A viscoelastic fluid flow through mixing grids

We study the asymptotic behaviour of a viscoelastic fluid in a porous medium Ω ε, (ε> 0) obtained by removing from an open set Ω some small obstacles (TVε) I<V<n(ε) of size aε periodically distributed on a hyperplane H which intersects Ω. We establish that the fluid behaves differently depending on whether the size aε is greater than or smaller than a critical size cε. If oε = cε a convolution term appears in the limit problem. This corresponds to a long memory effect. If aε is smaller than cε, the fluid behaves as if there where no obstacles. lf aε is greater than cε 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.