MICROMECHANICAL ESTIMATES FOR THE EFFECTIVE PERMEABILITY OF 2D POROUS MATERIALS WITH ARBITRARILY SHAPED PORES

Abstract

The present work aims to determine the effective permeability of two-dimensional (2D) porous materials consisting of an isotropic permeable solid matrix in which arbitrarily shaped pores are embedded. The interfaces between the solid phase and pores are characterized by the Beavers-Joseph-Saffman conditions. To achieve the objective, by combining the complex variable method with the conformal mapping technique, we first solve the fundamental coupled Darcy-Stokes problem concerning the fluid flow in an infinite permeable solid containing a pore of arbitrary shape and undergoing a remote uniform pressure gradient. Next, with the help of this solution, each fluid-filled pore is replaced with an equivalent permeable inclusion whose permeability is determined. Finally, the dilute distribution, Mori-Tanaka, and differential schemes of micromechanics are applied to obtain estimates for the effective permeability of 2D composites with pores of different shapes. These estimates are compared with the relevant numerical results provided by the finite element method (FEM) and the boundary element method (BEM). In particular, the dependence of the effective permeability on the pore shapes is discussed.