The effects of a complexing agent on travelling waves in autocatalytic systems with applied electric fields

The effects of electric fields on the reaction fronts that arise in a system governed by an autocatalytic reaction and a complexation reaction between the autocatalyst and a complexing agent are considered. The complexation reaction is assumed to be fast relative to the autocatalytic reaction and the equations for this limit are derived. The corresponding travelling waves are discussed, the case of quadratic autocatalysis being treated in detail. The existence of minimum speed waves is examined, being dependent on the ratio of diffusion coefficients D, the concentration S-0 and equilibrium constant K of the complexation reaction as well as the electric field strength E. It is seen that, for some parameter values, minimum speed waves have negative autocatalayst concentrations, and waves which have the lowest speed consistent with non-negative concentrations are also obtained. Numerical integrations of the initial-value problem are performed for representative parameter values. These show the development of the appropriate travelling wave (when it exists) as the large time behaviour of the system, and, in cases where no travelling wave exists, the numerical integrations show the electrophoretic separation of substrate and autocatalyst.