On the two-sphere problem in an absorbing medium

Abstract

The paper is devoted to the two-sphere absorption problem. Namely, let two identical spheres be embedded into an unbounded matrix. Defects are created within the spheres at constant rate and are absorbed, with different absorption coefficients, by the matrix and the spheres. The steady-state defect distribution in the medium has to be found. This problem appears in a antural way when evaluating the effective absorption coefficient of a random dispersion of spheres. The herein proposed analytical solution employes the twin-expansions method and it is convenient for numerical implementation.