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
Available under licence : See the attached licence file.
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.
|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|
|Publisher:||American Institute of Physics|