Boundary conditions for darcy's flow through porous media

Abstract

A novel formulation for the boundary conditions to be applied at a porous surface is proposed. Interfaces between porous and clear media and porous and solid media are considered. The well known Beavers & Joseph boundary condition is applicable for interfaces between porous and clear media. An equivalent boundary condition is obtained for interfaces between porous and impermeable media, namely, v · n = √(κ)∇ t · v 1 where v is the velocity field inside the porous medium, n denotes a unit vector normal to the interface pointing towards the porous medium, κ stands for the permeability and the subscript t refers to components tangential to the interface. A sample problem is solved for the flow fields exterior to a porous spherical particle and interior to it, assuming that the particle has a rigid concentric spherical core and that the submerging flow field is Newtonian. Stokesian and uniform at infinity. Both Brinkman's equation and Darcy's law are utilized to obtain general forms of the velocity and pressure fields. Comparison of the two solutions yields the desired boundary conditions applicable to the Darcy problem.