Effective-medium theory of diffusion and chemical reactions in the presence of stationary overlapping sinks

We calculate the effective reaction rate constant k∗ and the effective diffusion constant D∗ for a system of independently distributed overlapping sinks as functions of the volume fraction φ of the sinks and the Sherwood number Sh. The Sherwood number characterises the strength of the reaction on the sink surfaces. We use the effective-medium theory, which has been presented in two previous papers. A comparison of these results with those we have previously obtained for non-overlapping imperfect sinks shows that in an interval [0, φmax,Sh] the calculated values of k∗ for overlapping sinks lie above those for the non-overlapping ones. On the other hand, since the total reactive surface at a given φ-value is larger for non-overlapping traps the effective reaction rate should also be larger in this case for all φ. This leads to the conclusion that the observed discrepancy stems from the approximation of the pair distribution function by the first term of its virial expansion, which we used in a previous paper.