Velocity relaxation of a porous sphere immersed in a viscous incompressible fluid

Abstract

Velocity relaxation of a spherically symmetric polymer, immersed in a viscous incompressible fluid, and after a sudden small impulse or a sudden twist from a state of rest, is studied on the basis of the linearized Navier-Stokes equations with an added Darcy type drag term. Explicit expressions for the translational and rotational velocity relaxation functions of the polymer and for the flow pattern of the fluid are derived for a uniform permeable sphere. Surprisingly, it is found that the added mass vanishes. For fairly large values of the ratio of sphere radius to the screening length characterizing the permeability the velocity relaxation functions in the short and intermediate time regime differ significantly from that of a sphere with no-slip boundary condition. At long times both relaxation functions show universal power law behavior.