Viscous flow past a spherical void in porous media: Effect of stress jump boundary condition

The effect of the spherical void of characteristic size R-0 in porous media in an undisturbed uniform flow U-infinity is investigated analytically. The flow inside the void is governed by Stokes equation, and the flow in the porous region is governed by Brinkman equation. The stress jump boundary condition proposed by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer, 38, pp. 2636-2655, 1995) for the tangential stresses at the porous liquid interface along with the continuity of velocity components and normal stress is used. The flow field is computed by matching boundary conditions at the porous fluid interface, It is found that the effect of the void increases with the decrease of permeability. The effect of the stress jump coefficient and porosity on some of the physical quantities, such as volume flow coming inside the void, is analyzed.