Reaction fronts in an ionic autocatalytic system with an applied electric field

The effects of applying an electric field to an ionic autocatalytic reaction with a cubic rate law are discussed. The constant field strength approximation is made and the resulting equations for the model examined by first considering the corresponding travelling wave equations. These show ranges of field strength over which travelling waves do not exist, these ranges being dependent on whether D>1 or D<1, where D is the ratio of diffusion coefficients of autocatalyst and substrate. Numerical simulations of the full system are obtained and these show that, when travelling waves exist, these are formed as the long time behaviour of the system. When travelling waves do not exist, complete electrophoretic separation of the reacting ionic species results, forming separate fronts in autocatalyst and substrate, their direction of propagation depending on D. Comparisons with a related problem with a quadratic rate law are made and the implications for experiments based on the iodate-arsenous acid reaction assessed.