Modelling complex spatiotemporal behaviour in a Couette reactor

The development of spatiotemporal complexity in a chemical reaction in a 'C ouette reactor' is analysed through the Lengyel-Epstein model for the chlor ine dioxide-iodine-malonic acid (CDIMA) reaction which is characteristic of a system showing instability through supercritical Hopf bifurcation (as op posed to excitable systems). The Couette reactor comprises the annular gap between two concentric cylinders, the inner of which is rotated at a contro lled rate so as to establish Taylor-Couette flow, which dominates the trans port of molecules along the reactor. The 'boundary conditions' for the Coue tte reactor are set by well-stirred continuous flow reactors (CSTRs), which may be operated with different chemical inputs, so imposing background rea ctant concentrations along the Couette reactor. We examine this system anal ytically and numerically using a simplified representation of the Taylor-Co uette flow through an 'enhanced' reaction-diffusion model and restrict ours elves at this stage to operating conditions such that the steady states in the CSTRs are stable rather than oscillatory. Despite this, and the stabili sing effects of the boundary conditions thus imposed, complex spatiotempora l responses develop within the Couette reactor for a range of parameter val ues. We determine the variation in stability of the (spatially-dependent) s teady state concentration profiles and observe both saddle-node and Hopf bi furcations. The unsteady solutions that emerge from the Hopf bifurcations s how subsequent instabilities, possibly through a period-doubling-mixed-mode sequence to more complex structures.