MOMENTUM-TRANSFER AT THE BOUNDARY BETWEEN A POROUS-MEDIUM AND A HOMOGENEOUS FLUID .1. THEORETICAL DEVELOPMENT

The momentum transfer condition that applies at the boundary between a porous medium and a homogeneous fluid is developed as a jump condition based on the non-local form of the volume averaged momentum equation. Outside the boundary region this non-local form reduces to the classic transport equations, i.e. Darcy's law and Stokes' equations. The structure of the theory is comparable to that used to develop jump conditions at phase interfaces, thus experimental measurements are required to determine the coefficient that appears in the jump condition. The development presented in this work differs from previous studies in that the jump condition is constructed to join Darcy's law with the Brinkman correction to Stokes' equations. This approach produces a jump in the stress but not in the velocity, and this has important consequences for heat transfer processes since it allows the convective transport to be continuous at the boundary between a porous medium and a homogeneous fluid.