ON THE EFFECTIVE EQUATIONS OF A VISCOUS INCOMPRESSIBLE FLUID-FLOW THROUGH A FILTER OF FINITE THICKNESS

We consider an incompressible and nonstationary fluid flow, governed b y a given pressure drop, in a domain that contains a filter of finite thickness. The filter consists of a big number of tiny, axially symmet ric tubes with nonconstant sections. We prove the global existence for the epsilon-problem and find out the effective behavior of the veloci ty and the pressure fields. The effective velocity in the filter part is a constant vector in the axial direction, and the effective pressur e obeys the so-called fourth-power law. In the other parts of Omega, t he effective flow is determined through the stabilization constants of boundary layers. We prove Saint-Venant's principle and use those boun dary layers to prove the convergence as epsilon --> 0. (C) 1998 John W iley & Sons, inc.