A reduced-order model for porous flow through thin, structured materials

Abstract

Darcy's equations are frequently used as a coarse-grained numerical expedient for modeling multiphase flow through complex porous materials. In some applications, the porous material may be quite thin, allowing the possibility of further simplification of the equations.In this paper we derive a reduced-order shell finite-element model for flow through thin porous materials using an approach similar to that taken to derive the Reynolds' lubrication equation. We advance first a formulation that addresses generalized unstructured porous materials and then specialize the equations for certain structured cases. We also extend the model to account for multiphase, confined lubrication flow in an adjoining layer and gas transport within the pores. We apply the model to several problems of topical interest in micro-and nano-manufacturing processes.