A new and very general technique for simulating solid-uid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the uid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-ow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic uctuations in the uid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in the companion paper, extensive numerical tests of the method, for stationary ows, time-dependent ows, and nite Reynolds number ows, are reported.

We present a new method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation. The method is based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure. As an application of the method we have recomputed the free energy of the fcc hard-sphere solid at melting. Our results agree well with the single occupancy cell results of Hoover and Ree. The major source of error is the nature of the extrapolation procedure to the thermodynamic limit. We have also computed the free energy difference between hcp and fcc hard-sphere solids at densities close to melting. We find that this free energy difference is not significantly different from zero: −0.001<ΔF<0.002.

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

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The lattice-Boltzmann method has been refined to take account of near-contact interactions between spherical particles. First, we describe a comprehensive solution to the technical problems that arise when two discretized surfaces come into contact. Second, we describe how to incorporate lubrication forces and torques into lattice-Boltzmann simulations, and test our method by calculating the forces and torques between a spherical particle and a plane wall. Third, we describe an efficient update of the particle velocities, taking into account the possibility that some of the differential equations are stiff.