Capillarity and Wetting Phenomena

by Gennes, Pierre-Gilles De; Quere, David; Brochard-Wyart, Francoise; Reisinger, Axel; De Gennes, Pierre-Gilles

• ISBN13: 9780387005928
• ISBN10: 0387005927
• Format: Hardcover
• Copyright: 2003-10-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Preface	v
Introduction	xiii
References	xiv
1 Capillarity: Deformable Interfaces 1
1.1 Surface Tension	1	(14)
1.1.1 Physical Origin	2	(1)
1.1.2 Mechanical Definition: Surface Energy and Capillary Force	3	(5)
1.1.3 Measurements of Surface (or Tensions Interfacial)	8
1.1.4 Laplace Pressure	6	(3)
1.1.5 Minimal Surfaces	9	(4)
1.1.5.1 Jet	10	(1)
1.1.5.2 Drop on a Fiber	11	(2)
1.1.6 Minimal Surfaces With Zero Curvature	13	(2)
1.2 Contact Between Three Phases: Wetting	15	(14)
1.2.1 Two Types of Wetting: The Spreading Parameter S	16	(2)
1.2.2 Wetting Criteria: Zisman's Rule	18	(3)
1.2.3 Choice of Solid/Liquid Pairs	21	(6)
1.2.3.1 Ideal Liquids	21	(2)
1.2.3.2 Solid Substrates	23	(4)
1.2.4 Liquid Substrates: Neumann's Construction	27	(2)
Appendix: Minimal Surfaces - Euler-Lagrange Equations	29	(1)
References	30	(3)
2 Capillarity and Gravity	33	(36)
2.1 The Capillary Length k-1	33	(2)
2.2 Drops and Puddles in the Partial Wetting Regime	35	(8)
2.2.1 The Shape of Drops	35	(1)
2.2.2 Droplets (R « k-1)	36	(1)
2.2.3 Heavy Drops (R » k-1)	36	(2)
2.2.4 Experimental Techniques for Characterizing Drops	38	(5)
2.3 Menisci	43	(6)
2.3.1 Characteristic Size	43	(2)
2.3.2 Shape of a Meniscus Facing a Vertical Plate	45	(2)
2.3.3 Meniscus on a Vertical Fiber	47	(2)
2.4 Capillary Rise in Tubes: Jurin's Law	49	(5)
2.4.1 Historical Background	49	(2)
2.4.2 The Law of Capillary Rise	51	(1)
2.4.3 Pressure Argument for the Capillary Rise	52	(2)
2.5 Floating Lenses	54	(2)
2.5.1 The Spreading Parameter	54	(2)
2.5.2 The Shape of Floating Lenses (S less than 0) 54
2.6 Supplement on Techniques for Measuring Surface Tensions	56	(11)
2.6.1 The Shape of Drops	57	(4)
2.6.1.1 The Pendant Drop Method	57	(3)
2.6.1.2 Spinning Drops	60	(1)
2.6.2 Pressure Measurements	61	(1)
2.6.3 Force Measurements	62	(1)
2.6.4 Soft Solid Interfaces	63	(4)
References	67	(2)
3 Hysteresis and Elasticity of Triple Lines	69	(18)
3.1 Description of Phenomena	69	(3)
3.1.1 Advancing and Receding Angle	69	(2)
3.1.2 Pinning of the Triple Line	71	(1)
3.2 Elasticity of the Triple Line	72	(4)
3.2.1 The Myth of the Line Tension	72	(1)
3.2.2 The Fringe Elasticity of the Line of Contact	73	(3)
3.3 Hysteresis Due to Strong, Sparse Defects	76	(2)
3.4 Surfaces With Dense Defects	78	(2)
3.4.1 A Realistic Example	78	(1)
3.4.2 Small, Uncorrelated Defects	79	(1)
3.5 Two Cases Consistent With the Elasticity of Vibrating Strings	80	(4)
3.5.1 Hele-Shaw Cells	80	(1)
3.5.2 Puddle Edges	81	(2)
3.5.3 Puddle Distortions	83	(1)
3.6 The Role of Thermal Fluctuations	84	(1)
References	84	(3)
4 Wetting and Long-Range Forces	87	(20)
4.1 Energy and Properties of Film	87	(7)
4.1.1 Transition From Macroscopic to Microscopic	87	(1)
4.1.2 Thickness Change and Disjoining Pressure	88	(2)
4.1.3 Overall Stress in a Film	90	(1)
4.1.4 Three Types of Wetting	91	(3)
4.1.4.1 Stability Condition	91	(2)
4.1.4.2 Total Wetting	93	(1)
4.l.4.3 Partial Wetting	93	(1)
4.1.4.4 Wetting	93	(1)
4.2 The Nature of Long-Range Forces	94	(5)
4.2.1 van der Waals Forces	94	(2)
4.2.2 Case of Temperature-Dependent van der Waals Forces	96	(1)
4.2.3 Van der Waals Interactions in Layered Solids: Surface Treatments	97	(1)
4.2.4 Other Long-Range Forces	98	(1)
4.3 Some Manifestations of Long-Range Forces	99	(4)
4.3.1 Films on Slightly Rough Substrates: The Healing Length	99	(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