Arbitrary Stokes flow past a porous sphere
The flow fields interior to a porous sphere (where Darcy law holds) and exterior to it (Stokes flow region) are solved for the case when the velocity profile at a large distance is quite arbitrary. We use the velocity representation of Stokes equations which is due to the author, \textit{S. D. Nigam}, \textit{T. Amaranath} and \textit{R. Usha} [Q. J. Mech. Appl. Math. 45, No. 1, 47-56 (1992; Zbl 0754.76018)] together with the boundary conditions of \textit{I. P. Jones} [Proc. Cambridge philos. Soc. 73, 231-238 (1973; Zbl 0262.76061)]. The expressions for velocity fields (both interior and exterior) are given explicitly. The Faxen's laws for a porous sphere are derived and the limiting cases of rigid and shear-free (bubble) spheres are then deduced.
scientific article; zbMATH DE number 474574