On Interface Conditions for a Thin Film Flow Past a Porous Medium
Guy Bayada, Michèle Chambat · SIAM Journal on Mathematical Analysis · 1995
This paper is concerned with the problem of finding the boundary conditions at the interface between a fluid flow in a porous medium and an adjacent narrow layer of free fluid flow in, for instance, a lubrication area, or cracks in a porous medium. It is a two-small-parameter problem, which can be rigorously studied using both asymptotic analysis and homogenization theory. The existence of a critical ratio between the characteristic length of the porous medium microtexture and the characteristic width of the gap is proved. Interface conditions are found to be the continuity of the pressure and of the normal velocity while the tangential velocity vanishes. The existence and uniqueness of the coupled limit problem is obtained.