Dispersion curves in the diffusional instability of reaction fronts

Merkin, J H and Kiss, I Z (2005) Dispersion curves in the diffusional instability of reaction fronts. Physical Review E, 72 (2). ISSN 1539-3755

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Abstract

A (linear) stability analysis of planar reaction fronts to transverse perturbations is considered for systems based on cubic autocatalysis and a model for the chlorite-tetrathionate reaction. Dispersion curves (plots of the growth rate sigma against a transverse wave-number k) are obtained. In both cases it is seen that there is a nonzero value D-0 of D (the ratio of the diffusion coefficients of autocatalyst and substrate) at which sigma(max), the maximum value of sigma for a given value of D, achieves its largest value, with sigma(max) being less for other values of D and becoming small as D decreases to zero. The existence of the optimum value D-0 for initiating a diffusional instability is confirmed, in the cubic autocatalysis case, by an asymptotic analysis for small wave numbers.

Item Type: Article
Additional Information: Article Number: 026219
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Istvan Kiss
Date Deposited: 06 Feb 2012 19:32
Last Modified: 07 Mar 2017 08:30
URI: http://sro.sussex.ac.uk/id/eprint/21127

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