Effect of reaction heat on Maxwellian distribution functions and rate of reactions

Abstract

A binary gaseous mixture undergoing a reversible reaction of type is modeled with the chemical kinetic Boltzmann equation, assuming hard sphere cross sections for elastic collisions, and two different models with activation energy for reactive interactions, namely the line-of-centers and step cross-section models. The Chapman–Enskog method and Sonine polynomial representation of the distribution functions are used to obtain the solution of the Boltzmann equation in a chemical regime for which the reactive interactions are less frequent than the elastic collisions, i.e. in the early stage of the reaction when the constituent A is in a large amount with respect to B and the affinity of the reaction tends to infinity. The aim of this paper is twofold: (i) to evaluate the effect of the reaction heat on the Maxwellian distribution functions and on the production terms of both particle number densities and mixture energy density; (ii) to analyze spatially homogeneous solutions for the particle number density and temperature of the reactants when the chemical reaction advances. It is shown that the reaction heat changes the Maxwellian distribution functions, the production terms and hence the trend to equilibrium of the particle number density and temperature of the reactants. Moreover, these changes differ for exothermic and endothermic reactions.

Transport coefficients for the simple reacting spheres kinetic model I: Reaction rate and shear viscosity

“…At this level, the kinetic theory of chemically reactive mixtures improves the knowledge of the reaction dynamics and provides the expressions for the reaction rates of the chemical species [2,3,4]. There are many contributions in this field, after the pioneering works by Prigogine, Xhrouet and Mahieu [5,6], Present [7,8], Ludwig and Heil [9], Ross and Mazur [10], and here we quote, for example, papers [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] which essentially deal with reaction rates and non-equilibrium effects induced by chemical reactions, as well as transport properties and influence of the chemical reaction on transport coefficients.…”

Master equation for a bistable chemical system with perturbed particle velocity distribution function

“…This phenomenon is due to the selectivity of the reaction, which preferentially involves the more energetic particles, able to pass the activation barrier. Such a perturbation, later referred to as a nonequilibrium effect, can be determined for a dilute gaseous system using a perturbative solution of the Boltzmann equation [5][6][7][8][9]. The nonequilibrium effect is important in the physics of plasmas [10,11], in particular in hypersonic reentry into the earth's atmosphere [12], but at small scales as well, for example in homogeneous condensation related to nanofabrication [13].…”

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

“…Another important issue in applications of the Chapman-Enskog to the reactive Boltzmann equation is the distortion of the Maxwellian distribution functions by the reaction heat [2,14,26,31], which makes the reaction rate coefficients sensitive to the reaction heat.…”