The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.
Travelling waves and a fruitful ‘time’ reparametrization in relativistic electrodynamics
