Wetting of real surfaces

Preface . . vii
Notation . . ix

1 What is surface tension? . . 1
1.1 Surface tension and its definition . . 1
1.2 Physical origin of the surface tension of liquids . . 2
1.3 Temperature dependence of the surface tension . . 5
1.4 Surfactants . . 6
1.5 The Laplace pressure . . 6
1.6 Surface tension of solids . . 8
1.7 Values of surface tensions of solids . . 9
Appendix 1A. The short-range nature of intermolecular forces . . 10
Appendix IB. The Laplace pressure from simple reasoning . . 10
Bullets . . 11
References . . 12

2 Wetting of ideal surfaces . . 13
2.1 What is wetting? The spreading parameter . . 13
2.2 The Young equation . . 14
2.3 Wetting of flat homogeneous curved surfaces . . 17
2.4 Line tension . . 19
2.5 Disjoining pressure . . 20
2.6 Wetting of an ideal surface: influence of absorbed liquid layers and the liquid vapor . . 22
2.7 Gravity and wetting of ideal surfaces: a droplet shape and liquid puddles . . 24
2.8 The shape of the droplet and the disjoining pressure . . 27
2.9 Distortion of droplets by an electric field . . 29
2.10 Capillary rise . . 30
2.11 The shape of a droplet wetting a fiber . . 33
2.12 Wetting and adhesion. The Young-Dupre equation . . 35
2.13 Wetting transitions on ideal surfaces . . 36
2.14 How the surface tension is measured? . . 37
2.14.1 The Du Notiy ring and the Wilhelmy plate methods . . 37
2.14.2 The pendant drop method . . 38
2.14.3 Maximum bubble pressure method . . 39
2.14.4 Dynamic methods of measurement of surface tension . . 40
2.15 Measurement of surface tension of solids . . 43
Appendix 2A. Transversality conditions . . 44
Appendix 2B. Zisman plot . . 45
Bullets . . 46
References . . 46

3 Contact angle hysteresis . . 50
3.1 Contact angle hysteresis: its sources and manifestations . . 50
3.2 Contact angle hysteresis on smooth homogeneous substrates . . 52
3.3 Strongly and weakly pinning surfaces . . 53
3.4 Qualitative characterization of the pinning of the triple line . . 57
3.5 The zero eventual contact angle of evaporated droplets and its explanation . . 58
3.6 Contact angle hysteresis and line tension . . 59
3.7 More physical reasons for the contact angle hysteresis on smooth ideal surfaces . . 60
3.8 Contact angle hysteresis on chemically heterogeneous smooth surfaces: the phenomenological approach. hi. Acquaintance with the apparent contact angle . . 61
3.9 The phenomenological approach to the hysteresis of the contact angle developed by Vedantam and Panchagnula . . 62
3.10 The macroscopic approach to the contact angle hysteresis, the model of Joanny and de Gennes . . 63
3.10.1 Elasticity of the triple line . . 63
3.10.2 Contact angle hysteresis in the case of a dilute system of defects . . 66
3.10.3 Surfaces with dense defects and the fine structure of the triple line . . 66
3.11 Deformation of the substrate as an additional source of the contact angle hysteresis . . 68
3.12 How the contact angle hysteresis can be measured . . 69
3.13 Roughness of the substrate and the contact angle hysteresis . . 71
3.14 Use of contact angles tor characterization of solid surfaces . . 71
Appendix 3A. A droplet on an inclined plane . . 73
Bullets . . 75
References . . 75

4 Dynamics of wetting . . 78
4.1 The dynamic contact angle . . 78
4.2 The dynamics of wetting: the approach of Voinov . . 78
4.3 The dynamic contact angle in a situation of complete wetting . . 80
4.4 Dissipation of energy in the vicinity of the triple line . . 82
4.5 Dissipation of energy and the microscopic contact angle . . 83
4.6 A microscopic approach to the displacement of the triple line . . 83
4.7 Spreading of droplets: Tanner's law . . 84
4.8 Superspreading . . 85
4.9 Dynamics of filling of capillary tubes . . 85
4.10 The drag-out problem . . 87
4.11 Dynamic wetting of heterogeneous surfaces . . 88
Bullets . . 89
References . . 90

5 Wetting of rough and chemically heterogeneous surfaces: the Wenzel and Cassie models . . 92
5.1 General remarks . . 92
5.2 The Wenzel model . . 92
5.3 Wenzel wetting of chemically homogeneous curved rough surfaces . . 94
5.4 The Cassie-Baxter wetting model . . 96
5.5 The Israelachvili and Gee criticism of the Cassie-Baxter model . . 97
5.6 Cassie-Baxter wetting in a situation where a droplet partially sits on air . . 98
5.7 The Cassie-Baxter wetting of curved surfaces . . 101
5.8 Cassie-Baxter impregnating wetting . . 101
5.9 The importance of the area adjacent to the trinle line in the wetting of rough and chemically heterogeneous surfaces . . 103
5.10 Wetting of gradient surfaces . . 107
5.11 The mixed wetting state . . 108
5.12 Considering the line tension . . 109
Appendix 5A. Alternative derivation of the Young, Cassie, and Wenzel equations . . 111
Bullets . . 113
References . . 114

6 Superhydrophobicity, superhydrophilicity, and the rose petal effect . . 116
6.1 Superhydrophobicity . . 116
6.2 Superhydrophobicity and the Cassie-Baxter wetting regime . . 117
6.3 Wetting of hierarchical reliefs: approach of Herminghaus . . 119
6.4 Wetting of hierarchical structures: a simple example . . 10
6.5 Superoleophobicity . . 122
6.6 The rose petal effect . . 123
6.7 Superhydrophilicity . . 125
Bullets . . 125
References . . 126

7 Wetting transitions on rough surfaces . . 129
7.1 General remarks . . 129
7.2 Wetting transitions on rough surfaces: experimental data . . 129
7.3 Time-scaling of wetting transitions . . 131
7.4 Origin of the barrier separating the Cassie and Wenzel wetting states: the case of hydrophobia surfaces . . 132
7.4.1 The composite wetting state . . 132
7.4.2 Energy barriers and Cassie, Wenzel, and Young contact angles . . 134
7.5 Critical pressure necessary for wetting transition . . 137
7.6 Wetting transitions and de-pinning of the triple line; the dimension of a wetting transition . . 138
7.7 The experimental evidence for the ID scenario of wetting transitions . . 141
7.8 Wetting transitions on hydrophilic surfaces . . 142
7.8.1 Cassie wetting of inherently hydrophilic surfaces: criteria for gas entrapping . . 142
7.8.2 Origin of the energetic barrier separating Cassie and Wenzel wetting regimes on hydrophilic surfaces . . 143
7.8.3 Surfaces built of ensembles of balls . . 146
7.9 Mechanisms of wetting transitions: the dynamics . . 147
Bullets . . 148
References . . 149

8 Electrowetting and wetting in the presence of external fields . . 152
8.1 General remarks . . 152
8.2 Electro wetting . . 152
8.3 Wetting in the presence of external fields: a general case . . 153
Bullets . . 155
References . . 155

9 Nonstick droplets . . 156
9.1 General remarks . . 156
9.2 Leidenfrost droplets . . 156
9.3 Liquid marbles . . 158
9.3.1 What are liquid marbles? . . 158
9.3.2 Liquid marble/support interface . . 160
9.3.3 Liquid marble/vapor interface . . 161
9.3.4 Effective surface tension of liquid marbles . . 161
9.3.5 Scaling laws governing the shape of liquid marbles . . 162
9.3.6 Properties of liquid marbles: the dynamics . . 163
9.3.7 Actuation of liquid marbles with electric and magnetic fields . . 164
9.3.8 Applications of liquid marbles . . 165
9.4 Nonstick drops bouncing a fluid bath . . 165
Bullets . . 166
References . . 166

Index . . 169