Transport Coefficients for the Simple Reacting Spheres Kinetic Model II: Thermal Conductivity, Diffusion, Thermal-Diffusion Ratio

Abstract

We investigate the transport coefficients for a dilute reactive mixture of four constituents undergoing a chemical reaction of type $$A+B \rightleftharpoons C+ D$$ A + B ⇌ C + D , which is described by the Simple Reacting Spheres (SRS) kinetic model. The dynamics of the SRS model is very interesting and relatively simple. Both reactive and inert collisions obey to the hard spheres potential and the collisional operator incorporates a “correction” term that singles out those pre-collisional pairs of particles having enough energy to react chemically. Starting from this setting, we consider the mixture in a chemical regime for which both elastic and reactive collisions occur with comparable characteristic times and use the Chapman–Enskog method to determine the first-order approximation of the non-equilibrium solution to the SRS system. In a preceding paper (part I), the focus was on the coefficients associated to reaction rate and shear viscosity and in the present work we are interested on the coefficients associated to thermal conductivity, diffusion, and thermal-diffusion ratio. These coefficients are analysed numerically for both exothermic and endothermic reactions. The analysis allows to investigate the influence of the chemical reaction and the impact of the “correction” term proper of the SRS model on the transport coefficients.