On transport in stochastic, heterogeneous fibrous domains

Abstract

Design of porous, fibrous structures is needed in a number of important technological applications. We focus on material parameters relevant to conductive substrates in advanced battery systems, though similar microstructures arise in many engineered and natural materials. The conductivities of stochastically-generated fiber networks are examined, with an emphasis on the variance in observed properties based on material variability, scale dependence of solution, and the occurrence and strength of singularities encountered in solution of the high contrast cases. We show that rigorous bounds on material behavior are too wide to be practically useful in these stochastic networks, and that material property variance is reasonably predicted by use of our stochastic finite element-fiber network approach. We further show that the boundary conditions employed in solution of Laplace’s equation in heterogeneous domains critically affects solution, and suggest guidelines for solution for a general network based on sharpness of interior angles. Degree of contrast in material phases’ properties are also discussed in how they affect the simplicity of the approach which can be taken in modeling real networks. We further assess the scale-dependence of our calculations. Finally, we demonstrate that the stochastic finite element/stochastic network solutions are robust, and are able to accurately predict both effective conductivity, and variance in conductivity, in these materials.