Rate of diffusion-limited reactions in a cluster of spherical sinks

Abstract

The reaction rate is calculated for a cluster of perfectly absorbing, stationary spherical sinks in a medium containing a mobile reactant. The diffusive interactions are accurately taken into account by employing the first-passage technique. The configurations of the clusters include three spheres, four spheres, regular polygons, linear chains, squares, and finite cubic arrays. For a given number of sinks, the reaction rate is decreased with increasing the compactness of the structure due to the screening effect. For a specified configurations, the asymptotic expressions for the reaction rate varying with the number of sinks are confirmed. By comparing results with these “exact” data, the method of multipole expansions up to the dipole level, which is suitable for a finite system of many sinks, proved to be an excellent approximation.