action of colloidal forces when discuss-ing the equilibrium and dynamics of wetting. It is our belief that this has hamperedprogress in the area of wetting phenomena for decades.

Chapter 4 and Chapter 5 are devoted to a detailed discussion of some recent,albeit still fragmentary, developments regarding the kinetics of spreading overporous solid substrates, including the case of hydrophobic substrates in thepresence of surfactants. Noteworthy are some new and universal spreading lawsin the case of spreading over thin porous layers discussed in Chapter 4. Somearguments and theory in Chapter 5 are experiment-discussion oriented and heu-ristic or semiempirical in approach (Section 5.4 and Section 5.5) and should bejudged accordingly. To our understanding, little is well established about spread-ing over hydrophobic substrates in the presence of surfactants. Our treatment ofthe spontaneous adsorption of surfactant molecules on a bare hydrophobic sub-strate ahead of the moving liquid front, making an initially hydrophobic substratepartially hydrophilic, allows a good description of a number of phenomena. Yetan understanding of the actual mechanism of transfer of surfactant molecules ina vicinity of the three-phase contact line will require considerable theoretical andexperimental efforts. We close the book with a few comments and warnings ina chapter of conclusions.

Victor M. Starov Loughborough University, Leicestershire, United Kingdom

Manuel G. VelardeInstituto Pluridisciplinar, Universidad Complutense, Madrid, Spain

Clayton J. RadkeUniversity of California at Berkeley


Acknowledgments

In 1974 Victor M. Starov met Prof. Nikolay V. Churaev, the beginning of acollaboration that has continued for more than 30 years and for which authorStarov would like to express very special thanks. Churaev involved Starov in theinvestigation of wetting and spreading phenomena in the former Surface ForcesDepartment, Moscow Institute of Physical Chemistry (MIPCh), Russian Academyof Sciences. This collaboration soon included a number of other colleaguesfrom MIPCh; appreciation is extended to these, especially professors Boris V.Derjaguin, Georgy A. Martynov, Vladimir D. Sobolev, and Zinoviy M. Zorin.

In 1981 Starov took the position of head of the Department of AppliedMathematics, Moscow University of Food Industry. He organized a weekly sem-inar there, where virtually all problems presented in this book were either solved,initiated, or at least discussed. These seminars were carried on until the Soviet Unioncollapsed. Author Starov would like to thank all members of the seminar butespecially professors Anatoly N. Filippov and Vasily V. Kalinin, and Drs. YuryE. Solomentsev, Vladimir I. Ivanov, Sergey I. Vasin, and Vjacheslav G. Zhdanov.

In 1987, the University of Sofia celebrated its centennial. This book’s firsttwo authors, Victor M. Starov and Manuel G. Velarde, were honored by beingchosen by Prof. Ivan B. Ivanov to be centennial lecturers at his university. Beyondbeing an honor, this was a lucky event in their lives. Both knew of Ivanov forquite some time but had not met him earlier nor had they worked together in thesame field, although both had common interests in the interfacial phenomena.While in Sofia, hearing each other lecturing and discussing science “and beyond,”they felt that it would be interesting to work together one day, particularly inexploring the consequences of surface tension and surface tension gradients, thelatter of which, e.g., creates flow or alters an existing one (the Marangoni effect).

In 1991 Starov was able to visit with Manuel G. Velarde at the InstitutoPluridisciplinar of the Universidad Complutense, Madrid, Spain. Both were for-tunate once more in being visited by Dr. Alain de Ryck, a young French scientistand brilliant experimentalist. He produced experiments where both Starov andVelarde were able to observe the striking role of the Marangoni effect in thespreading of a surfactant droplet over the thin aqueous layer. Later, the scientificrelationship between the first two authors of this book was strengthened by thevisit of Prof. Vladimir D. Sobolev, MIPCh, an outstanding scientist who wentbeyond being a highly skilled experimentalist. His work cemented the earliermentioned scientific relationship and collaboration between Starov and Velarde.It was further enhanced when the former moved from Moscow to the ChemicalEngineering Department, Loughborough University, United Kingdom, in 1999.There, Sobolev also worked with both Starov and Velarde, and this was the


beginning of numerous Loughborough–Madrid exchanges involving also severalyounger colleagues: Drs. Serguei R. Kosvintsev, Serguei A. Zhdanov, and AndreL. Zuev.

Then in 2001, the first two authors of this book jointly organized a summerschool on wetting and spreading dynamics and related phenomena at El Escorial,Madrid, under the sponsorship of the Universidad Complutense Summer Pro-gramme. Economic support also came from the European Union (under theICOPAC Network), the European Space Agency (ESA), Fuchs Iberica, L’Oreal,Inescop, and Unilever, Spain. Among the prestigious speakers from Bulgaria,France, Germany, Israel, the United States, and Spain was one of the invitedlecturers, the third author of this book, Clayton J. Radke. We decided not toproduce proceedings of that school, but soon after, the three future coauthors ofthis book started thinking of writing a joint monograph. Indeed, the present bookis the result of our concern about the lack of systematized knowledge on wettingand spreading dynamics, i.e., the lack of a monograph for the use of basic andapplied scientists, applied mathematicians, chemists, and engineers.

Two other schools are also worth mentioning. One on complex fluids, wetting,and spreading-related topics, coordinated by Velarde, took place in 1999 atLa Rabida, Huelva, Spain. The other course, much more focused on spreadingproblems, coordinated by Starov, was scheduled in 2003 at CISM (InternationalCenter for Mechanical Sciences) in Udine, Italy. There are proceedings of thelatter (“Fluid mechanics of surfactant and polymer solutions,” edited by Starovand Ivanov; Springer Verlag, 2004)) but not of the former. In the past few yearsseveral other workshops, discussion meetings, and international conferences tookplace in Madrid and Loughborough on the subject.

The authors would like to express their gratitude to Nadezda V. Starova.Without her energy, endless patience, kindness, and expertise, this book mostsurely would have never been finished. We are also happy to thank Maria-JesusMartin (Madrid) for her help in the preparation of the manuscript.

We wish to express our gratitude to the coauthors of our joint publications:Nikolay N. Churaev, Boris V. Derjaguin (deceased), Ivan B. Ivanov, VladimirI. Ivanov, Vasiliy V. Kalinin, Olga A. Kiseleva, Serguei R. Kosvintsev, Georgy A.Martynov, David Quere, Alain de Ryck, Ramon G. Rubio, Victor M. Rudoy,Vladimir D. Sobolev, Serguei A. Zhdanov, Pavel P. Zolotarev, and Zinoviy M.Zorin.

We also would like to recognize the following colleagues, fruitful discussionswith whom stimulated our research: Anne-Marie Cazabat, Pierre-Gilles deGennes, Benoit Goyeau, George (Bud) Homsy, Dominique Langevin, FranciscoMonroy, Alex T. Nikolov, Francisco Ortega, Len Pismen, Yves Pomeau, UweThiele, and Darsh T. Wasan.

Preparation of the manuscript was supported by a grant from the RoyalSociety, United Kingdom, which we would like to acknowledge. We wish toparticularly acknowledge the support by Prof. John Enderby. The final revisionof the manuscript was done while Manuel G. Velarde was Del Amo FoundationVisiting Professor with the Department of Mechanical Engineering and Environ-


mental Sciences of the University of California at Santa Barbara. This waspossible thanks to the hospitality of Prof. George M. Homsy.

Last but not least, we acknowledge the support for the research leading tothis book which came from the Engineering and Physical Sciences ResearchCouncil, United Kingdom (Grants EP/D077869 and EP/C528557), and from theMinisterio de Educacion y Ciencia, Spain (Grants MAT2003-01517, BQU2003-01556, and VEVES).


dk3417fm.pdf

Documents

alain de ryck

moving shock front

silicone oil drops

uri zoller part

phase contact line

mixed surfactant systems

flat solid substrates

partial wetting case