Capillarity and Wetting Phenomena

The study of capillarity is in the midst of a veritable explosion. Hence the temptation to write a new book, aiming at an audience of students. What is offered here is not a comprehensive review of the latest research but rather a compendium of principles.How does one turn a hydrophilic surface into one that is hydrophobic, and vice versa? We will describe a few solutions. Some rely on chemical treatments, such as coating a surface with a molecular layer. Others are based on physics, for instance by controlling the roughness of a surface. We will also examine the dynamics of wetting. Drops that spread spontaneously do so at a rate that slows down with time. They can be tricked into covering large areas by spreading them suddenly. We will describe a few of the many facets of their dynamical properties.Special additives are required for water to foam. Foams are desirable in a shampoo but can be a nightmare in a dishwasher detergent. Antifoam agents have been developed and are well known, but how do they work? It is also possible to generate bubbles and foams without special additives, for example in pure and viscous liquids such as glycerin, molten glass, and polymers. As we will see, the laws of draining and bursting then turn out to be quite different from the conventional ones.This book will enable the reader to understand in simple terms such questions that affect every day life -- questions that also come up during in industry. The aim is to view systems that often prove quite complex in a way that isolates a particular physical phenomenon, often avoiding descriptions requiring advanced numerical techniques will oftentimes in favor of qualitative arguments. This strategy may at times jeopardize scientific rigor, but it makes it possible to grasp things efficiently and to invent novel situations.

Preface

Introduction

xiii

References

xiv

1 Capillarity: Deformable Interfaces 1

1.1 Surface Tension

(14)

1.1.1 Physical Origin

(1)

1.1.2 Mechanical Definition: Surface Energy and Capillary Force

(5)

1.1.3 Measurements of Surface (or Tensions Interfacial)

1.1.4 Laplace Pressure

(3)

1.1.5 Minimal Surfaces

(4)

1.1.5.1 Jet

(1)

1.1.5.2 Drop on a Fiber

(2)

1.1.6 Minimal Surfaces With Zero Curvature

(2)

1.2 Contact Between Three Phases: Wetting

(14)

1.2.1 Two Types of Wetting: The Spreading Parameter S

(2)

1.2.2 Wetting Criteria: Zisman's Rule

(3)

1.2.3 Choice of Solid/Liquid Pairs

(6)

1.2.3.1 Ideal Liquids

(2)

1.2.3.2 Solid Substrates

(4)

1.2.4 Liquid Substrates: Neumann's Construction

(2)

Appendix: Minimal Surfaces - Euler-Lagrange Equations

(1)

References

(3)

2 Capillarity and Gravity

(36)

2.1 The Capillary Length k-1

(2)

2.2 Drops and Puddles in the Partial Wetting Regime

(8)

2.2.1 The Shape of Drops

(1)

2.2.2 Droplets (R « k-1)

(1)

2.2.3 Heavy Drops (R » k-1)

(2)

2.2.4 Experimental Techniques for Characterizing Drops

(5)

2.3 Menisci

(6)

2.3.1 Characteristic Size

(2)

2.3.2 Shape of a Meniscus Facing a Vertical Plate

(2)

2.3.3 Meniscus on a Vertical Fiber

(2)

2.4 Capillary Rise in Tubes: Jurin's Law

(5)

2.4.1 Historical Background

(2)

2.4.2 The Law of Capillary Rise

(1)

2.4.3 Pressure Argument for the Capillary Rise

(2)

2.5 Floating Lenses

(2)

2.5.1 The Spreading Parameter

(2)

2.5.2 The Shape of Floating Lenses (S less than 0) 54

2.6 Supplement on Techniques for Measuring Surface Tensions

(11)

2.6.1 The Shape of Drops

(4)

2.6.1.1 The Pendant Drop Method

(3)

2.6.1.2 Spinning Drops

(1)

2.6.2 Pressure Measurements

(1)

2.6.3 Force Measurements

(1)

2.6.4 Soft Solid Interfaces

(4)

References

(2)

3 Hysteresis and Elasticity of Triple Lines

(18)

3.1 Description of Phenomena

(3)

3.1.1 Advancing and Receding Angle

(2)

3.1.2 Pinning of the Triple Line

(1)

3.2 Elasticity of the Triple Line

(4)

3.2.1 The Myth of the Line Tension

(1)

3.2.2 The Fringe Elasticity of the Line of Contact

(3)

3.3 Hysteresis Due to Strong, Sparse Defects

(2)

3.4 Surfaces With Dense Defects

(2)

3.4.1 A Realistic Example

(1)

3.4.2 Small, Uncorrelated Defects

(1)

3.5 Two Cases Consistent With the Elasticity of Vibrating Strings

(4)

3.5.1 Hele-Shaw Cells

(1)

3.5.2 Puddle Edges

(2)

3.5.3 Puddle Distortions

(1)

3.6 The Role of Thermal Fluctuations

(1)

References

(3)

4 Wetting and Long-Range Forces

(20)

4.1 Energy and Properties of Film

(7)

4.1.1 Transition From Macroscopic to Microscopic

(1)

4.1.2 Thickness Change and Disjoining Pressure

(2)

4.1.3 Overall Stress in a Film

(1)

4.1.4 Three Types of Wetting

(3)

4.1.4.1 Stability Condition

(2)

4.1.4.2 Total Wetting

(1)

4.l.4.3 Partial Wetting

(1)

4.1.4.4 Wetting

(1)

4.2 The Nature of Long-Range Forces

(5)

4.2.1 van der Waals Forces

(2)

4.2.2 Case of Temperature-Dependent van der Waals Forces

(1)

4.2.3 Van der Waals Interactions in Layered Solids: Surface Treatments

(1)

4.2.4 Other Long-Range Forces

(1)

4.3 Some Manifestations of Long-Range Forces

(4)

4.3.1 Films on Slightly Rough Substrates: The Healing Length

(2)

4.3.2 Fine Structure of the Triple Line

101

(2)

4.4 Stratified Film

103

(1)

References

104

(3)

5 Hydrodynamics of Interfaces

107

(32)

5.1 Mechanics of Films: The Lubrication Approximation

107

(32)

5.2 Dynamics of Thin Films

111

(11)

5.2.1 Thinning of a Vertical Film

111

(1)

5.2.2 Levelling of a Horizontal Film

112

(3)

5.2.3 Rayleigh-Taylor Instability

115

(3)

5.2.4 Instability

118

(4)

5.3 Forced Wetting

122

(7)

5.3.1 The Landau-Levich-Derjaguin Model (and Variant Thereof)

122

(4)

5.3.2 Soapy Liquids

126

(1)

5.3.3 Other Geometries

127

(2)

5.4 Dynamics of Impregnation

129

(4)

5.4.1 Description of the Phenomenon

129

(1)

5.4.2 Washburn's Law

130

(1)

5.4.3 Inertial Regime

131

(2)

5.5 Waves and Ripples

133

(3)

5.5.1 Deep Water Condition

133

(1)

5.5.2 Dispersion Relation in the Inertial Regime

134

(1)

5.5.3 Attenuation

135

(1)

References

136

(3)

6 Dynamics of the Triple Line

139

(14)

6.1 Basic Experiment

139

(2)

6.2 Relation Between Force and Velocity

141

(5)

6.2.1 Mechanical Model (Viscous Dissipation)

142

(2)

6.2.2 Chemical Model

144

(2)

6.3 Oscillations Modes of a Triple Line

146

(2)

6.4 Dynamics of Total Wetting

148

(2)

References

150

(3)

7 Dewetting

153

(38)

7.1 Critical Thickness for Dewetting

155

(5)

7.1.1 Film on a Solid Substrate

155

(3)

7.1.2 Film on a Liquid Substrate

158

(1)

7.1.3 Sandwiched Liquid Films

159

(1)

7.2 Viscous Dewetting

160

(14)

7.2.1 Ideal Solid Substrates

161

(5)

7.2.2 Imperfect Solid Substrates

166

(3)

7.2.2.1 Surfaces With Hysteresis

166

(2)

7.2.2.2 "Slippery" Substrates

168

(1)

7.2.3 Liquid Substrates

169

(1)

7.2.4 Spinodal Dewetting

170

(4)

7.3 Inertial Dewetting

174

(7)

7.3.1 The Reynolds Number

175

(2)

7.3.2 The Froude Number (Condition for Shock Waves)

177

(3)

7.3.3 Liquid/Liquid Inertial Dewetting

180

(1)

7.4 Visco-Elastic Dewetting

181

(6)

7.4.1 Rupture of Ultra-Viscous Films

182

(3)

7.4.2 Life and Death of Viscous Bubbles

185

(2)

References

187

(4)

8 Surfactants

191

(24)

8.1 Frustrated Pairs

191

(3)

8.1.1 Principle

191

(1)

8.1.2 The Notion of Hydrophilic/Lipophilic Balance (HLB)

192

(2)

8.2 Aggregation of Surfactants

194

(6)

8.2.1 Aggregation in Volume: Micelles

194

(2)

8.2.2 Water/Air Interfaces

196

(4)

8.2.2.1 Insoluble Monolayers

197

(1)

8.2.2.2 Soluble Monolayers

197

(3)

8.2.2.3 Dynamical Surface Tensions 199

8.3 Some Applications of Surfactants

200

(6)

8.3.1 Flotation

200

(2)

8.3.2 Detergents

202

(1)

8.3.3 Emulsification

203

(1)

8.3.4 Surfactants as Wetting and Dewetting Agents

204

(2)

8.4 Soap Films and Bubbles

206

(6)

8.4.l Fabrication of Films

206

(1)

8.4.2 The Role of Surfactants

207

(1)

8.4.3 Draining Mechanisms

208

(1)

8.4.4 Aging and Death of Films

209

(2)

8.4.5 The Case of Bubbles

211

(1)

References

212

(3)

9 Special Interfaces

215

(30)

9.1 Outline

215

(1)

9.2 Wetting of Textured Surfaces

216

(19)

9.2.1 Basic Model

216

(3)

9.2.1.1 Experiment of Johnson and Dettre

216

(1)

9.2.1.2 Wenzel's Model

217

9.2.1.3 The Cassie-Baxter Model

210

(9)

9.2.2 Composite Rough Surfaces

219

(7)

9.2.2.1 Hydrophilic Surfaces

219

(2)

9.2.2.2 Hydrophobic Surfaces

221

(4)

9.2.2.3 Summary

225

(1)

9.2.3 Liquid Pearls and Marbles

226

(9)

9.2.3.1 Implementation

226

(3)

9.2.3.2 Static States

229

(1)

9.2.3.3 Dynamical States

230

(5)

9.3 Wetting and Porous Media

235

(5)

9.3.1 Capillary Rise in a Porous Medium

235

(2)

9.3.2 Equilibrium Angle at the Surface of a Porous Medium

237

(1)

9.3.3 Suction Experiments on Drops

238

(1)

9.3.4 Suction Experiments on Films

239

(1)

9.4 Wetting at Soft Interfaces

240

(5)

9.4.1 Principles of "Elastic" Wetting

241

(2)

9.4.1.1 The Spreading Parameter S

242

(1)

9.4.1.2 Young's Relation No Longer Holds!

242

(1)

9.4.1.3 Penny-Shaped Trapped Drops

242

(1)

9.4.2 Experimental Observation of Elastic Wetting

243

(3)

9.4.2.1 The Three Partners: Soft Solid, Liquid, and Elastomer

243

(2)

9.4.2.2 Observation of the Contact: Reflection Interference Contrast Microscopy 244

9.4.2.3 Drop Profile and Measurement of S

245

(16)

9.4.3 "Elastic" Dewetting of Wedged-in Films

246

(6)

9.4.3.1 Drainage

247

(1)

9.4.3.2 Controlled Dewetting: Nucleators

248

(4)

9.4.4 Wetting Transitions Under Shear: The Principle of Hydroplaning

252

(3)

9.4.5 Role of Nucleators in Forced Wetting: Cerenkov Wake

255

(1)

9.4.6 Conclusion

256

(2)

References

258

(3)

10 Transport Phenomena

261

(28)

10.1 Chemical Gradients

261

(7)

10.1.1 Experiments With Vapors

261

(2)

10.1.2 Transport Toward Wettable Regions

263

(5)

10.2 Thermal Gradients

268

(7)

10.2.1 Drops Favoring the Cold

268

(3)

10.2.2 Finger Formation

271

(4)

10.3 Reactive Wetting

275

(6)

10.3.1 Examples

275

(1)

10.3.2 Liquid Column in a Capillary

276

(2)

10.3.3 Bidrops

278

(2)

10.3.4 "Running Drops" on a Solid Planar Surface

280

(1)

10.4 Transport by Electric Field

281

(5)

10.4.1 Relevance of Microsystems

281

(1)

10.4.2 Electrocapillarity

282

(1)

10.4.3 Principle of Electro-Osmosis

283

(1)

10.4.4 Examples

283

(3)

10.4.4.1 Electrostatic Lenses

283

(2)

10.4.4.2 Transfer of Bubbles

285

(1)

10.4.4.3 Limitations

285

(1)

10.4.4.4 Comparison with Capacitive Effects

286

(1)

References

286

(3)

Index

289

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Capillarity and Wetting Phenomena

9780387005928

0387005927

Summary

Table of Contents

Supplemental Materials

Rewards Program

Digital License