On the effective equations of a viscous incompressible fluid flow through a filter of finite thickness

Abstract

We consider an incompressible and nonstationary fluid flow, governed by a given pressure drop, in a domain that contains a filter of finite thickness. The filter consists of a big number of tiny, axially symmetric tubes with nonconstant sections. We prove the global existence for the ε-problem and find out the effective behavior of the velocity and the pressure fields. The effective velocity in the filter part is a constant vector in the axial direction, and the effective pressure obeys the so-called fourth-power law. In the other parts of Ω, the effective flow is determined through the stabilization constants of boundary layers. We prove Saint-Venant's principle and use those boundary layers to prove the convergence as ε → 0. © 1998 John Wiley & Sons, Inc.