A simplified theoretical analysis of nonequilibrium effects in bimolecular gas phase reactions

Abstract

There can be significant differences between the rates of activated chemical reactions calculated as if the reactants and products were in states of mutual thermal equilibrium and the rates associated with concentration and species temperatures obtained from solutions of Boltzmann equations. The theory presented here is based on the assumption that the particle distribution functions can be represented by Boltzmann functions with time-dependent concentrations and species temperatures. This leads from the Boltzmann equations to a set of coupled nonlinear equations of change for the concentrations and temperatures. Solutions of these equations have been obtained and used to calculate the rates of reaction. Numerical results generated by this procedure are found to agree quite well with the outputs of Nanbu–Babovsky Monte Carlo simulations and with predictions based on quasistationary perturbative solutions of the Boltzmann equations.

Nonequilibrium Effects in a Bimolecular Chemical Reaction in a Dilute Gas

“…The results obtained in this paper have been confirmed by additional investigations [28] and [29]. The results (obtained in Minnesota University), based on the solution of the set of differential equations [28], permitted to get results even for sF as small as 0.01 and 0.001.…”

“…Recently, the results from Ref. [23] have been confirmed by a simple theoretical analysis [28] assuming that nonequilibrium effects are mainly resulting from a change of temperature in the Maxwell-Boltzmann velocity distribution function. For slow chemical reactions our analytical results from Ref.…”

“…This paper cited as Ref. [13] in the recent paper [28] has been prepared with a delay because of the unexpected death of Prof. J. Popielawski. …”

“…The results (obtained in Minnesota University), based on the solution of the set of differential equations [28], permitted to get results even for sF as small as 0.01 and 0.001. The last results fully confirmed our perturbation solution of the Boltzmann equation.…”

“…The authors of Ref. [28] were successful not only in the analysis of the role of neglecting of product concentration but also of the effect of neglecting of the reverse reaction. In the meantime Gorecki developed a phenomenological kinetic theory [29] in which this anthor showed that if sF → 0 the result for the Shizgal-Karplus temperature (see Eq.…”