Capillarity and Wetting Phenomena

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1 ? Pierre-Gilles de Gennes Frangoise Brochard-Wyart David Quere Capillarity and Wetting Phenomena Drops, Bubbles, Pearls, Waves Translated by Axel Reisinger With 177 Figures Springer

2 Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo

3 Preface Introduction References v xiii xiv 1 Capillarity: Deformable Interfaces Surface Tension Physical Origin Mechanical Definition: Surface Energy and Capillary Force Measurements of Surface (or Interfacial) Tensions Laplace Pressure Minimal Surfaces Jet Drop on a Fiber Minimal Surfaces With Zero Curvature Contact Between Three Phases: Wetting Two Types of Wetting: The Spreading Parameter S Wetting Criteria: Zisman's Rule Choice of Solid/Liquid Pairs Ideal Liquids Solid Substrates Liquid Substrates: Neumann's Construction 27

4 viii Contents Appendix: Minimal Surfaces - Euler-Lagrange Equations References 30 2 Capillarity and Gravity The Capillary Length KT Drops and Puddles in the Partial Wetting Regime The Shape of Drops Droplets (R <C K" 1 ) Heavy Drops (i?»k" 1 ) Experimental Techniques for Characterizing Drops Menisci Characteristic Size Shape of a Meniscus Facing a Vertical Plate Meniscus on a Vertical Fiber Capillary Rise in Tubes: Jurin's Law Historical Background The Law of Capillary Rise Pressure Argument for the Capillary Rise Floating Lenses The Spreading Parameter The Shape of Floating Lenses (S < 0) Supplement on Techniques for Measuring Surface Tensions The Shape of Drops The Pendant Drop Method Spinning Drops Pressure Measurements Force Measurements Soft Solid Interfaces 63 References 67 3 Hysteresis and Elasticity of Triple Lines Description of Phenomena Advancing and Receding Angle Pinning of the Triple Line Elasticity of the Triple Line The Myth of the Line Tension The Fringe Elasticity of the Line of Contact Hysteresis Due to Strong, Sparse Defects Surfaces With Dense Defects A Realistic Example Small, Uncorrelated Defects Two Cases Consistent With the Elasticity of Vibrating Strings 80

5 ix Hele-Shaw Cells Puddle Edges Puddle Distortions The Role of Thermal Fluctuations 84 References 84 Wetting and Long-Range Forces Energy and Properties of Films Transition From Macroscopic to Microscopic Thickness Change and Disjoining Pressure Overall Stress in a Film Three Types of Wetting Stability Condition Total Wetting Partial Wetting Pseudo-Partial Wetting The Nature of Long-Range Forces van der Waals Forces Case of Temperature-Dependent van der Waals Forces Van der Waals Interactions in Layered Solids: Surface Treatments Other Long-Range Forces Some Manifestations of Long-Range Forces Films on Slightly Rough Substrates: The Healing Length Fine Structure of the Triple Line Stratified Film 103 References 104 Hydrodynamics of Interfaces Mechanics of Films: The Lubrication Approximation Dynamics of Thin Films Ill Thinning of a Vertical Film Ill Levelling of a Horizontal Film Rayleigh-Taylor Instability Plateau-Rayleigh Instability Forced Wetting The Landau-Levich-Derjaguin Model (and Variant Thereof) Soapy Liquids Other Geometries Dynamics of Impregnation Description of the Phenomenon Washburn's Law 130

6 5.4.3 Inertial Regime Waves and Ripples Deep Water Condition Dispersion Relation in the Inertial Regime Attenuation 135 References 136 Dynamics of the Triple Line Basic Experiment Relation Between Force and Velocity Mechanical Model (Viscous Dissipation) Chemical Model Oscillations Modes of a Triple Line Dynamics of Total Wetting 148 References 150 Dewetting Critical Thickness for Dewetting Film on a Solid Substrate Film on a Liquid Substrate Sandwiched Liquid Films Viscous Dewetting Ideal Solid Substrates Imperfect Solid Substrates Surfaces With Hysteresis "Slippery" Substrates Liquid Substrates Spinodal Dewetting Inertial Dewetting The Reynolds Number The Froude Number (Condition for Shock Waves) Liquid/Liquid Inertial Dewetting Visco-Elastic Dewetting Rupture of Ultra-Viscous Films Life and Death of Viscous Bubbles 185 References 187 Surfactants Frustrated Pairs Principle The Notion of Hydrophilic/Lipophilic Balance (HLB) Aggregation of Surfactants Aggregation in Volume: Micelles 194

7 xi Water/Air Interfaces Insoluble Monolayers Soluble Monolayers Dynamical Surface Tensions Some Applications of Surfactants Flotation Detergents Emulsification Surfactants as Wetting and Dewetting Agents Soap Films and Bubbles Fabrication of Films The Role of Surfactants Draining Mechanisms Aging and Death of Films The Case of Bubbles 211 References 212 Special Interfaces Outline Wetting of Textured Surfaces Basic Model Experiment of Johnson and Dettre Wenzel's Model The Cassie-Baxter Model Composite Rough Surfaces Hydrophilic Surfaces Hydrophobic Surfaces Summary Liquid Pearls and Marbles Implementation Static States Dynamical States Wetting and Porous Media Capillary Rise in a Porous Medium Equilibrium Angle at the Surface of a Porous Medium Suction Experiments on Drops Suction Experiments on Films Wetting at Soft Interfaces Principles of "Elastic" Wetting The Spreading Parameter Young's Relation No Longer Holds! Penny-Shaped Trapped Drops Experimental Observation of Elastic Wetting

Capillarity and Wetting Phenomena

Capillarity and Wetting Phenomena Capillarity and Wetting Phenomena Pierre-Gilles de Gennes Frangoise Brochard-Wyart David Quere Capillarity and Wetting Phenomena Drops, Bubbles, Pearls, Waves Translated by Axel Reisinger With 177 Figures

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