A viscoelastic fluid flow through mixing grids

Abstract

We study the asymtotic behaviour of a viscoelastic fluid in a porous medium obtained by removing from an open set small obstacles of size periodically distributed on a hyperplane H which intersects . We establish that the fluid behave differently depending on whether the size is greater than or smaller than a critical size . If , a convolution term appears in the limit problem. This corresponds to a long memory effect. If is smaller than , the fluid behaves as if there where no obstacles. If is greater than or is of the order of the period, the fluid adheres on the hyperplane H which plays a thin solid plate role and the fluid behaves separately on each side of this plate.