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

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.