Diffusion and mobility driven instabilities in a reaction-diffusion system: a review

Abstract

Interplay of reaction and diffusion in a chemical system may lead to many interesting selforganization phenomena like stationary pattern, waves, spirals and targets etc. in spatially extended nonlinear dynamical systems far from equilibrium. One may trace their origin to different instabilities. In this review we have presented a pedagogical exposition of two such instabilities relating to stationary pattern formation. The first one is the diffusion-driven instability, the Turing instability, arising from disparate diffusivities of two reacting components in a reaction-diffusion system under appropriate condition. The second one is the differential flow induced chemical instability which can be brought in by application of electric and magnetic fields. The analysis of instabilities and simulation of patterns have been carried out on chlorine dioxide-iodine-malonic acid reaction (CIDIMA), which has served as an experimental testing ground for various theories in the last two decades.