Hydrodynamic scattering theory of flow about a sphere

We formulate the solution of the linear Navier-Strokes equations for time-dependent incompresible flow about a spherical particle in terms of a scattering formalism. The solution is written as an expansion in terms of incident and scattered waves. The amplitudes of the outgoing waves are related to a set of spherical force multipoles which themselves can be found from the amplitudes of the incident waves with the help of a resistance matrix. The resistance matrix is evaluated explicitly for hard spheres with mixed slip-stick boundary conditions. Transformation equations are given which relate the time-dependent solutions found here to previously studied solutions for the time-independent steady flow case.