Enhancement of the Production Rate in Chemical Reactions with Thresholds

Abstract

In nonlinear chemical reactions with threshold properties, exceptionally large enhancements of the production rate in a chemical flow reactor may be achieved by external periodic forcing. A threshold may be represented by the turning point in a bistability curve or by a Hopf bifurcation between a focal steady state and a limit cycle. Since the production rate is equal to the (mathematical) product of the flow rate and the reaction yield, large production rate enhancements will be achieved at high flow rates with short pulses to lower flow rates if the product yield increases with decreasing flow rate into the reactor. Sinusoidal flow rate perturbations and perturbations using short pulses give equally large production rate enhancements over the free running reaction if the comparison is made at the same average flow rate. If the comparison is made for identical perturbation amplitudes, the pulse perturbations lead to larger production rate enhancements than the sinusoidal perturbations. An easy way to achieve unusually large production rate enhancements (∼100%) is to simply turn the flow rate periodically on and off in analogy to the bang-bang method. This is demonstrated experimentally in the minimal bromate oscillator using a subcritical Hopf bifurcation as a threshold and by corresponding NFT model calculations.