Role of size distributions on physical properties: Real size renormalization group

Abstract

This study looks at the role of particle size distributions in modifying the physical properties of inhomogeneous materials and develops an efficient technique for modeling these effects. This technique, which we call the real size renormalization group (RZRG), is a discretized version of the differential equivalent medium method, but it keeps track of the local densities of the smaller particles that can greatly influence the average properties. Using this method, we demonstrate the conditions under which the symmetric equivalent medium method gives very good results. We also apply the method to the electrical properties of sandstones. When only grain size distributions are given, the modeling is nonunique, as different pore size distributions can also be present. The RZRG models that fit the electrical data appear very similar to views of the rock samples and involve some inefficiency in the pore space distribution. The RZRG modeling is also able to determine the volume density and size distributions of sulphide particles in a sandstonelike environment using induced polarization data.