Abstract
We study hydrodynamic interactions in suspensions with periodic boundary conditions with the purpose of performing computer simulations with many particles per unit cell. The use of periodic boundary conditions minimizes surface effects. The formulation of the problem is complicated due to the long range nature of the hydrodynamic interactions. We show how macroscopic considerations may be used to arrive at a periodic solution of the flow equations. We derive expressions for the mobility tensors of freely moving particles, as well as for the friction tensor of a rigid array. Finally we discuss the high frequency effective viscosity of suspensions with periodic boundary conditions.
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