The influence of periodic pressure variations on chain reactions

Abstract

A theoretical study is made of the effect of simultaneous periodic variations in temperature and volume for chain reactions, with particular emphasis on the frequency dependence of the perturbation. If a kinetic mechanism is postulated for any given gas-phase chain reaction, a system of first order differential equations describing the time rate of change of the various species can be obtained by applying the Mass Action Law. This system of differential equations can be written to include explicitly the simultaneous temperature-volume perturbation. Such a system of equations is generally nonlinear and can be integrated usually only by numerical successive approximation techniques. If this is to be done with any rapidity, a high-speed computer is required. It is shown, however, that the extreme cases of very low and very high perturbation frequencies can be treated analytically with regard to average rate of formation of product species. Specific calculations are made for the low and high frequency cases for the HBr chain reaction. Numerical evaluation of the rate enhancement for the formation of HBr at intermediate frequencies is performed using an IBM-650 digital computer. A slow fall-off in the rate is predicted with increasing frequency. However, the high frequency rate is still significantly greater than the unperturbed rate.