Bifurcation and stability analysis of micromixing effects in the chlorite—iodide reaction

Abstract

Experimental investigations of the chlorite—iodide reaction in a flow reactor have shown that its dynamical behavior can be very sensitive to mixing effects. This finding is of fundamental importance for the kinetic study of chemical oscillators since it implies that (finite-dimensional) perfectly mixed CSTR models may be insufficient for understanding their dynamical behavior. The simplest model which includes micromixing effects has the form of a nonlinear, partial, integro-differential equation (unsteady-state IEM model). Both parametric continuation and linear stability analysis results are reported for the steady-state IEM model using the Citri—Epstein mechanism with the kinetic constants employed by Fox and Villermaux (1990, Chem. Engng Sci. 45, 2857–2876). Numerical results, presented in the form of one- and two-parameter bifurcation diagrams using the mean residence time and the micromixture time as parameters, are in qualitative agreement with experimental results. The existence of periodic solutions after potential Hopf bifurcation points has been verified by transforming the unsteady-state IEM model into an infinite system of ordinary differential equations using a Laguerre polynomial expansion, and solving for a truncated set of expansion coefficients. Bifurcation analysis of the steady-state model is shown to be a useful tool for understanding the bifurcation behavior of the (infinite-dimensional) unsteady-state IEM model.