On modified simple reacting spheres kinetic model for chemically reactive gases

Abstract

We consider the modified simple reacting spheres (MSRS) kinetic model that, in addition to the conservation of energy and momentum, also preserves the angular momentum in the collisional processes. In contrast to the line-of-center models or chemical reactive models considered in [23], in the MSRS (SRS) kinetic models, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justified. In the MSRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard spheres-like. We consider a four component mixture A, B, A * , B * , in which the chemical reactions are of the type A + B A * + B * , with A * and B * being distinct species from A and B. We provide fundamental physical and mathematical properties of the MSRS model, concerning the consistency of the model, the entropy inequality for the reactive system, the characterization of the equilibrium solutions, the macroscopic setting of the model and the spatially homogeneous evolution. Moreover, we show that the MSRS kinetic model reduces to the previously considered SRS model (e.g., [21], [27]) if the reduced masses of the reacting pairs are the same before and after collisions, and state in the Appendix the more important properties of the SRS system.

On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting

“…where the term A ε is given by (72). Moreover, we have used properties (35) and (36), respectively, with ψ(v, I) = 1, for the vanishing of the first two terms on the right hand side of equation (73). To obtain the last term on the right hand side of equation (73), we have used the more convenient form of the reactive operator Q react i , given in (65).…”

“…where property (35) was used with ψ(v, I) = v to obtain the vanishing of the first term on the right hand side. Moreover, concerning the term B ε i on the right-hand side of (78) we have used the elastic bi-species operator Q e ij given in (64) and the decomposition of the elastic bi-species kernel indicated in (66) to obtain the expression for B ε i given in (75).…”

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

“…In this section we briefly describe the SRS kinetic model for a dilute reactive mixture. For a detailed description, see, for example, [35,36,37] and the references cited therein.…”

“…Finally, we point out that the SRS kinetic system considered in this work does not necessarily satisfy conservation of the angular momentum during reactive collisions, unless µ ij /µ kl = 1. On the other hand, the modified SRS kinetic model considered in [37] has conservation of the angular momentum built into the collisional processes. The exponent 2 in the quotient µ ij /µ kl of (6) for J R i is specific to the SRS model considered here, while the corresponding exponent in expression for J R i in the modified SRS model is equal to 3.…”

“…Additionally, the SRS kinetic theory, if considered in its general formulation, provides a kinetic system of equations of the revised Enskog type for reactive mixtures and this permits to extend the mathematical approach to moderate dense regimes. For the details on the SRS model, see the original papers [13,31,32] and also the mathematical analysis developed in papers [33,34,35,36,37].…”