Relation between macroscopic conductance and microscopic structural parameters of stochastic networks with application to fluid transport in porous materials

Abstract

The effective medium approximation is used to relate explicitly the conductance of a macroscopic model stochastic network to the structural characteristics of its constituent microscopic elements. The expressions obtained are relevant to the description of thermal, electrical or fluid transport properties of microscopically non-homogeneous or composite solid materials. Here, they are applied to two regimes of fluid transport in porous media where conductance depends on the radius or on the cube of the radius representing diffusion in slit-like pores and dilute gas flow in cylindrical pores, respectively. The network permeability is obtained in the form of expansions with readily evaluated terms describing the effect of the breadth and shape of the pore radius distribution and of the connectivity of the network. The validity of these expansions is tested by comparison with results obtained from direct numerical solutions and is shown to be acceptable for most applications over a wide range of parameter values. As a result of this work, a deeper insight into the role of various microscopic structural features on macroscopic permeability is gained, and the task of predicting network permeability in specific cases is greatly simplified.