Creeping motions of a composite sphere in a concentric spherical cavity

An analytical study is presented for the quasisteady translation and steady rotation of a spherically symmetric composite particle composed of a solid core and a surrounding porous shell located at the center of a spherical cavity filled with an incompressible Newtonian fluid. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field of the system, and the hydrodynamic drag force and torque exerted by the fluid on the particle which is proportional to the translational and angular velocities, respectively, are obtained in closed forms. For a given geometry, the normalized wall-corrected translational and rotational mobilities of the particle decrease monotonically with a decrease in the permeability of its porous shell. The boundary effects of the cavity wall on the creeping motions of a composite sphere can be quite significant in appropriate situations. In the limiting cases, the analytical solutions describing the drag force and torque or mobilities for a composite sphere in the cavity reduce to those for a solid sphere and for a porous sphere.