Spatio-temporal structures in a differential flow reactor with cubic autocatalator kinetics

A model of a differential-flow reactor with Gray-Scott kinetics is consider ed in which the reactant is immobilised while the autocatalyst is allowed t o flow (with uniform velocity) and to diffuse. A linear stability analysis shows that there is a critical flow rate above which the spatially uniform stationary state is convectively unstable. A weakly nonlinear analysis (clo se to criticality) results in a complex Ginzburg-Landau equation (CGLE) whi ch governs the envelope amplitude of the packet of differential-flow-induce d waves being the first derivation of such a modulation equation for such a problem. The analysis of the CGLE shows that this bifurcation is supercrit ical with proparating wave packets developing for flow rates above the crit ical value and identifies a region of parameter space close to the Hopf bif urcation in the kinetic scheme where more complex propagating wave structur es can arise. The theoretical predictions are confirmed by numerical integr ations of the initial-value problem which also give results for flow rates well in excess of those amenable to analysis. (C) 1998 Elsevier Science B.V .