Chapman–Enskog Method in Chemical Kinetics

Abstract

Nonequilibrium effects in gas-phase reactions associated with the perturbation of the Maxwell speed distribution by the reaction have been investigated by Prigogine and others using the Chapman–Enskog method in the lowest-order approximation. We have extended these calculations to the second order in the Burnett expansion of the perturbation in a series of Sonine polynomials. In the case of the reaction A + A→B + C in which the products B and C are removed and no inert gas is present, the appropriate elastic collision integrals have been evaluated for the model of rigid elastic spheres and the reactive collision integrals have been evaluated for two reaction cross sections, one corresponding to the simple collision theory of bimolecular reactions with activation energy ε* and the other to the “centrifugal barrier” theory of free-radical recombinations. For the activated reactions the detailed results show that the Chapman–Enskog method is useless when the reaction is fast (ε* / kT ≲ 5) because the perturbation method fails and is also useless when the reaction is slow because the Sonine polynomial expansion then diverges, as anticipated by Takayanagi. In free-radical reactions the Chapman–Enskog procedure is satisfactory and the nonequilibrium corrections to the reaction rate are negligibly small (<0.1%) in first and second orders.