Diffusion of a sphere in homogeneous flow

We derive the diffusion equation for a sphere immersed in an incompressible fluid in homogeneous flow. The effect of the finite size of the sphere is taken into account. The generalized Green-Kubo formula and the Stokes-Einstein relation are derived. As special cases, we analyze the diffusion coefficient for the cases of the simple shear flow and the pure rotational flow in detail. The relation between nonanalytic dependence on the velocity gradient and on the frequency is discussed.