Effect of Permeabilities on the Translational Motion of a Spherical Particle with Porous Core in a Concentric Spherical Cavity

An analytical investigation for the creeping motion of a spherically symmetric fluid-permeable composite sphere composed by a uniform porous core and a uniformly surrounded porous shell located at the center of a spherical cavity filled with an incompressible Newtonian fluid is presented here. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field of the system. The hydrodynamic drag force exerted by the fluid on the composite sphere and wall correction factors are also obtained here. For a given geometry and permeability ratio, the variations of the wall correction factor are discussed. However, Keh and Chou [3] studied translation and rotation of a spherical particle composed by solid core and a surrounding porous shell located at the center of a spherical cavity filled with a fluid but this paper is different from that paper as core is taken porous here in place of solid core taken by above author. Another interesting thing is that permeability of core and surface layer on the core are taken unequal here. For the purpose of verification of results, in particular for the limiting cases, the analytical solutions describing the drag force on a composite sphere in the spherical cavity are reduced here for a simple solid sphere and simple porous sphere and obtained the results similar to Keh and Chou [3].