Mobility-induced instability and pattern formation in a reaction-diffusion system

Ions undergoing a reaction-diffusion process are susceptible to electric field. We show that a constant external field may induce a kind of instability on the state stabilized by diffusion in a reaction-diffusion system giving rise to formation of pattern even when the diffusion coefficients of the reactants are equal. The origin of the pattern is due to the difference in mobilities of the two species and is thus markedly different from that of deformed Turing pattern in presence of the field. While this differential flow instability had been shown earlier to result in traveling waves, we realize in the context of stationary pattern formation in a typical reaction-diffusion-advective system. Our analysis is based on a numerical simulation of a generic model on a two-dimensional domain.