Approximations for the Non-Equilibrium Reaction and Relaxation Rates.

The general approach for solving kinetic equations for gas mixtures with internal degrees of freedom and for deriving corresponding equations for reaction and relaxation rates (Kolesnichenko and Gorbachev, 2010, 2012, Gorbachev 2016) is ex-ploited for obtaining approximations for those parameters. Both spatially homogeneous and inhomogeneous effects on reaction and relaxation rates (RRR) are considered. Non-equilibrium RRR’s are determined by the corrections to the quasi-equilibrium distribution functions. Special attention is drawn to the method of solving the integral equations for those corrections. The main issue consists in the non-symmetry of the corresponding integral operators and presence of the eigenfunctions (summational invariants) with the zeroth eigenvalues. Those corrections are expanded in a series over the complete set of polynomials. Since the operators are non-symmetrical, the projection method is used for obtaining the set of equations for the expansion coefficients. As discussed, those equations should include the projections on the summational invariants. Examples of dissociation and exchange reactions are considered. Possibility of neglecting the contribution from the reactive collisions into the equations for expansion coefficients is discussed. [ABSTRACT FROM AUTHOR]