Slip and no-slip velocity boundary conditions at interface of porous, plain media

Abstract

The hydrodynamic boundary condition at the interface between a porous and a plain medium is examined by direct simulation of the two-dimensional flow field near the interface of a porous medium made of cylinders. The existing slip boundary condition, which contains a slip coefficient [alpha], and the noslip boundary condition, which contains an effective viscosity [mu]', are examined. The dependence of [alpha] on the direction of the flow (with respect to the interfacial plane), the porosity, the Reynolds number (based on the unit cell length and the Darcean velocity), the selection of the interfacial location, and the arrangement of the cylinders (structure) is examined in detail. The numerical results show that [alpha] is not only a function of the structure but also depends on the flow direction, the Reynolds number, the extent of the plain medium, and the nonuniformities in the arrangement of the surface particles. It is also shown that for an accurate prediction of the local velocity near the interface (inside the porous medium), [mu]' must vary within the porous medium. This shows that the Brinkman extension based on a uniform [mu]', and the associated screening distance, do not satisfactorily model the flow field in the porous medium.