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The effect of the order of the autocatalysis on the transverse stability of reaction fronts

Merkin, J.H. (2008) The effect of the order of the autocatalysis on the transverse stability of reaction fronts. The Journal of Chemical Physics, 129 (3). Art. No. 034507. ISSN 0021-9606

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A linear stability analysis of planar reaction fronts to transverse perturbations is considered for a system based on an autocatalytic reaction of general order p. Dispersion curves, plots of the growth rate σ against a transverse wavenumber k, are obtained for a range of values of p and D, where D is the ratio of the diffusion coefficients of autocatalyst and substrate. A value D0 of D, dependent on p, is found at which σmax, the maximum value of σ in the unstable regime, is largest, with D0 increasing as p is increased. An asymptotic analysis for small wavenumbers is derived, which enables the region in the (p,D) parameter space for instability to be determined. An analysis for D small is undertaken, which leads to upper bounds on the wavenumber for a possible instability.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 American Institute of Physics. This is an author produced version of a paper published in The Journal of Chemical Physics. Uploaded in accordance with the publisher's self archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 28 Aug 2008 10:45
Last Modified: 04 Jun 2014 22:01
Published Version: http://dx.doi.org/10.1063/1.2953313
Status: Published
Publisher: American Institute of Physics
Identification Number: 10.1063/1.2953313
URI: http://eprints.whiterose.ac.uk/id/eprint/4468

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