- Needham, D.J. and Leach, J.A. and Merkin, J.H., The effects of a complexation reaction on travelling wave-fronts in a quadratic autocatalytic system,
Q. J. Mech. Appl. Math. (UK), vol. 58
pp. 577 - 99 [hbi022] .
(last updated on 2007/04/06)
A model which describes the effect that a complexation reaction can have on the propagation of reaction fronts in a quadratic autocatalytic system is considered. An initial-value problem is set up, which involves the (dimensionless) parameters K, the equilibrium constant for the complexation reaction, and σ, the initial concentration of the complexing agent. This initial-value problem is analysed, with global existence and uniqueness being established. Numerical integrations indicate the formation of permanent-form travelling waves at large times. The equations that govern the travelling waves in the model are treated in detail. It is determined that there is a minimum propagation speed υmin lying in the range υ0≡2/(1+σ)⩽υmin⩽2, with the value υ0 corresponding to the minimum speed derived from the linearization of the travelling wave equations. The existence of a curve C is established, which divides the (K,σ) parameter plane into two regions, one where υmin=υ0 and one where υmin> υ0 with waves propagating faster than their linearized speed in this region. The curve C is determined numerically together with the dependence of υmin on K and σ
initial value problems;integration;reaction kinetics theory;wave equations;wave propagation;