Effective transport properties of disordered, multi-phase composites: Application of real-space renormalization group theory

Abstract

Real-space renormalization group theory (RSRG) provides a powerful tool for the estimation of effective transport coefficients of disordered, two- and three-phase composites on the basis of the intraphase transport coefficients. In this paper, we present methods for estimating effective transport coefficients of space-filling composites modelled by square, hexagonal and cubic tessellations. These methods are particularly useful for composites whose phases differ from each other in their individual transport coefficients by two or more orders of magnitude and whose effective transport properties are predominantly influenced by the connectedness of the phases. Problems of interest could include evaluation of effective diffusion coefficients of small molecules in incompatible polymer blends, effective thermal conductivities of porous media, effective electrical conductivities of metal-filled polymers, and effective elastic moduli of disordered composites.