Kinetic description of diffusion-limited reactions in random catalytic media

TL;DR

This paper develops a kinetic formalism to describe diffusion-limited bimolecular reactions in media with randomly distributed catalytic sites, providing explicit formulas for reaction rates and reactant decay in various dimensions.

Contribution

It introduces a novel kinetic model for catalytic reactions with immobile, random catalysts, extending existing theories to include explicit rate expressions.

Findings

Derived explicit formulas for effective reaction rates.

Analyzed reactant concentration decay over time.

Applicable to various spatial dimensions.

Abstract

We study the kinetics of bimolecular, catalytically-activated reactions (CARs) in d-dimensions. The elementary reaction act between reactants takes place only when these meet in the vicinity of a catalytic site; such sites are assumed to be immobile and randomly distributed in space. For CARs we develop a kinetic formalism, based on Collins-Kimball-type ideas; within this formalism we obtain explicit expressions for the effective reaction rates and for the decay of the reactants' concentrations.