PROPAGATION FAILURE IN ARRAYS OF COUPLED BISTABLE CHEMICAL REACTORS

We consider a one-dimensional array of coupled stirred tank reactors. Each reactor operates with the bistable chlorite-iodide reaction. The reaction admits two stable steady states (A and B). At time zero, all reactors are at steady state A except the first reactor which is at steady state B. Provided the coupling (exchange rate) between each reactor is sufficiently large, a propagating wave joining A to B is initiated. We determine the speed of the front and show that it fails to propagate if the exchange rate is below a nonzero value. In addition, we investigate the time history of the front and identify three distinct stages. First, we note a small time regime dominated by a diffusion mechanism; second, we note a front propagating with almost constant speed; third, we note a boundary layer regime corresponding to the end of the front and the approach to the final uniform steady state. We explain all three stages by analyzing a simple model.