Preface |
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ix | |
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1 | (2) |
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2 Geometry of Porous Media |
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3 | (16) |
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2.1 Three-Dimensional Packing of Spheres |
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3 | (6) |
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9 | (6) |
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2.3 Minkowski Functionals |
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15 | (2) |
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2.4 Visualization of Porous Media |
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17 | (2) |
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18 | (1) |
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19 | (44) |
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3.1 Box-Counting Dimension |
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21 | (4) |
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25 | (2) |
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3.3 Measuring the Fractal Dimension with Log-Log Plots |
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27 | (1) |
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28 | (3) |
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31 | (14) |
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45 | (14) |
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59 | (4) |
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61 | (2) |
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63 | (22) |
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4.1 Statistical Description of Percolation Clusters |
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66 | (2) |
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4.2 Critical Exponents and Fractal Dimension of Clusters |
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68 | (4) |
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4.3 Renormalization Group Derivation of v on the Triangular Lattice |
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72 | (2) |
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74 | (1) |
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4.5 Directed Percolation* |
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75 | (5) |
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4.6 Transport Properties and Multifractality* |
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80 | (5) |
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83 | (2) |
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5 Laminar Flow in Channels and Pipes |
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85 | (14) |
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5.1 Laminar Flow in a Channel |
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85 | (4) |
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5.2 Laminar Flow in a Pipe |
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89 | (2) |
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91 | (8) |
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98 | (1) |
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6 The Hydrodynamic Equations |
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99 | (28) |
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6.1 The Continuity Equation |
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99 | (1) |
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6.2 Conservation of Momentum |
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100 | (5) |
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105 | (2) |
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6.4 The Navier-Stokes Equation |
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107 | (1) |
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108 | (2) |
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6.6 The Reynolds Number and Scaling |
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110 | (4) |
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6.7 Two Theorems Based on the Steady Euler Equation |
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114 | (2) |
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6.8 The Stream Function and Moffatt Eddies* |
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116 | (5) |
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6.9 Stokes Flow Past a Sphere* |
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121 | (6) |
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124 | (3) |
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127 | (30) |
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7.1 Derivation of Darcy's law |
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129 | (1) |
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7.2 Differential Form of Darcy's law |
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129 | (3) |
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7.3 Model Calculations for the Permeability |
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132 | (1) |
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132 | (4) |
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7.5 Kozeny Expression for k |
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136 | (6) |
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7.6 Katz-Thompson Model for Permeability* |
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142 | (5) |
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7.7 When the Porous Medium Is Rarified: The Brinkman Equation* |
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147 | (1) |
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7.8 When the Flow Is Rarified: The Klinkenberg Correction* |
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148 | (1) |
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149 | (8) |
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154 | (3) |
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157 | (30) |
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157 | (5) |
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8.2 The Central Limit Theorem |
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162 | (2) |
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8.3 Advection-Diffusion Equation |
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164 | (5) |
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169 | (5) |
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8.5 Geometric Dispersion* |
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174 | (6) |
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180 | (7) |
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185 | (2) |
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187 | (29) |
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9.1 Surface Tension Thermodynamics |
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188 | (3) |
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9.2 The Young-Laplace Law |
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191 | (2) |
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193 | (3) |
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196 | (8) |
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9.5 Bubble Flow in a Capillary |
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204 | (3) |
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9.6 Funicular Flow in a Capillary |
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207 | (9) |
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214 | (2) |
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10 The Hele-Shaw Cell and Linear Stability Analysis |
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216 | (17) |
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10.1 Viscous Fingering and Linear Stability |
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216 | (2) |
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10.2 Linear Stability Analysis |
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218 | (5) |
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10.3 Observations of Viscous Fingers* |
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223 | (3) |
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10.4 The Nonlinear Regime* |
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226 | (3) |
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10.5 Experiments on Viscous Finger Dynamics* |
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229 | (4) |
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232 | (1) |
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11 Displacement Patterns in Porous Media |
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233 | (31) |
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11.1 Flow in Porous Media Dominated by Capillary Forces |
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233 | (2) |
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11.2 Flow in Porous Media Dominated by Viscous Forces |
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235 | (3) |
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11.3 Crossover from Capillary to Viscous Behavior |
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238 | (2) |
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11.4 Displacement under the Effect of Gravity |
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240 | (4) |
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11.5 Steady State Multiphase Flow* |
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244 | (5) |
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11.6 Steady-State Flow in the Capillary Fiber Bundle Model* |
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249 | (9) |
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11.7 Mean Field Theory for Steady-State Immiscible Two-Phase Flow* |
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258 | (6) |
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263 | (1) |
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12 Continuum Descriptions of Multiphase Flow |
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264 | (26) |
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12.1 Generalizing the Darcy Law to Two-Phase Flow: The Continuum Limit* |
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271 | (1) |
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12.2 Relative Permeabilites |
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272 | (4) |
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12.3 Continuity Equations |
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276 | (5) |
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12.4 Euler Scaling Theory* |
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281 | (9) |
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289 | (1) |
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13 Particle Simulations of Multiphase Flows |
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290 | (39) |
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13.1 Random Walks and the Simulation of the Advection-Diffusion Equation |
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290 | (3) |
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13.2 Molecular Dynamics Simulations |
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293 | (5) |
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13.3 Lattice Gas Model for Hydrodynamics |
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298 | (14) |
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13.4 Lattice Boltzmann Models |
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312 | (17) |
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324 | (5) |
Appendix Porosity Distributions |
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329 | (5) |
References |
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334 | (10) |
Index |
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344 | |