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Capillarity and Wetting Phenomena : Drops, Bubbles, Pearls, Waves

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  • ISBN : 9780387005928
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Review by P. R. Douville, emeritus, Central Connecticut State University

"You are an intelligent spider sitting on your web. Early morning light forms tiny rainbows as it passes through the beads of dew strung along the filaments composing your hard-earned handiwork. Why beads? What happened to the water in between each drop? To answer this question, our eight-legged intellectual must first gain an understanding of how liquids such as water actually wet surfaces and why such liquids fail to wet other surfaces. The problem encompasses such subjects as liquids rising up capillary tubes, paint spreading on solid surfaces or liquids spreading on other liquids, the fascinating subject of bubble formation and stability, and why water streams down some surfaces and forms droplets on other surfaces. De Gennes (CollA¡§ge ((College) de France; Institute Curie), Brochard-Wyart (Institut Curie), and QuA¨ÏrA¨Ï (Quere) (CollA¡§ge ((College) de France) have written an excellent treatise on these phenomena that opens with a very poetic introduction relating esoteric concepts to everyday observations, and includes chapter references, historical sketches, and a very good discussion of each problem at chapter beginnings. For readers with backgrounds in mathematics, physics, and chemistry, although it is not beyond advanced undergraduates in the sciences and technological fields. Summing Up: Highly recommended. Upper-division undergraduates through professionals; two-year technical program students."

"This book is designed as an elementary introduction to the conceptual framework used in research on wetting/dewetting processes and related capillary phenomena. ¡¦ a simple and inspiring style of writing allows the authors to ¡®convey the sense of curiosity and joy¡¯ that unites researchers in this area ¡¦ . The range of topics covered and a host of physical ideas and principles the authors describe as guidelines in the field are likely to make this book interesting to a wide audience ¡¦ ." (Dr. Y. D. Shikhmurzaev, Contemporary Physics, Vol. 46 (1), 2005)

"Capillarity refers to the study of surface phenomena involving at least one liquid phase. ¡¦ This book brings together (almost) everything which is known in a single volume. In view of the fact that the history of capillarity covers several centuries, this is a real ¡®tour de force¡¯. ¡¦ It contains a wealth of practical information about a very large variety of surface phenomena. ¡¦ This book should be of interest to a large variety of scientists (not only physicists)." (Marc Baus, Physicalia, Vol. 57 (3), 2005)

"Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves is a translation of the earlier French Gouttes, Bulles, Perles et Ondes ¡¦ . It has been wonderfully translated by Axel Reisinger. The English is fully fluent and idiomatic ¡¦ . The book can be read with pleasure and profit by the uninitiated, but it is also a valuable - and even an indispensable reference work for the expert. ¡¦ contains a whole bookshelf of information £¿ all of it useful and much of it fascinating." (Benjamin Widom, Physics Today, December, 2004)

"De Gennes (College ((College) de France; Institute Curie), Brochard-Wyart (Institut Curie), and Quere (Quere) (College (College) de France) have written an excellent treatise ¡¦ with a very poetic introduction relating esoteric concepts to everyday observations, and includes chapter references, historical sketches, and a very good discussion of each problem at chapter beginnings. ¡¦ Summing Up: Highly recommended. Upper-division undergraduates through professionals: two-year technical program students." (P. R. Douville, CHOICE, May, 2004)

"The whole book is in the same spirit, which is very enjoyable ¡¦ . Thus it contains many illuminating examples and sketches ¡¦ . it will also act as a reference for those working in the field. In conclusion, the intended readers of this book, whether they be soft matter students or scientists or simply the curious, should find therein not just a very good source of information but also an impressive collection of exciting and simple explanations of very complex phenomena." (Dr. Roberto Cerbino, Europhysics News, Vol. 37 (1), 2006)

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Chapter Page
Preface v
Introduction xiii
References xiv
1. Capillarity: Deformable Interfaces 1
1.1 Surface Tension 1
1.1.1 Physical Origin 2
1.1.2 Mechanical Definition: Surface Energy and Capillary Force 3
1.1.3 Measurements of Surface (or Interfacial) Tensions 6
1.1.4 Laplace Pressure 6
1.1.5 Minimal Surfaces 9
1.1.5.1 Jet 10
1.1.5.2 Drop on a Fiber 11
1.1.6 Minimal Surfaces With Zero Curvature 13
1.2 Contact Between Three Phases: Wetting 15
1.2.1 Two Types of Wetting: The Spreading Parameter S 16
1.2.2 Wetting Criteria: Zisman's Rule 18
1.2.3 Choice of Solid/Liquid Pairs 21
1.2.3.1 Ideal Liquids 21
1.2.3.2 Solid Substrates 23
1.2.4 Liquid Substrates: Neumann's Construction 27
Appendix Minimal Surfaces - Euler-Lagrange Equations 29
References 30
2. Capillarity and Gravity 33
2.1 The Capillary Length [kappa superscript -1] 33
2.2 Drops and Puddles in the Partial Wetting Regime 35
2.2.1 The Shape of Drops 35
2.2.2 Droplets (R << [kappa superscript -1]) 36
2.2.3 Heavy Drops (R >> [kappa superscript -1]) 36
2.2.4 Experimental Techniques for Characterizing Drops 38
2.3 Menisci 43
2.3.1 Characteristic Size 43
2.3.2 Shape of a Meniscus Facing a Vertical Plate 45
2.3.3 Meniscus on a Vertical Fiber 47
2.4 Capillary Rise in Tubes: Jurin's Law 49
2.4.1 Historical Background 49
2.4.2 The Law of Capillary Rise 51
2.4.3 Pressure Argument for the Capillary Rise 52
2.5 Floating Lenses 54
2.5.1 The Spreading Parameter 54
2.5.2 The Shape of Floating Lenses (S < 0) 54
2.6 Supplement on Techniques for Measuring Surface Tensions 56
2.6.1 The Shape of Drops 57
2.6.1.1 The Pendant Drop Method 57
2.6.1.2 Spinning Drops 60
2.6.2 Pressure Measurements 61
2.6.3 Force Measurements 62
2.6.4 Soft Solid Interfaces 63
References 67
3. Hysteresis and Elasticity of Triple Lines 69
3.1 Description of Phenomena 69
3.1.1 Advancing and Receding Angle 69
3.1.2 Pinning of the Triple Line 71
3.2 Elasticity of the Triple Line 72
3.2.1 The Myth of the Line Tension 72
3.2.2 The Fringe Elasticity of the Line of Contact 73
3.3 Hysteresis Due to Strong, Sparse Defects 76
3.4 Surfaces With Dense Defects 78
3.4.1 A Realistic Example 78
3.4.2 Small, Uncorrelated Defects 79
3.5 Two Cases Consistent With the Elasticity of Vibrating Strings 80
3.5.1 Hele-Shaw Cells 80
3.5.2 Puddle Edges 81
3.5.3 Puddle Distortions 83
3.6 The Role of Thermal Fluctuations 84
References 84
4. Wetting and Long-Range Forces 87
4.1 Energy and Properties of Films 87
4.1.1 Transition From Macroscopic to Microscopic 87
4.1.2 Thickness Change and Disjoining Pressure 88
4.1.3 Overall Stress in a Film 90
4.1.4 Three Types of Wetting 91
4.1.4.1 Stability Condition 91
4.1.4.2 Total Wetting 93
4.1.4.3 Partial Wetting 93
4.1.4.4 Pseudo-Partial Wetting 93
4.2 The Nature of Long-Range Forces 94
4.2.1 van der Waals Forces 94
4.2.2 Case of Temperature-Dependent van der Waals Forces 96
4.2.3 Van der Waals Interactions in Layered Solids: Surface Treatments 97
4.2.4 Other Long-Range Forces 98
4.3 Some Manifestations of Long-Range Forces 99
4.3.1 Films on Slightly Rough Substrates: The Healing Length 99
4.3.2 Fine Structure of the Triple Line 101
4.4 Stratified Film 103
References 104
5. Hydrodynamics of Interfaces 107
5.1 Mechanics of Films: The Lubrication Approximation 107
5.2 Dynamics of Thin Films 111
5.2.1 Thinning of a Vertical Film 111
5.2.2 Levelling of a Horizontal Film 112
5.2.3 Rayleigh-Taylor Instability 115
5.2.4 Plateau-Rayleigh Instability 118
5.3 Forced Wetting 122
5.3.1 The Landau-Levich-Derjaguin Model (and Variant Thereof) 122
5.3.2 Soapy Liquids 126
5.3.3 Other Geometries 127
5.4 Dynamics of Impregnation 129
5.4.1 Description of the Phenomenon 129
5.4.2 Washburn's Law 130
5.4.3 Inertial Regime 131
5.5 Waves and Ripples 133
5.5.1 Deep Water Condition 133
5.5.2 Dispersion Relation in the Intertial Regime 134
5.5.3 Attenuation 135
References 136
6. Dynamics of the Triple Line 139
6.1 Basic Experiment 139
6.2 Relation Between Force and Velocity 141
6.2.1 Mechanical Model (Viscous Dissipation) 142
6.2.2 Chemical Model 144
6.3 Oscillations Modes of a Triple Line 146
6.4 Dynamics of Total Wetting 148
References 150
7. Dewetting 153
7.1 Critical Thickness for Dewetting 155
7.1.1 Film on a Solid Substrate 155
7.1.2 Film on a Liquid Substrate 158
7.1.3 Sandwiched Liquid Films 159
7.2 Viscous Dewetting 160
7.2.1 Ideal Solid Substrates 161
7.2.2 Imperfect Solid Substrates 166
7.2.2.1 Surfaces With Hysteresis 166
7.2.2.2 "Slippery" Substrates 168
7.2.3 Liquid Substrates 169
7.2.4 Spinodal Dewetting 170
7.3 Inertial Dewetting 174
7.3.1 The Reynolds Number 175
7.3.2 The Froude Number (Condition for Shock Waves) 177
7.3.3 Liquid/Liquid Inertial Dewetting 180
7.4 Visco-Elastic Dewetting 181
7.4.1 Rupture of Ultra-Viscous Films 182
7.4.2 Life and Death of Viscous Bubbles 185
References 187
8. Surfactants 191
8.1 Frustrated Pairs 191
8.1.1 Principle 191
8.1.2 The Notion of Hydrophilic/Lipophilic Balance (HLB) 192
8.2 Aggregation of Surfactants 194
8.2.1 Aggregation in Volume: Micelles 194
8.2.2 Water/Air Interfaces 196
8.2.2.1 Insoluble Monolayers 197
8.2.2.2 Soluble Monolayers 197
8.2.2.3 Dynamical Surface Tensions 199
8.3 Some Applications of Surfactants 200
8.3.1 Flotation 200
8.3.2 Detergents 202
8.3.3 Emulsification 203
8.3.4 Surfactants as Wetting and Dewetting Agents 204
8.4 Soap Films and Bubbles 206
8.4.1 Fabrication of Films 206
8.4.2 The Role of Surfactants 207
8.4.3 Draining Mechanisms 208
8.4.4 Aging and Death of Films 209
8.4.5 The Case of Bubbles 211
References 212
9. Special Interfaces 215
9.1 Outline 215
9.2 Wetting of Textured Surfaces 216
9.2.1 Basic Model 216
9.2.1.1 Experiment of Johnson and Dettre 216
9.2.1.2 Wenzel's Model 217
9.2.1.3 The Cassie-Baxter Model 218
9.2.2 Composite Rough Surfaces 219
9.2.2.1 Hydrophilic Surfaces 219
9.2.2.2 Hydrophobic Surfaces 221
9.2.2.3 Summary 225
9.2.3 Liquid Pearls and Marbles 226
9.2.3.1 Implementation 226
9.2.3.2 Static States 229
9.2.3.3 Dynamical States 230
9.3 Wetting and Porous Media 235
9.3.1 Capillary Rise in a Porous Medium 235
9.3.2 Equilibrium Angle at the Surface of a Porous Medium 237
9.3.3 Suction Experiments on Drops 238
9.3.4 Suction Experiments on Films 239
9.4 Wetting at Soft Interfaces 240
9.4.1 Principles of "Elastic" Wetting 241
9.4.1.1 The Spreading Parameter S 242
9.4.1.2 Young's Relation No Longer Holds! 242
9.4.1.3 Penny-Shaped Trapped Drops 242
9.4.2 Experimental Observation of Elastic Wetting 243
9.4.2.1 The Three Partners: Soft Solid, Liquid, and Elastomer 243
9.4.2.2 Observation of the Contact: Reflection Interference Contrast Microscopy 244
9.4.2.3 Drop Profile and Measurement of S 245
9.4.3 "Elastic" Dewetting of Wedged-in Films 246
9.4.3.1 Drainage 247
9.4.3.2 Controlled Dewetting: Nucleators 248
9.4.4 Wetting Transitions Under Shear: The Principle of Hydroplaning 252
9.4.5 Role of Nucleators in Forced Wetting: Cerenkov Wake 255
9.4.6 Conclusion 256
References 258
10. Transport Phenomena 261
10.1 Chemical Gradients 261
10.1.1 Experiments With Vapors 261
10.1.2 Transport Toward Wettable Regions 263
10.2 Thermal Gradients 268
10.2.1 Drops Favoring the Cold 268
10.2.2 Finger Formation 271
10.3 Reactive Wetting 275
10.3.1 Examples 275
10.3.2 Liquid Column in a Capillary 276
10.3.3 Bidrops 278
10.3.4 "Running Drops" on a Solid Planar Surface 280
10.4 Transport by Electric Field 281
10.4.1 Relevance of Microsystems 281
10.4.2 Electrocapillarity 282
10.4.3 Principle of Electro-Osmosis 283
10.4.4 Examples 283
10.4.4.1 Electrostatic Lenses 283
10.4.4.2 Transfer of Bubbles 285
10.4.4.3 Limitations 285
10.4.4.4 Comparison with Capacitive Effects 286
References 286
Index 289>

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The study of capillarity and related phenomena requires both an acute faculty of observation and an intensity of imagination that truly allow one to see "all the world in a grain of sand." The process by which morning dew condenses into the unstable droplets that grace a spider's web, for example, has important implications for the industrial treatment of textile fibers. And an appreciation of underlying physical principles provides an answer to common questions about everyday phenomena-for example, why large drops of rain roll down a car windshield, while others descend leaving a trail of water behind them.

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