Modeling reaction–diffusion pattern formation in the Couette flow reactor

Abstract

We report on a numerical and theoretical study of spatio–temporal pattern forming phenomena in a one-dimensional reaction–diffusion system with equal diffusion coefficients. When imposing a concentration gradient through the system, this model mimics the sustained stationary and periodically oscillating ‘‘front structures’’ observed in a recent experiment conducted in the Couette flow reactor. Conditions are also found under which oscillations of the nontrivial spatial patterns become chaotic. Singular perturbation techniques are used to study the existence and the linear stability of single-front and multi-front patterns. A nonlinear analysis of bifurcating patterns is carried out using a center manifold/normal form approach. The theoretical predictions of the normal form calculations are found in quantitative agreement with direct simulations of the Hopf bifurcation from steady to oscillating front patterns. The remarkable feature of these sustained spatio–temporal phenomena is the fact that they organize due to the interaction of the diffusion process with a chemical reaction which itself would proceed in a stationary manner if diffusion was negligible. This study clearly demonstrates that complex spatio–temporal patterns do not necessarily result from the coupling of oscillators or nonlinear transport.