Research Of Stokes Flow Past A Layered Porous Sphere

The uniform Stokes flow(low Reynolds number) past a layered porous sphere has been studied. A heterogeneous porous sphere containing two-layer porous medium with internal radius b and external radius a is considered. Darcy-Brinkman equations are adopted to describe the flow in the porous region, and Stokes equations are adopted to describe the flow in the clear fluid region. The tangential stress jump conditions are taken at the interface between the porous and clear fluid region. The exact flow and drag solutions has been derived and verified by comparing with the solutions derived in other researchers‘ work in three limiting cases in which the sphere structure is a homogeneous porous sphere or a porous sphere with a solid core or a porous spherical shell with a concentric spherical cavity. It is found that our solutions are equivalent to the exiting solutions in these limiting cases. Some conclusions are obtained by discussing the drag on the sphere for different values of governing parameters. Both the permeability and the stress jump coefficient have significant effects on the drag. The drag increases as the average permeability of the whole porous region decreases, and decreases with the increase of stress jump coefficient. In addition, the drag on the porous is more affected by the parameters of the external porous medium. The drag becomes negative for some large stress jump coefficient. To keep a positive value of drag, the proper range of the stress jump coefficient can be obtained based on the solutions in this paper.With the support of the study above, the hydrodynamic permeability of the porous membranes built up by the spherical particles covered by two-layer heterogeneous porous medium has been studied. By introducing the porous layer, the change of the membrane's structure in the course of filtration of a liquid through the membrane can be simulated. The tangential stress jump conditions are taken at the porous/fluid interface either. The analytical solution of the hydrodynamic permeability has been derived by cell model and verified in two limiting cases in which the sphere structure becomes a completely porous particles in a cell or a solid sphere in a cell. It is found that the hydrodynamic permeability depends on the stress jump coefficient, particle volume fraction, the average permeability of the whole porous region and the the effective viscosity ratio.