Quasistatic hydrodynamic interactions in suspensions

We present a method to determine the grand mobility matrix for a system of N spherical particles, interacting hydrodynamically, with stick boundary conditions in an unbounded fluid. In the case of a system of two spherical particles we compare the results with those obtained from the reflection method. Finally we determine virial expansions for some diffusion coefficients, the translational sedimentation and the rotational sedimentation. We compare some of them with results available from the literature; other results are new, such as the second order virial coefficient of the short time rotational self-diffusion coefficient and the virial expansion of the rotational sedimentation. Our conclusion is that the method is generally applicable and offers a more systematic convergence than e.g. the reflection method. It leads to satisfactory results in the case of the two particle problem.