Modelling complex spatiotemporal behaviour in a Couette reactor

Abstract

The development of spatiotemporal complexity in a chemical reaction in a ‘Couette reactor’ is analysed through the Lengyel–Epstein model for the chlorine dioxide–iodine–malonic acid (CDIMA) reaction which is characteristic of a system showing instability through supercritical Hopf bifurcation (as opposed to excitable systems). The Couette reactor comprises the annular gap between two concentric cylinders, the inner of which is rotated at a controlled rate so as to establish Taylor–Couette flow, which dominates the transport of molecules along the reactor. The ‘boundary conditions ’ for the Couette reactor are set by well-stirred continuous flow reactors (CSTRs), which may be operated with different chemical inputs, so imposing background reactant concentrations along the Couette reactor. We examine this system analytically and numerically using a simplified representation of the Taylor–Couette flow through an ‘enhanced’ reaction–diffusion model and restrict ourselves at this stage to operating conditions such that the steady states in the CSTRs are stable rather than oscillatory. Despite this, and the stabilising effects of the boundary conditions thus imposed, complex spatiotemporal responses develop within the Couette reactor for a range of parameter values. We determine the variation in stability of the (spatially-dependent) steady state concentration profiles and observe both saddle-node and Hopf bifurcations. The unsteady solutions that emerge from the Hopf bifurcations show subsequent instabilities, possibly through a period-doubling–mixed-mode sequence to more complex structures.