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

We obtain the many-body hydrodynamic friction and mobility matrices describ ing 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 m ultipole 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 dis cussed 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 il lustrate the method by performing Stokesian dynamics simulation of particle s near a hard wall. The simulations exhibit the rapid convergence of the mu ltipole truncation scheme including lubrication corrections. (C) 2000 Ameri can Institute of Physics. [S0021-9606(00)50104-4].