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 autocatalyticreaction with a quadratic rate law are considered, where thereacting species, A⁺ and B⁺, are present in a system which alsoincludes non-reacting species C^- and D⁺. The conditions areestablished under which the general terms which describe theelectric field effects in the reaction-diffusion equations canbe simplified to those used in previous studies, where theseeffects are modelled by linear advection terms. The resultingequations are then studied in detail by first obtaining conditionsfor the existence of travelling waves of permanent form. Thisdiscussion shows that _B, the ratio of the diffusion coefficientsof B⁺ and A⁺, is a critical parameter, with different formsof behaviour arising for _B < 1 and _B > 1. This analysisis augmented by obtaining solutions valid for large times andlarge values of (the dirnensionless applied field). Numericalsolutions of initial-value problems are obtained for a rangeof values of and _B, guided by and interpreted through the analysispreviously obtained. These numerical integrations show the formationof reaction fronts, with the possibility of greatly increasedreaction rates caused by the applied electric field, as wellas propagating electrophoretic fronts in B⁺ being formed incases where a reaction front is also initiated. There is alsothe possibility of separate electrophoretic fronts in A⁺ andB⁺ being formed, which become increasingly separated as timeincreases with the reaction being completely inhibited.