Symmetry of a periodic array of particles and a viscous fluid flow in the stokes approximation

A suspension in which rigid spherical particles of the same radius form a periodic array is considered. A general solution of the Stokes equations periodic with respect to this array is obtained. With reference to a fluid flow through a fixed array and a shear flow with frozen-in particles it is shown that taking the array structure and the symmetry of the conditions on the particle surface into account leads to a considerable simplification of the problem and makes it possible to determine the velocity and pressure distributions over the fluid.