STOKES FLOW PAST A TWO-LAYER HETEROGENEOUS POROUS SPHERE WITH THE EFFECT OF STRESS JUMP CONDITION: AN EXACT SOLUTION

摘要

A heterogeneous porous sphere containing two-layer porous medium with internal radius r_1 and external radius r_2 is considered, which is immersed in a uniform stream of the inflow velocity U. The internal porous region, the external porous region and the free fluid region are denoted by regions Ⅰ, Ⅱ and Ⅲ respectively. Darcy-Brinkman equations are adopted to describe the flow in region Ⅰ and Ⅱ, and Stokes equations are adopted to describe the flow in region Ⅲ. The continuity of the velocity components and stresses are taken at the interface between region Ⅰ and Ⅱ. The continuity of the velocity components and normal stress and tangential stress jump conditions are taken at the interface between region Ⅱ and Ⅲ. The exact flow and drag solutions are derived and verified in some limiting cases by comparing with the solutions derived in other researchers' works. In addition, it is found that both the permeability and the stress jump coefficient have significant effect on the drag.