Abstract.
A probability density function (pdf) formulation is applied to a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase in a batch. This system is described by a stochastic differential equation with multiplicative noise. Both linear and nonlinear kinetic rate laws are considered. An effective rate constant for the mean field approximation describing the change in mean concentration with time is derived. The effective rate constant decreases with increasing time eventually approaching zero as the system approaches equilibrium. This behavior suggests that a possible explanation for the observed discrepancy between laboratory measured rate constants on uniform grain sizes and field measurements may in part be caused by the heterogeneous distribution of grain sizes in natural systems.
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This work was supported in part by the US Department of Energy under the DOE/BES Program in the Applied Mathematical Sciences, Contract KC-07-01-01, and the Environmental Management Science Program, Office of Biological and Environmental Research. This work made use of shared facilities supported by SAHRA (Sustainability of Semi-Arid Hydrology and Riparian Areas) under the STC Program of the National Science Foundation under agreement EAR-9876800. Los Alamos National Laboratory is operated by the University of California for the US Department of Energy under contact W-7405-ENG-36.
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Lichtner, P., Tartakovsky, D. Stochastic analysis of effective rate constant for heterogeneous reactions. Stochastic Environmental Research and Risk Assessment 17, 419–429 (2003). https://doi.org/10.1007/s00477-003-0163-3
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DOI: https://doi.org/10.1007/s00477-003-0163-3