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Index

adhesion force, 35 chemical potential, 303 adhesion parameter, 76 coalescence, 351 advancing contact angle, 216 coexistence, 150 analytical solution, 58, 108, 311, 317 coflow, 117 apparent contact angle, 217 cohesion force, 73 artificial gradient, 302 color-gradient model, 7 Atwood number, 207, 208 compressibility, 77, 93, 207, 208 axisymmetric boundary condition, 258, 263 compressibility effect, 310 axisymmetric model, 334, 345 contact angle, 34, 78, 80, 82, 114, 154, 210 axisymmetric multiphase LBM, 255 contact angle hysteresis, 215 axisymmetric two-phase N-S equation, 339 contact line, 216 contact point, 216 BD (biased difference), 298, 302 continuity equation, 100, 143, 254 BGK (Bhatnagar-Gross-Krook), 2, 3, 72, 274 corresponding states, 26 biased derivative, 303 critical temperature, 22 body force, 42 curvature-induced pressure, 151 Bond number, 13, 38 cylindrical coordinates, 335, 338 bounce-back, 35, 39, 103, 155, 158, 206, 211, 258, 299, 311, 354 D2Q7, 4 boundary condition, 33, 35, 38, 39, 47, 59, 83, 87, D2Q9, 4 89, 91, 95, 112, 117, 151, 154, 175, 206, 207, D2Q9 velocity model, 140 211, 215, 258, 260, 299, 314, 317, 348, D3Q15, 4, 167 354 D3Q19, 4 breakthrough, 118 Darcy velocity, 13 bubble rise, 279, 281, 353 density derivatives, 143 bubble wake, 286 density shift, 357 bulk free-energy density, 137 diffuse-interface method, 54 directional derivative, 298, 341 C-S EOS, 34, 36 discrete velocity, 3, 255 Cahn-Hilliard equation, 173, 196, 253, 255, 291 discrete velocity models, 4 capillary filling, 111, 112 displacement, 83–85, 87, 91 capillary fingering, 118 dissolved density, 76, 78 , 12, 118 distribution function, 3 capillary pressure, 84, 111 drainage, 111 capillary rise, 36, 213 drop impacting, 253 Carnahan-Starling (C-S) EOS, 26, 27, 198, 253 droplet collision, 175, 265 Cartesian mesh, 19, 258, 277 droplet splashing, 299, 342 Cellular Automata, 2 dummy index, 15 central difference (CD), 298, 302 dummy variable, 15 central difference scheme, 156 Central Processing Unit (CPU), 6 COPYRIGHTED MATERIALEDF (Equilibrium Distribution CFD (computational fluid dynamics), 6 Function), 335 CFL (Courant-Friedrichs-Lewy) number, 12 chain rule, 146 effective mass, 73 Chapman-Enskog, 199 Einstein summation, 14 Chapman-Enskog expansion, 99, 143, 170, 288, ellipsoidal droplet, 219, 259 338 EOS (Equation of State), 19, 21, 152

Multiphase Lattice Boltzmann Methods: Theory and Application, First Edition. Haibo Huang, Michael C. Sukop and Xi-Yun Lu. © 2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd. Companion Website: www.wiley.com/go/huang/boltzmann

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372 Index

equilibrium distribution function, 3, 138, 168, 255, isotropic discretization, 301, 334, 341 302, 336, 347 isotropy, 110 equilibrium momentum tensor, 147 equilibrium state, 20 kinematic viscosity, 3, 72, 102, 197, 281, equilibrium stress tensor, 148, 149 299 equilibrium velocity, 20 kinetic energy, 176 Euler equation, 74, 101, 147 Kronecker delta, 15 exact difference method, 41, 44 Eötvös number, 281 l’Hôpital’s rule, 258 Lamb’s natural resonance frequency, 220 FE (free energy), 8 Laplace law, 77, 83, 84, 95, 110, 155, 203, 258, filter technique, 279 282, 306, 307 first-order Euler scheme, 278 Laplacian, 267, 270 first-order partial derivative, 155 Lattice Boltzmann Equation, 72, 143 flow pattern, 120 lattice Gas model, 94 fluid-fluid cohesion, 72, 73 lattice pinning, 94 fluid-solid adhesion, 72, 73 lattice speed, 5 forcing term, 40, 41, 43, 44 lattice tensor, 15 fourth-order difference, 270 lattice unit, 11 free-energy, 137 layered two-phase flow, 204, 311, 317 free-energy-based multiphase LBM, 136 Lee-Lin model, 10, 280 front-tracking method, 6 level set method, 6

Galilean invariance, 146, 201, 313, 314 main fluid density, 78 Geometric scheme, 215 mass conservation, 260, 289, 356 ghost cells, 215 mass correction, 278 gravity, 38, 207 mass correction technique, 334, 357 gravity acceleration, 214 Maxwell Construction, 24, 49, 150, 175, 295 grid-independence study, 12 mechanical stability condition, 49, 50 mixed direction derivative, 303 H theorem, 6 mobility, 177, 197, 253, 292, 351 HCZ (He-Chen-Zhang) model, 9, 196 molecular interactions, 196 head-on collision, 176, 265, 352 momentum conservation, 289 head-on droplet collision, 342, 348 momentum equation, 171 high density ratio, 48 momentum flux tensor, 101 high-density-ratio model, 298 , 281 high-density-ratio two-phase flows, 167, 292 MRT (Multiple-Relaxation-Time), 92, 113, horizontal interface, 151 274 hydrodynamic pressure, 198, 255, 336 MRT collision model, 257 hysteresis, 215 multi-component, 81 hysteresis effect, 217 Multi-Component MultiPhase (MCMP), 7, 71 hysteresis window, 216, 218 multirange pseudopotential, 55 ideal wall, 218 natural boundary condition, 154 ideal-gas equation of state, 6 Navier-Stokes (N-S), 143 implementation, 347 no-slip wall, 35, 103, 117, 258, 354 implicit method, 301 non-equilibrium bounce-back, 89 Inamuro model, 167 non-equilibrium distribution function, 172, 177 incompressibility, 174, 282 non-Galilean invariance, 148, 149 incompressible flow, 174 non-ideal surfaces, 216 index function, 196, 198, 255, 256, 301 non-wetting fluid, 118 inter-particle force, 20, 21, 55, 57 numerical instability, 207 Inter-particle Force Model A, 31, 32 numerical stability, 342, 348 Inter-particle Force Model B, 31, 33 interface-tracking, 196 oblate ellipsoidal, 284 interface-tracking equation, 202 oblate ellipsoidal cap, 284 interfacial tension, 34, 95, 98, 99, 110, 168 , 266 intermolecular forcing term, 293, 338 oil-water flow, 12 intrinsic permeability, 118 order parameter, 168 invariant form, 26 oscillation, 219, 259 Trim Size: 170mm x 244mm Huang bindex.tex V3 - 05/08/2015 12:07 A.M. Page 373

Index 373

parallel flow, 39, 58, 85, 103 spike, 208 perturbation operator, 94 spurious currents, 8, 19, 94, 115, 151, 259, phase separation, 153, 202 309 Poisson equation, 167, 174 stable displacement, 118 porous medium, 91 stress form, 294, 337 post-stream, 294 supercritical state, 22, 28 post-streaming collision, 297 surface tension, 32, 33, 50, 52, 202, 277, 335 post-streaming step, 341 surface tension model, 302 potential form, 294, 337 pre-stream, 294 tangent plane, 216 pre-streaming collision, 297, 340 Taylor expansion, 31, 56, 74, 99, 346 pressure boundary condition, 84, 88 temporal derivative, 171 pressure tensor, 21, 29, 33, 137, 173 thermodynamic coexistence, 56 thermodynamic consistency, 29, 42, 48, 49, 57 random number, 153 thermodynamic instability, 151 Rayleigh–Taylor, 196 thermodynamic pressure, 197, 253 Rayleigh-Benard , 196 time step-independence study, 12 Rayleigh-Taylor instability, 196, 205, 209 toroidal shape, 176 receding contact angle, 216 typographical error, 148, 256, 276, 297, 303, 335, recoloring step, 94, 98 336, 338 Redlich-Kwong (R-K), 26, 27 relative permeabilities, 39, 40, 59 upwind finite difference scheme, 278 relative velocity, 176 relaxation time, 3, 12, 72, 97, 174, 197, 198, 255, 259, 263, 282, 342 van der Waals, 22, 25, 27 , 175, 207, 265, 299, 342 van der Waals EOS, 155, 169 RK model, 95 van der Waals fluid, 138 Rothman-Keller (RK), 7 viscosity term, 102 viscous dissipation, 219, 259 viscous fingering, 118 satellite droplets, 266 viscous stress tensor, 168, 172, 177, 293 satellite drops, 263 viscous tensor, 172 SC (Shan-Chen) model, 7, 18 volume-of-fluid, 6 second-order derivative, 155 secondary wake circulations, 286 Shan-Chen (SC) EOS, 29 wall density, 35, 73 shrinkage, 357 , 175, 208, 265, 299, 342 Single Component MultiPhase (SCMP), 7, 18 weighting coefficients, 3, 142, 197 sixth-order central difference, 270 wettability, 218 slip boundary condition, 258 wetting fluid, 118 slip wall, 299 wetting potential, 154 sound speed, 3, 72 source term, 3, 337, 339 Young-Laplace equation, 36, 79