Motion of a permeable sphere at finite but small Reynolds numbers

The problem of the motion of a porous sphere in a Viscous fluid has three pertinent characteristic times: two for the external flow field of the viscous fluid and a third one for the internal flow field, inside the porous material. Because of this, a singular perturbation method must be used to obtain an analytical solution to the governing differential equations and for the determination of the flow field outside the porous sphere. Such a method is used here, and a solution is obtained, by using the so-called Saffman boundary condition at the interface between the porous sphere and the outside fluid. This solution is valid at finite but small Reynolds numbers. Thus, general expressions for the hydrodynamic force acting on the porous sphere and, hence, for the drag coefficient of the sphere are obtained. This general expression yields, as special cases, other known expressions for the drag coefficients, which were derived under more restrictive conditions, such as creeping flow, no-slip boundary conditions or zero permeability (solid) spheres. (C) 1998 American Institute of Physics.