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

The reaction rate is calculated for a cluster of perfectly absorbing, stati onary spherical sinks in a medium containing a mobile reactant. The diffusi ve interactions are accurately taken into account by employing the first-pa ssage technique. The configurations of the clusters include three spheres, four spheres, regular polygons, linear chains, squares, and finite cubic ar rays. For a given number of sinks, the reaction rate is decreased with incr easing 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 t hese "exact" data, the method of multipole expansions up to the dipole leve l, which is suitable for a finite system of many sinks, proved to be an exc ellent approximation. (C) 2001 American Institute of Physics.