Stirring Effects and Phase-Dependent Inhomogeneity in Chemical Oscillations:  The Belousov−Zhabotinsky Reaction in a CSTR

The imperfect mixing of reactants in a continuously fed stirred tank reactor generates inhomogeneous perturbations that are responsible for stirring and mixing effects. Using a cellular mixing model and a kinetic model of the Belousov−Zhabotinsky reaction, we studied the statistical properties and dynamical consequences of the reactor inhomogeneities during limit cycle oscillations. Our key resultthe time-dependent probability distributiondepends dramatically on oscillation phase: it is sharply peaked during the slow phase and broadens during the rapid phase of oscillation, where reaction is fast compared to mixing, and inhomogeneities and fluctuations are prominent. Observables are obtained from the probability distribution by appropriate averaging. We studied the stirring dependence of fluctuations and of the average oscillation amplitude and period, as well as the variance of these oscillation attributes.