Rate of diffusion-controlled reactions in a random array of monopole sinks

We study the rate of diffusion-controlled reactions in a random array of stationary spherical sinks. We simplify the system to a monopole model and show that different theories proposed in the literature lead to different results for the first few terms in the density expansion of the rate coefficient. We derive a new expression for the rate coefficient valid to terms linear in the volume fraction occupied by sinks and analyze the shortcomings of the earlier theories.