Diffusion-controlled reactions: Upper bounds on the effective rate constant

For a diffusion-controlled reaction in a static, reactive bed of nonoverlapping spherical traps, upper bounds on the effective reaction-rate constant have been obtained from a variational principle of Rubinstein and Torquato. The bounds remain finite for all volume fractions and arbitrary distributions of traps. We have obtained two kinds of bounds: one kind depends on the trap volume fraction only; the other includes, in addition, a nearest-neighbor-distance distribution of the traps. The bounds have been explicitly evaluated, in the latter case using the distribution corresponding to the hard-sphere equilibrium ensemble.