Slow viscous flow about a permeable circular cylinder

Abstract

Slow steady two-dimensional motion of a viscous incompressible fluid about a porous circular cylinder is considered, using Darcy law for the flow in the porous region and Jones conditions on the contour of the cylinder. The problem is formulated in terms of Stokes stream function and velocity, and pressure fields of the modified flow in the presence of porous cylindrical boundary are obtained explicitly. lt is observed that the Stokes paradox exists even in this case. Several other illustrative examples are presented to justify the usefulness of the method. It is found that the potential (point) singularities in the presence of a cylinder produce uniform flow at large distances, its strength being independent of porosity. However, the Stokes singularities (such as Stokeslet etc.) produce uniform flow at infinity, and its strength depends on the porosity as well as on the location of those singularities in the presence of the cylinder. The known results in two-dimensional Stokes flow are deduced as special cases from our result.