Extinction cross section of an arbitrary body in a viscous incompressible fluid

When analyzing time-dependent Stokesian flow around an arbitrary body in terms of time-harmonic phasors, analytic techniques commonly used for frequency-domain scattering can be brought to bear. A common measure of the scattering response of a body is the extinction cross section. However, as the wave number for a Stokesian flow is necessarily complex, the usual interpretation of the extinction cross section is untenable for this problem. It is shown here that a detector-based interpretation of the extinction cross section is unambiguous and experimentally relevant. An almost exact formula is derived for the extinction cross section for flow around an arbitrary body. Computed values for the cross section are presented for a spherical body using two different boundary condition cases: pure stick (i.e., no slip) and pure slip.