Mobility matrix for arbitrary spherical particles in solution

We review the theory of the extended mobility matrix for N arbitrary, spherically symmetric particles immersed in an incompressible fluid. The two-particle mobility functions can be evaluated to any desired order in the inverse interparticle distance by means of an algebraic computer program implementing exact recursion relations. We correct some earlier published expressions and summarize known results for the scattering coefficients which characterize the hydrodynamic properties of the particles. Explicit results are presented for stick and slip hard spheres, for permeable spheres and for fluid droplets.