HYDRODYNAMIC RESPONSE OF A SPHERE IN A PLANE-WAVE FLOW

We consider a sphere immersed in an incompressible, viscous fluid described by the linearized Navier-Stokes equations. We assume that in the absence of the sphere a plane wave fluid motion is generated by a transverse plane-wave force density, oscillating in time and acting on the fluid, or alternatively, that a plane wave pressure field is generated by a longitudinal plane-wave force density. We study how the fluid velocity and pressure are modified by the presence of the freely moving sphere. The problem is of interest in the calculation of the effective properties of dilute suspensions of spherical particles. We calculate some of the relevant plane-wave matrix elements.