Hydrodynamic transport coefficients of random dispersions of hard spheres

Abstract

Accurate values for the hydrodynamictransport properties of random dispersions of hard spheres have been determined by numerical simulation. The many‐body hydrodynamic interactions are calculated from a multipole‐moment expansion of the force density on the surface of the solid particles; the singular lubrication forces are included exactly for pairs of particles near contact. It has been possible to calculate the transport properties of small periodic systems, at all packing fractions, with uncertainties of less than 1%; but for larger systems we are limited computationally to lower order, and therefore less accurate, moment approximations to the induced force density. Nevertheless, since the higher‐order moment contributions are short range they are essentially independent of system size and we can use small system data to correct our results for larger systems. Numerical calculations show that this is a reliable and accurate procedure. The ensemble‐averaged mobility tensors are strongly dependent on system size, with deviations from the thermodynamic limit varying as N −1/3. We show that these deviations can be accounted for by a straightforward calculation based on the length of the unit cell and the suspensionviscosity and mobility. The remaining number dependencies are small. Problems involved in implementing this method for larger numbers of particles are considered, and alternative methods are discussed.