Jump Conditions and Surface-Excess Quantities at a Fluid/Porous Interface: A Multi-scale Approach

We present a two-step up-scaling approach that allows to derive the jump conditions that must be imposed at the interface to account for transport phenomena in a fluid/porous domain. This general approach is first applied to a heat conduction problem to illustrate the main steps of the analysis. The heat flux and temperature jump conditions are related to surface-excess quantities, whose values depend on the interface location. Good agreement between the mesoscopic and macroscopic results are obtained, whatever the position of the interface inside the transition region. The approach is then applied to the problem of a laminar flow over a porous medium. The Beavers and Joseph relation is recovered, but only for a particular position of the interface.