Mobilities of polydisperse hard spheres near a no-slip wall

We have derived an analytical formulation for far-field hydrodynamic interactions among unequal size hard spheres near a no-slip wall and have implemented the formulation in a Stokesian dynamics model to simulate a suspension of polydisperse particles in a semi-bounded domain. The formulation is based on the multipole expansion of the boundary integral of Stokes flow, and the mobility tensors are deduced from Fáxen's law together with Green's function for Stokes flow near a no-slip wall. Lubrication approximation is incorporated to account for the close-distance interactions between any two particles and also between the particles and the wall. The implementation is validated against previous formulations for equal size particles and against a boundary-element code for unequal size particles. The code can be used to simulate the Stokesian or Brownian interaction of unequal particles in presence of a no-slip wall. In the current study, we applied the Stokesian dynamics model to investigate the trajectories of two unequal hard spheres and their redistribution during sedimentation parallel to a wall. We further used it to demonstrate the cases of many-particle sedimentation toward or parallel to a wall.