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

Abstract

In this work, we consider a dilute reactive mixture of four constituents undergoing the reversible reaction A + B C + D. The mixture is described by the Simple Reacting Spheres (SRS) kinetic model which treats both elastic and reactive collisions as hard spheres type and introduces a "correction" term in the elastic operator in order to prevent double counting of the events in the collisional integrals. We use the Chapman-Enskog method, at the first-order level of the Enskog expansion, to determine the non-equilibrium solution to the SRS system in a chemical regime for which both elastic and reactive collisions occur with comparable characteristic times. We then determine the transport coefficients and focus our analysis on the evaluation of those coefficients associated with the reaction rate and the shear viscosity. Our numerical evaluation of the transport coefficients allows for the investigation of their behaviour in a suitably chosen parametric space with an opportunity to check how these coefficients are influenced by the chemical reaction and by the "correction" term proper of the SRS model.

A Hard Sphere Model for Bimolecular Recombination of Heavy Ions

“…Within the framework of hard sphere models (impulsive models), the description of the motion of the particles in the zone of strong repulsive interaction is radically simplified. Namely, these particles are treated as balls which exchange energies and momenta at their contacts with each other according to the elastic impact law [4,[26][27][28][29][30] (inelastic encounters of balls are also sometimes considered). In addition, simulation of the particle motion outside the zone of strong repulsive interaction is also greatly simplified.…”

“…Hard sphere models of the CID reactions (1) have been considered in many works [4,9,10,26,28,[34][35][36][37][38]. Hard sphere models have been used in the theory of atomic and molecular collisions in the gas phase until recently [29][30][31][32][39][40][41][42][43].…”

“…Consequently, the value averaged over all the possible locations of the M + ion with is equal to After selecting the initial conditions of a collision RM + + X -, further simulation of the particle motion, as was already noted in the introduction, was carried out in exactly the same way as in the hard sphere model of direct three-body recombination (3) [31,32]. It was assumed that at a contact of any two balls representing the particles, their velocities instantly change according to the elastic impact law [4,[26][27][28][29][30]. In the time intervals between the encounters of the balls, the R atom and the center of mass of the ionic pair move under no forces, whereas the relative motion of the ions was determined by solving numerically the Newtonian equations of motion corresponding to a material point in the Coulomb potential field on a plane orthogonal to the conserved angular momentum vector of the M + -Xsystem (the mass of the point being equal to the reduced mass of the ions; denotes the vector connecting the nuclei of the ions).…”