Diffusion controlled processes among stationary reactive sinks: Effective medium approach

We formulate an effective medium theory for diffusion controlled processes among randomly distributed, stationary, reactive sinks. An implicit expression for the exact ‘‘self-energy’’ of the combined reactive density field and sinks is obtained in terms of the exact medium propagator. The lowest order truncation of this expression can be solved by numerical iteration for the self-energy. The rate and diffusion coefficients as a function of sink concentration are extracted from this self-energy. We also consider the next order truncation which explicitly introduces the pair correlation function of the sinks.