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

Published online by Cambridge University Press:  26 April 2006

Anthony J. C. Ladd
Anthony J. C. Ladd
Affiliation:
Lawrence Livermoore National Laboratory, Livermore, CA 94550, USA
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 271 , 25 July 1994 , pp. 311 - 339
Copyright
© 1994 Cambridge University Press

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References

Alder, B. J. & Wainwright, T. E. 1970 Decay of the velocity autocorrelation function. Phys. Rev. A 1, 18.Google Scholar
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.Google Scholar
Bossis, G. & Brady, J. F. 1987 Self-diffusion of Brownian particles in concentrated suspensions under shear. J. Chem. Phys. 87, 5437.Google Scholar
Fornberg, B. 1991 Steady incompressible flow past a row of circular cylinders. J. Fluid Mech. 225, 625.Google Scholar
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.Google Scholar
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.Google Scholar
Hauge, E. H. & Martin-Löf, A. 1973 Fluctuating hydrodynamics and Brownian motion. J. Statist. Phys. 7, 259.Google Scholar
Hinch, E. J. 1975 Application of the Langevin equation to fluid suspensions. J. Fluid Mech. 72, 499.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Ladd, A. J. C. 1984 Equations of motion for non-equilibrium molecular dynamics simulations of viscous flow in molecular fluids. Mol. Phys. 53, 459.Google Scholar
Ladd, A. J. C. 1988 Hydrodynamic interactions in a suspension of spherical particles. J. Chem. Phys. 88, 5051.Google Scholar
Ladd, A. J. C. 1990 Hydrodynamic transport coefficients of random dispersions of hard spheres. J. Chem. Phys. 93, 3484.Google Scholar
Ladd, A. J. C. 1993a Dynamical simulations of sedimenting spheres. Phys. Fluids A 5, 299.Google Scholar
Ladd, A. J. C. 1993b Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation. Phys. Rev. Lett. 70, 1339.Google Scholar
Ladd, A. J. C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Phillips, R. J., Brady, J. F. & Bossis, G. 1988 Hydrodynamic transport properties of hard-sphere dispersions. II. Porous media. Phys. Fluids 31, 3473.Google Scholar
Sangani, A. S. & Acrivos, A. 1982 Slow flow past periodic arrays of cylinders with application to heat transfer. Intl J. Multiphase Flow 8, 193.Google Scholar
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.Google Scholar
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.Google Scholar
Zick, A. A. & Homsy, G. M. 1982 Stokes flow through periodic arrays of spheres. J. Fluid Mech. 115, 13.Google Scholar