Transformations of the equations of the first approximation of Chapman–Enskog methods and vector transport relations for mixtures of polyatomic gases

Transformations of the systems of equations of the first approximation of the classical and generalized Chapman–Enskog methods are proposed for those terms of the distribution functions by means of which one can calculate the vector transport relations for mixtures of polyatomic gases, connecting the diffusion and heat fluxes and gradients of the scalar gas-dynamic variables. The solutions of the transformed systems are expressed in terms of diffusion rates and gradients of the macroparameters. The derivation and formulae for the coefficients of the Stefan–Maxwell relations and their generalizations are simplified, and rigorous results for the matrices of the transport coefficients are established. Approximate vector transport relations are given for mixtures of non-equilibrium reacting polyatomic gases.