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

J. Blawzdziewicz, G. Szamel, H. Van Beijeren

Research output: Contribution to journalArticlepeer-review

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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.

Original languageEnglish
Pages (from-to)7967-7971
Number of pages5
JournalThe Journal of Chemical Physics
Issue number12
StatePublished - 1991


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