Hydrodynamic interaction of two permeable spheres II: Velocity field and friction constants

By a method of reflections described in a previous article we construct the approximate velocity field produced by the motion of two permeable spheres through an incompressible fluid. The permeability is described by the Debye-Bueche equations. We consider contributions to the velocity field from seven reflections. From the velocity field we evaluate the forces and torques acting on the spheres. Expressions for the force are given through order 1/l7 and for the torque through order 1/l6, where l is the separation of the two spheres.