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A boundary-driven reaction front

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Abstract

A model reaction scheme in which two species \(A\) and \(B\) react to form an inert product is considered, with the possible linear decay of \(A\) to a further inert prduct also included. The reaction between \(A\) and \(B\) is maintained by the input of \(A\) from the boundary which keeps \(A\) at a constant concentration. The cases when \(B\) is immobile or free to diffuse are treated. In the former case reaction fronts in \(B\) are seen to develop. Large time asymptotic solutions are derived which show that these fronts propagate across the reactor at rates proportional to \(t^{1/2}\) or \(\log t\) (\(t\) is a dimensionless time) depending on whether the extra decay step is included. A similar situation is seen when \(B\) can diffuse when the linear decay step is not present. However, when this extra step is included in the reaction scheme the reaction zone reaches only a finite distance fronm the boundary at large times.

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  1. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    J. H. Merkin

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  1. J. H. Merkin
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Correspondence to J. H. Merkin.

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Merkin, J.H. A boundary-driven reaction front. J Math Chem 51, 1056–1075 (2013). https://doi.org/10.1007/s10910-012-0137-0

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  • DOI: https://doi.org/10.1007/s10910-012-0137-0

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