Boundary conditions on hydrodynamics in simulations of dense suspensions

Abstract

The problem of the hydrodynamic boundary conditions on a simulation sample of a hydrodynamically dense colloid in Brownian dynamics is described and the necessity of a periodic boundary condition shown. The lattice sum for the leading-order pairwise hydrodynamic mobility tensor in periodic boundary conditions is analysed and shown to be associated with a quite unphysical model periodic system in which infinite suspending fluid velocities certainly occur. A more complicated boundary condition is introduced, in which a large spherically shaped array of cubic simulation sample copies is surrounded by a stationary spherical container with stick boundary condition. Analysis of this boundary condition shows that the resulting simulation sample is physically consistent with a properly defined positive definite hydrodynamic mobility tensor. Some effects of this definition of the simulation sample on simulation measurements are discussed.