Hydrodynamic interaction of two permeable spheres III: Mobility tensors

By assuming free rotation and the inverting previously obtained friction tensors, we obtain the mobility tensors describing the hydrodynamic interaction between two permeable spheres through order 1/l7, where l is the particle separation. We show that the dimensionless constants which appear in the mobilities serve as measures of the moments of the inverse permeabilities assumed for the spheres. We give analytic closed form expressions for these mobilities in the case of uniform or shell-like particles. Finally, we conclude that even a relatively low permeability reduces the hydrodynamic interaction of permeable spheres substantially below that to be expected for hard spheres of the same size.