Hydrodynamic interactions in a suspension of spherical particles

A long standing problem in numerical statistical mechanics has been the incorporation of the long range, many‐body hydrodynamic forces between particles in suspension. In this paper I describe a general computational method for calculating the forces and torques exerted by slowly moving spheres suspended in an incompressible fluid. In particular, the method correctly incorporates the effect of periodic boundary conditions on the hydrodynamic flow field. Results are presented for the friction and mobility matrices of small clusters of spheres as a function of the size of the periodic unit cell. An expression for the viscosity of a suspension of freely moving spheres is derived for a system with periodic boundary conditions, and numerical results are obtained for a suspension of spheres arranged in a simple‐cubic lattice.