The effects of an electric field on an autocatalytic ionic reaction in a system with high ionic strength

The effects of an applied electric field on an ionic autocatalytic reaction with a quadratic rate law are considered, where the reacting species, A(+) and B+, are present in a system which also includes non-reacting species C- and D+. The conditions are established under which the general terms which describe the electric field effects in the reaction-diffusion equations can be simplified to those used in previous studies, where these effects are modelled by linear advection terms. The resulting equations are then studied in detail by first obtaining conditions for the existence of travelling waves of permanent form. This discussion shows that delta(B), the ratio of the diffusion coefficients of B+ and A(+), is a critical parameter, with different forms of behaviour arising for delta(B) < 1 and delta(B) > 1. This analysis is augmented by obtaining solutions valid for large times and large values of phi (the dimensionless applied field). Numerical solutions of initial-value problems are obtained for a range of values of phi and delta(B), guided by and interpreted through the analysis previously obtained. These numerical integrations show the formation of reaction fronts, with the possibility of greatly increased reaction rates caused by the applied electric field, as well as propagating electrophoretic fronts in B+ being formed in cases where a reaction front is also initiated. There is also the possibility of separate electrophoretic fronts in A(+) and B+ being formed, which become increasingly separated as time increases with the reaction being completely inhibited.