Nonequilibrium effects in reactive systems; the effect of reaction products and the validity of the Chapman-Enskog method

Abstract

The rates of gas phase reactions can be calculated from the averages of the appropriate reactive cross sections with the velocity distribution functions of the reacting species. The reactive process, especially for reactions with activation energy, removes translationally energetic species and the velocity distribution functions depart from Maxwellian. The rate coefficients can differ from the equilibrium rate calculated with the Maxwell-Boltzmann distribution. The extent of the departure of the distribution function from Maxwellian can be estimated from solutions of the Boltzmann equation with appropriate choices for the elastic and reactive collision cross sections. If there is a good separation in the elastic and reactive collision time scales, a steady solution of the Boltzmann equation can be obtained with a procedure analogous to the Chapman-Enskog method for transport coefficients. In the present paper, the nonequilibrium effects for model reactive systems of the type A + A ⇌ B + B with and without the reverse reaction, and the reaction A + C → products are examined with both a Chapman-Enskog method along with an explicity time-dependent solution for the irreversible reaction A + A → B + B. The main objectives are to study the effect of the inclusion of the products with and without a reverse reaction as well as the range of validity of the Chapman-Enskog method.