Friction and mobility for colloidal spheres in Stokes flow near a boundary: The multipole method and applications

Abstract

We obtain the many-body hydrodynamic friction and mobility matrices describing the motion in a fluid of N hard-spheres with stick boundary conditions in the presence of a planar hard wall or free surface using (1) a multipole expansion of the hydrodynamic force densities induced on the spheres and (2) an image representation to account for the fluid boundary. The coupled multipole equations may be truncated at any order to give positive definite approximations to the exact friction and mobility matrices. An extension of the Bossis–Brady lubrication correction to the friction matrix is also discussed and included. The resulting method for computing the mobility matrix may be used for the Stokesian or Brownian dynamics simulation of N spheres subject to interparticle and external forces and imposed shear flow. We illustrate the method by performing Stokesian dynamics simulation of particles near a hard wall. The simulations exhibit the rapid convergence of the multipole truncation scheme including lubrication corrections.