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Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results

  • Anthony J. C. Ladd (a1)

A new and very general technique for simulating solid–fluid suspensions has been described in a previous paper (Part 1); the most important feature of the new method is that the computational cost scales linearly with the number of particles. In this paper (Part 2), extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.

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Alder, B. J. & Wainwright, T. E. 1970 Decay of the velocity autocorrelation function. Phys. Rev. A 1, 18.
Allen, M. P. & Tildesley, D. J. 1987 Computer Simulation of Liquids. Clarendon.
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245.
Bossis, G. & Brady, J. F. 1987 Self-diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys. 87, 5437.
Fornberg, B. 1991 Steady incompressible flow past a row of circular cylinders. J. Fluid Mech. 225, 625.
Frisch, U., D'Humières, D., Hasslacher, B., Lallemand, P., Pomeau, Y. & Rivet, J.-P. 1987 Lattice gas hydrodynamics in two and three dimensions. Complex Systems 1, 649.
Hansen, J. P. & McDonald, I. R. 1986 Theory of Simple Liquids. Academic.
Happel, J. & Brenner, H. 1986 Low-Reynolds Number Hydrodynamics. Martinus Nijhoff.
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317.
Hauge, E. H. & Martin-Löf, A. 1973 Fluctuating hydrodynamics and Brownian motion. J. Statist. Phys. 7, 259.
Hinch, E. J. 1975 Application of the Langevin equation to fluid suspensions. J. Fluid Mech. 72, 499.
Hoover, W. G., Evans, D. J., Hickman, R. B., Ladd, A. J. C., Ashurst, W. T. & Moran, B. 1980 Lennard–Jones triple-point bulk and shear viscosities. Green–Kubo theory, Hamiltonian mechanics, and nonequilibrium molecular dynamics. Phys. Rev. A 22, 1690.
Hughes, T. J. R., Lin, W. K. & Brookes, A. 1979 Finite-element analysis of incompressible viscous flows by the penalty-function formulation. J. Comput. Phys. 30, 1.
Kao, M. H., Yodh, A. G. & Pine, D. J. 1993 Observation of Brownian motion on the time scale of the hydrodynamic interaction. Phys. Rev. Lett. 70, 242.
Ladd, A. J. C. 1984 Equations of motion for non-equilibrium molecular dynamics simulations of viscous flow in molecular fluids. Mol. Phys. 53, 459.
Ladd, A. J. C. 1988 Hydrodynamic interactions in a suspension of spherical particles. J. Chem. Phys. 88, 5051.
Ladd, A. J. C. 1990 Hydrodynamic transport coefficients of random dispersions of hard spheres. J. Chem. Phys. 93, 3484.
Ladd, A. J. C. 1993a Dynamical simulations of sedimenting spheres. Phys. Fluids A 5, 299.
Ladd, A. J. C. 1993b Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation. Phys. Rev. Lett. 70, 1339.
Ladd, A. J. C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285.
Lahbabi, A. & Chang, H.-C. 1985 High Reynolds number flow through cubic arrays of spheres: Steady-state solution and transition to turbulence. Chem. Engng Sci. 40, 435.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Addison-Wesley.
Lebowitz, J. L., Percus, J. K. & Verlet, L. 1967 Ensemble dependence of fluctuations with application to machine computations. Phys. Rev. 153, 250.
Lovalenti, P. M. & Brady, J. F. 1993 The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561.
Phillips, R. J., Brady, J. F. & Bossis, G. 1988 Hydrodynamic transport properties of hard-sphere dispersions. II. Porous media. Phys. Fluids 31, 3473.
Sangani, A. S. & Acrivos, A. 1982 Slow flow past periodic arrays of cylinders with application to heat transfer. Intl J. Multiphase Flow 8, 193.
Tompson, A. F. B. 1983 LAMFLOW: Three dimensional, laminar, incompressible flow. Tech. Rep. WR-83-3. Department of Civil Engineering, Princeton University.
Weitz, D. A., Pine, D. J., Pusey, P. N. & Tough, R. J. A. 1989 Nondiffusive Brownian motion studied by Diffusing-Wave Spectroscopy. Phys. Rev. Lett. 63, 1747.
Zhu, J. X., Durian, D. J., Müller, J., Weitz, D. A. & Pine, D. J. 1992 Scaling of transient hydrodynamic interactions in concentrated suspensions. Phys. Rev. Lett. 68, 2559.
Zick, A. A. & Homsy, G. M. 1982 Stokes flow through periodic arrays of spheres. J. Fluid Mech. 115, 13.
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Journal of Fluid Mechanics
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  • EISSN: 1469-7645
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