Dispersion curves in the diffusional instability of reaction fronts

This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available. Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A ͑linear͒ 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 ␴ against a transverse wave-number k͒ 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 substrate͒ at which ␴ max , the maximum value of ␴ for a given value of D, achieves its largest value, with ␴ 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.