The effects of a complexing agent on the transverse stability of cubic autocatalytic reaction fronts.
The effects of adding a complexing agent on the propagation and transverse stability of reaction fronts in a system based on cubic autocatalysis is considered. Adding the complexing agent is seen to reduce the propagation speed, alter the reaction dynamics and the concentration of the final reaction product of the propagating reaction fronts. A linear stability analysis (LSA) is considered to determine how the complexing agent affects the stability of planar reaction fronts through the numerical calculation of dispersion curves, plots of the growth rate sigma against wavenumber k. These dispersion curves show that adding the complexing agent can make the system unstable when it would otherwise be stable and, when the system is diffusionally unstable without the complexing agent, weaken this instability. An analysis valid for small values of k is undertaken, which confirms the results from the LSA and indicates how the critical value D(c) of the diffusion coefficient ratio D for the onset of an instability is changed by the addition of the complexing agent.
Merkin
J H
JH
Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom. amtjhm@maths.leeds.ac.uk