# Calculation of Transport Coefficients with Khimera

The importance of quantitative information on transport properties for multicomponent reacting gas mixtures needs no comments. Khimera makes possible calculation of all the necessary mixture transport coefficients

##### Set of Transport Coefficients Accessible for Treatment by Khimera

- mixture viscosity μ;
- mixture thermal conductivity (translational λtr, internal λint, total λ=λtr+λint );
- thermodiffusion coefficients DTi and thermodiffusion ratios kTi for all species (
*i*=1,...,*N*); - multicomponent diffusion coefficients Dik and multicomponent resistance coefficients Δik for all pairs of species (
*i,k*=1,...,*N*).

Here, N is the total number of species.

Calculations of the transport coefficients for a multicomponent gas mixture under thermal and chemical equilibrium (LTE) are performed by the accurate formulas of the Chapman-Enskog method. The calculations are made with account for higher approximations 1<ξ<4, where ξ is the number of approximations, i.e., the number of retained terms in the Sonine polynomial expansions.

The Euken-Hirschfelder formula is used to calculate the contribution to thermal conductivity of polyatomic gases due to the internal degrees of freedom of molecules.

Khimera provides the coefficients for both the traditional form of the Stefan-Maxwell relations (fluxes via forces) following the works by Hirschfelder and Devoto (DTi, Dik) and the new form of Stefan-Maxwell relations (forces via fluxes) following Tirskii-Kolesnikov (kTi, Δik).

In the current Kimare version, the interparticle potential function for each pair of species is approximated by the Lennard-Jones (126) potential, so the temperature range should be restricted to 2000-4000 K to provide a reasonable accuracy of transport coefficients. The next version of Khimera (under development now) will provide a possibility to use more accurate model potential functions including Buckingham-Corner exp6f potential for nonpolar gases, Stockmayer potential for polar gases, Born-Mayer potential for high temperature calculations, Aziz HFD potentials for noble gases.

##### Case Study Examples: calculation of viscosity and thermal conductivity for argon

Viscosity and thermal conductivity were calculated for the two cases: LTE argon and dissociated air. In both cases calculations were done at a pressure of P=1 atm in the temperature range 300≤T≤4000 K by the accurate formulas of the Chapman-Enskog method with account for higher approximations, e.g., ξ=2 for viscosity and ξ=4 for translational thermal conductivity.

Dissociated air (78% N2, 21% O2, 1% Ar) consists of the 6 components (N2, O2, Ar, NO, N, O).

Figures 1-2 present a comparison of the Khimera results (blue line) with available experimental and theoretical data.