Wave-induced chaos in a continuously fed unstirred reactor

Abstract

The spatiotemporal evolution of a simple, cubic autocatalytic model for chemical feedback under conditions appropriate to a continuous-flow unstirred reactor (CFUR) is examined. It is found that, even under conditions for which all the species have equal diffusivities and for an initial uniform distribution of the reactant, complex dynamics can result from localised initiation with the autocatalyst. The complex dynamics are induced initially by the propagation of a constant-velocity constant-form reaction wave that traverses the reaction domain, leaving behind a temporally unstable steady state of the corresponding well stirred system. As the local concentrations evolve away from this residual unstable state, there is an effective local resetting of the chemical clockwork, allowing further wave events to be initiated, which then propagate into the ‘recovered’ region. The chaotic nature of this self-sustaining, spatiotemporal response is confirmed by the method of proper orthogonal decomposition and by illustrating extreme sensitivity to initial conditions.