Mechanics and Physics of Porous Solids

MECHANICS AND
PHYSICS OF
POROUS SOLIDS......Page 5
Contents......Page 9
Preface......Page 15
1 The Strange World of Porous Solids......Page 17
2.1.1 Free energy and chemical potential......Page 27
2.2.1 Derivation of the Gibbs–Duhem equation......Page 29
2.2.2 Molar Gibbs–Duhem equation......Page 30
2.2.3 Ideal gases......Page 31
2.2.5 Partial molar property......Page 32
2.3.1 Ideal gas mixture......Page 33
2.3.3 Entropy of mixing......Page 35
2.3.5 Dilute ideal solution – Henry’s law......Page 37
2.3.6 Osmotic pressure......Page 39
2.3.7 Electrostatics and excess of osmotic pressure......Page 41
2.3.8 Reactive ideal mixture......Page 48
2.3.9 Unconditional stability of ideal solutions......Page 50
2.4.1 Regular solutions and the interaction between molecules......Page 52
2.4.2 Conditional stability of regular solutions......Page 53
Further Reading......Page 56
3 The Deformable Porous Solid......Page 57
3.1.1 Deformation gradient and displacement......Page 58
3.1.2 Strain tensor......Page 59
3.2.1 The hypothesis of local contact forces......Page 61
3.2.2 The action–reaction law......Page 62
3.2.3 The Cauchy stress tensor......Page 63
3.2.4 Local mechanical equilibrium......Page 65
3.2.5 Symmetry of stress tensor......Page 66
3.3.2 Strain work in infinitesimal transformations......Page 67
3.4.1 Porosity and deformation......Page 68
3.4.2 Pore pressure and stress partition......Page 70
3.4.3 Free energy balance for the fluid-solid mixture......Page 71
3.4.4 Free energy balance for the porous solid......Page 72
3.4.5 Strain work and the effective stress ‘principle’......Page 73
Further Reading......Page 75
4.1.1 The linear poroelastic solid......Page 77
4.1.2 Microporoelasticity......Page 79
4.1.3 The nonlinear poroelastic solid......Page 84
4.2 Filling the Porous Solid......Page 87
4.2.2 Filling by a mixture containing gas bubbles - bubble pressure......Page 88
4.2.3 Undrained poroelasticity......Page 91
4.3.1 The linear thermoporoelastic solid......Page 94
4.3.2 The linear thermoporoelastic fluid-solid mixture......Page 95
4.4.1 The linear viscoelastic solid matrix......Page 96
4.4.2 The linear poroviscoelastic solid......Page 98
Further Reading......Page 99
5 Fluid Transport and Deformation......Page 101
5.1.2 Dissipation associated with transport......Page 102
5.1.3 Fick’s law......Page 105
5.1.4 Darcy’s law......Page 106
5.2 Coupling the Deformation and the Flow......Page 112
5.2.1 The Navier equation......Page 113
5.2.2 The diffusion equation......Page 114
5.3.1 Consolidation equation......Page 116
5.3.3 Any time solution......Page 119
5.3.4 Layer apparent creep......Page 120
Further Reading......Page 122
6 Surface Energy and Capillarity......Page 123
6.1.1 Origin of surface energy......Page 124
6.1.2 Basic approach to van der Waals forces......Page 125
6.1.3 Surface and interface energy......Page 127
6.1.4 Surface energy and cohesion......Page 129
6.1.5 Surface energy and surface stress......Page 130
6.1.6 Wettability, angle of contact and the Young–Dupré equation......Page 134
6.1.7 The Laplace equation......Page 137
6.1.8 Pore invasion and interface energy change......Page 138
6.1.9 Interface energy and adsorption......Page 141
6.1.10 The disjoining pressure......Page 145
6.2.1 Capillary pressure curve and interface energy......Page 148
6.2.2 Capillary rise......Page 149
6.2.3 Porosimetry......Page 151
6.2.4 Capillary hysteresis......Page 152
6.3.1 Relative permeability......Page 156
6.3.2 Injection......Page 157
Further Reading......Page 162
7 The Unsaturated Poroelastic Solid......Page 165
7.1.1 Interface energy and saturated poroelasticity......Page 166
7.1.2 Adsorption-induced deformation......Page 169
7.2.1 Lagrangian and Eulerian saturations......Page 170
7.2.2 Lagrangian saturation and free energy balance......Page 172
7.3.2 Unsaturated microporoelasticity......Page 175
7.3.3 Double porosity approach to the brittle fracture of liquid-infiltrated materials......Page 178
7.4.1 The nonlinear poroelastic solid in unsaturated conditions......Page 180
7.4.2 Accounting for interface stress effects upon deformation......Page 181
Further Reading......Page 182
8 Unconfined Phase Transition......Page 183
8.1.2 Chemical potential of a pure substance in any form......Page 184
8.1.3 Supersaturation......Page 187
8.1.4 Phase transition as an instability......Page 188
8.2.1 The Kelvin equation......Page 191
8.2.2 Effect of a solute......Page 194
8.3.1 The Thomson equation......Page 195
8.3.2 Salt crystallization – the Correns equation......Page 198
8.5 Surface Energy and Phase Transition......Page 201
8.5.1 Nucleation......Page 202
8.5.2 The precondensed liquid film, the disjoining pressure and the Gibbs adsorption isotherm......Page 206
8.5.3 The premelted liquid film and crystallization......Page 210
Further Reading......Page 212
9 Phase Transition in Porous Solids......Page 213
9.1.1 Liquid saturation, pore-entry radius distribution and phase transition......Page 214
9.1.2 Spherical stress state and stability of in-pore crystallization......Page 217
9.1.3 Intermolecular forces and in-pore phase transition......Page 220
9.2.1 Continuum approach to drying kinetics......Page 227
9.2.2 Drying asymptotics......Page 231
9.2.3 Drying mechanics......Page 237
9.3.1 Cryogenic swelling......Page 239
9.3.2 The hydraulic pressure......Page 241
9.3.3 Freezing and air voids......Page 245
9.3.4 Weathering and the crystallization of sea-salts......Page 251
Further Reading......Page 254
10 The Poroplastic Solid......Page 255
10.1.1 Plastic loading function and flow rule......Page 256
10.1.2 The principle of maximum plastic work......Page 258
10.1.3 Hardening plasticity......Page 262
10.1.4 Dilatancy......Page 266
10.1.5 Three-dimensional plasticity......Page 269
10.1.6 Limit analysis and stability of dry sandpiles......Page 270
10.2.1 The poroplastic solid......Page 272
10.2.2 Critical state and the Cam-clay model......Page 276
10.2.3 Capillary hardening and capillary collapse......Page 279
10.2.4 Stability of wet sandpiles......Page 282
10.3 From Material to Structure......Page 283
Further Reading......Page 285
11 By Way of Conclusion......Page 287
Further Reading......Page 291
Index......Page 293