Time-dependent, diffusion-controlled reactions: The influence of boundaries

A configurational averaging procedure is presented for the analysis of diffusion-controlled reactions in a medium containing a hard-sphere distribution of spherical sinks. The hierarchy of equations produced from the averaging procedure is truncated assuming low concentration of sinks. The method is shown to reproduce previous results for the decay of an initially uniform distribution of reactant in an unbounded medium and is subsequently applied to determine the reactant flux on the boundary of a semiinfinite domain. In the latter problem, the boundary has a significant effect which cannot be accounted for by the usual rate coefficient.