@article {1559,
	title = {On the use temperature parameterized rate coefficients in the estimation of non-equilibrium reaction rates},
	journal = {Physica a-Statistical Mechanics and Its Applications},
	volume = {365},
	number = {2},
	year = {2006},
	note = {ISI Document Delivery No.: 044QSTimes Cited: 11Cited Reference Count: 58},
	month = {Jun},
	pages = {317-332},
	type = {Article},
	abstract = {The present paper considers a detailed analysis of the nonequilibrium effects for a model reactive system with the Chapman-Eskog (CE) solution of the Boltzmann equation as well as an explicit time dependent solution. The elastic cross sections employed are a hard sphere cross section and the Maxwell molecule cross section. Reactive cross sections which model reactions with and without activation energy are used. A detailed comparison is carried out with these solutions of the Boltzmann equation and the approximation introduced by Cukrowski and coworkers [J. Chem. Phys. 97 (1992) 9086; Chem. Phys. 89 (1992) 159; Physica A 188 (1992) 344; Chem. Phys. Lett. A 297 (1998) 402; Physica A 275 (2000) 134; Chem. Phys. Lett. 341 (2001) 585; Acta Phys. Polonica B 334 (2003) 3607.] based on the temperature of the reactive particles. We show that the Cukrowski approximation has limited applicability for the large class of reactive systems studied in this paper. The explicit time dependent solutions of the Boltzmann equation demonstrate that the CE approach is valid only for very slow reactions for which the corrections to the equilibrium rate coefficient are very small. (c) 2005 Elsevier B.V. All rights reserved.},
	keywords = {BIMOLECULAR CHEMICAL-REACTION, Boltzmann equation, BOLTZMANN-EQUATION, Chapman-Enskog, CHAPMAN-ENSKOG METHOD, CHEMISTRY, DILUTE GAS, LORENTZ GAS, MULTICOMPONENT SYSTEMS, NITROGEN-ATOMS, nonequilibrium, PERTURBATION, REACTIONS, VELOCITY DISTRIBUTION},
	isbn = {0378-4371},
	url = {<Go to ISI>://000237687900006},
	author = {Shizgal, B. D. and Chikhaoui, A.}
}
@article {3813,
	title = {Nonequilibrium effects in reactive systems; The effect of reaction products and the validity of the Chapman-Enskog method},
	journal = {Physica a-Statistical Mechanics and Its Applications},
	volume = {223},
	number = {1-2},
	year = {1996},
	note = {ISI Document Delivery No.: TQ402Times Cited: 30Cited Reference Count: 62},
	month = {Jan},
	pages = {50-86},
	type = {Article},
	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 reversible arrow B + B, with and without the reverse reaction, and the reaction A + C {\textendash}> products are examined with both a Chapman-Enskog method along with an explicitly time-dependent solution for the irreversible reaction A + A {\textendash}> 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.},
	keywords = {ANOMALOUS TRANSPORT, DISTRIBUTIONS, EQUILIBRIUM, HEAT-FLUX, hydrodynamics, KINETIC-THEORY, LASER-INDUCED FLUORESCENCE, PERTURBATION, PLASMA, STRONGLY INHOMOGENEOUS SYSTEMS, VELOCITY},
	isbn = {0378-4371},
	url = {<Go to ISI>://A1996TQ40200005},
	author = {Shizgal, B. D. and Napier, D. G.}
}
