ON THE ABSORPTION PROBLEM FOR RANDOM DISPERSIONS

Abstract

This paper is devoted to the steady-state problem of absorption of a diffusing species (say, irradiation defects) in a random dispersion of spheres. The defects are created at a constant rate throughout the medium and are absorbed afterward, with different sink strengths, by the matrix and by the inclusions. One is to find the random diffusing species field and, in particular, the effective sink strength of the dispersion, having assumed the statistics of the spheres known. The problem is modeled by a Helmhotz equation with a random coefficient (the randomly fluctuating sink strength of the dispersion). The statistical solution of the latter is explicitly constructed, in a simple form, by means of the so-called factorial functional series, recently introduced by one of the authors. In particular, analytical formulas, correct to the order “square of sphere fraction,” are obtained for the effective sink strength of the dispersion and for the two-point correlation function of the diffusing species field. An effective numerical procedure, allowing to specify these quantities, is described and numerical results are finally presented and discussed.