A multiple scattering solution for the effective permittivity of a sphere mixture

Abstract

A recursive algorithm for calculating the exact solution of a random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a one-sphere T matrix. The scattering from two spheres is expressed in terms of two-sphere T matrices, which are related to the one-sphere T matrix. A recursive algorithm to deduce the (n+1)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N/sup 2/ algorithm rather than the normal N/sup 3/ algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>