Diffusion and reversible reaction in a medium with penetrable sinks

A theory of diffusion controlled reactions with randomly distributed penetrable sinks is presented. The model considered includes a reversible reaction between a diffusing species, and a fixed reactive sink. For low reactivity, both steady state and initial value problems are discussed. The dependence on the sink concentration of the rate coefficients and the diffusion coefficients is found. By considering the limit of fast irreversible reaction, the connection is made with previous work.