Kinetic Theory of Simple Reacting Spheres I

Abstract

We consider physical and mathematical aspects of the model of simple reacting spheres (SRS) in the kinetic theory of chemically reacting fluids. The SRS, being a natural extension of the hard-sphere collisional model, reduces itself to the revised Enskog theory when the chemical reactions are turned off. In the dilute-gas limit, it provides an interesting kinetic model of chemical reactions that has not been considered before. In contrast to other reactive kinetic theories (e.g., line-of-centers models), the SRS has built-in detailed balance and microscopic reversibility conditions. The mathematical analysis of the work consists of global existence result for the system of partial differential equations for the model of SRS.

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

“…f and k (1) f being defined by (35) and (45), respectively. Figures 1-6 illustrate how the coefficient k * f varies in dependence on the dimensionless forward activation energy γ *…”

“…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.…”

“…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].…”

On modified simple reacting spheres kinetic model for chemically reactive gases

“…In particular, in the frame of the kinetic theory of chemically reacting gases, several contributions have been advanced, after the pioneering papers by Prigogine and collaborators [19], [20], and further works by Present [18], Ross 514 JACEK POLEWCZAK AND ANA JACINTA SOARES and Mazur [22], Shizgal and Karplus [24], and many others. Besides theoretical and formal studies which in particular deal with existence theory [9], [16], [17], there exists a rather vast bibliography oriented to other connected relevant topics, such as the modeling of multicomponent reactive flows [7], [10], [12], [23], analysis of transport properties [14], [25], investigation of the non-equilibrium effects induced by the chemical reactions [5], [15], construction of generalized BGK theories [1], [13], [14], as well as applications to combustion [8], just to cite a few of them.…”

“…In this work, we are interested in the simple reacting spheres (SRS) model of the kinetic theory for chemically reacting gases, that has been developed by N. Xystris, J. S. Dahler [27] and further advanced by J. S. Dahler and L. Qin in [21], [6]. Mathematical aspects of SRS, including global existence in a dilute regime, were studied in [16] and [17]. In [11] the SRS model was compared to a model of chemical reacting gases proposed in [23].…”