Many-sphere hydrodynamic interactions

Abstract

A scheme for the evaluation of many-sphere hydrodynamic interactions including interactions with container walls is presented. For a system consisting of a suspension of N spherical particles in an unbounded incompressible viscous fluid general formulae for the many sphere mobility tensors were obtained with explicit expressions for three- and four-body contributions up to order R^–7 with R a typical interparticle distance. Explicit expressions were also obtained to order R^–n R₀^–m, n+m⩽ 3, for the three-body problem consisting of two suspended spheres at arbitrary positions within a spherical container of radius R₀. The influence of hydrodynamic interactions on transport properties, in particular their essential non-additivity and the influence of wall effects, is then discussed for self-diffusion and sedimentation.