DARCY-BRINKMAN FLOW WITH SOLID INCLUSIONS

Abstract

The slow viscous flow in a Darcy-Brinkman porous medium with solid inclusions is studied. The general separable solutions in spherical and cylindrical coordinates are applied to the flow over a sphere and a circular cylinder. The problem is governed by a parameter k representing the effect of the porous medium. As k approaches zero, the solutions approach the Stokes flow solution for the sphere, but singularly vanish for the cylinder, confirming the Stokes paradox. For large k, the influence of the sphere or cylinder is limited to its immediate surroundings. The pressure drop due to multiple inclusions is then predicted.

Keywords:

• Darcy-Brinkman
• Flow
• Porous media