Boundary conditions at fluid porous interfaces

We derive boundary conditions at the interface of a homogeneous and isotropic porous medium and an overlying fluid layer by averaging the generalized transport equations in the interfacial region and rewriting the obtained jump conditions at the effective sharp interface dividing the homogeneous fluid and porous layers, thus taking into account the thickness of the diffuse interface. We obtained jump boundary conditions in terms of geometrical parameters, namely the Brinkman penetration depth δ B , the ratio a = ∆/δ B of the thickness of the interfacial region to the Brinkman depth, and the location of the effective dividing interface. This is the first attempt to determine the appropriate location of the diving interface by matching the solutions to the one-domain and two-domain approaches. Jump boundary conditions reduce to the slip-transpiration-resistance model proposed by Lācis et al. [29], either in the thick interface limit (e a ≫ 1) or if the Darcy law is assumed to apply in the porous medium. In these limits, adequate choice of the dividing interface location enables to replace the slip condition by the continuity of the tangential velocity, yielding a simpler Dirichlet-transpiration-resistance model. Our formulation has the advantage that the effective coefficients depend explicitly on geometrical parameters that are easy to estimate in practice and, therefore, can be easily implemented. Numerical tests for parallel and non-parallel flows using the obtained boundary conditions or the generalized transport equations show excellent agreement. Our results can be easily extended to deal with 3D configurations and anisotropic porous media