 | de Gennes P.-G. Capillarity and wetting phenomena: drops, bubbles, pearls, waves / de Gennes P.-G., Brochard-Wyart F., Quere D.; transl. by Reisinger A. - New York: Springer, 2004. - xv, 291 p.: ill. - ISBN 978-0-387-00592-8
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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 k-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 << k-1) ................................ 36
2.2.3. Heavy Drops {R >> k-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 Waak 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 Inertial 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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