2019, Zaznoba, V. A., Stepanenko, A. A., Zhdanov, V. M., Степаненко, Александр Александрович

© 2019 Author(s).The slip phenomena in multicomponent gas mixtures are studied. The moment equations, derived from the linearized Boltzmann equation by using the 13-moment approximation of the Grad's method, are used to obtain the full (containing the contribution from the Knudsen layer) and asymptotic (valid far from the plane physical boundary of the domain) expressions for the nonequilibrium macroscopic parameters of the mixture species. The latter relations are employed to deduce the expressions for the mixture slip velocity and the viscous, thermal, and diffusion slip coefficients by using the modified Maxwell method and the diffuse-specular model of molecule scattering on the wall. The derived relations for the slip coefficients are given in the convenient form expressed in terms of basic transport coefficients, such as partial viscosity and thermal conductivity coefficients, diffusion and thermal diffusion coefficients, and coefficients of molecule momentum accommodation at the wall. The expressions found are used to calculate the slip coefficients for binary (He-Ar) and ternary (He-Ar-Xe) gas mixtures. The numerical results are in good agreement with the data calculated by using other methods.

2021, Zhdanov, V. M., Stepanenko, A. A., Степаненко, Александр Александрович

© 2021, Springer Science+Business Media, LLC, part of Springer Nature.The authors have studied the influence of the adsorption and surface diffusion of one component of a binary gas mixture on pore walls on the effect of separation of the gas mixture during its flow through a nanosize porous membrane in a free molecular regime. A capillary porous-medium model obtained by the momentum-balance method was taken as a basis for analysis. Expressions have been determined for the separation factor and the concentration jump of the adsorbed component for an assigned pressure difference on the membrane, which make it possible to analyze the influence of the initial concentration of the adsorbable component and of the temperature on the separation effect. Calculations have been performed of the concentration jump for a number of commercial gas mixtures (CO2/H2, CO/H2, CH4/H2, and N2/He). It has been shown that taking account of surface diffusion may lead to appreciable variations (of several tens of percent) of the obtained values from Knudsen values of the effect in the absence of adsorption.

2020, Stepanenko, A. A., Zhdanov, V. M., Степаненко, Александр Александрович

We present the results of analysis of relaxation phenomena in thermal molecular plasmas. The physical assumptions and the general scalar moment equations, obtained in the 17-moment approximation of the Grad method, are given. By using these equations, we derive the expressions for the relaxation pressure and bulk viscosity coefficients associated with heavy plasma components (atoms, molecules and their ions) and electrons. To gain a deeper understanding of how the physical parameters of particles and inter-particle interactions influence on the plasma relaxation properties, we also employ the semi-qualitative model of energy relaxation for plasma components. Within this model, the expressions for the partial relaxation pressures and bulk viscosity coefficients are derived and analyzed. It is demonstrated that depending on the plasma degree of ionization and the ratio of the characteristic timescales of energy exchange between particles, the partial relaxation pressures and bulk viscosity coefficients can not only vary but also change their signs.

2021, Makarov, S. O., Coster, D. P., Rozhansky, V. A., Kaveeva, E. G., Stepanenko, A. A., Zhdanov, V. M., Степаненко, Александр Александрович

© 2021 Author(s).New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improved versions of the expressions written in Zhdanov [Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)], based on Grad's 21N-moment method. Both explicit and approximate approaches for the calculation of transport coefficients are considered. Accurate application of this closure for the Braginskii transport equations is discussed. Viscosity dependence on the heat flux is taken into account. Improved expressions are implemented into the SOLPS-ITER code and tested for deuterium and neon ITER cases. Some typos found in Zhdanov [Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)] are corrected.

2021, Zaznoba, V. A., Zhdanov, V. M., Stepanenko, A. A., Степаненко, Александр Александрович

© 2021 Author(s).The binary gas mixture flow, diffusion, and heat transfer through a long tube in the near-continuum regime (moderately small Knudsen numbers) are analyzed. The system of linearized third-order moment equations, obtained by Grad's method, is used. An expression for the total mass flux of a binary gas mixture is deduced by using the extension of the procedure, proposed in the work by Zhdanov ["Slip and barodiffusion phenomena in slow flows of a gas mixture,"Phys. Rev. E 95, 033106 (2017)] for the study of slip phenomena in slow flows of a gas mixture. Relations for diffusion and heat fluxes are determined from the initial system of moment equations, averaged over the channel cross section, and supplied with several moments of the distribution function at the channel wall found with the modified Maxwell method. Analytical formulas for kinetic coefficients of the Onsager matrix, which connect averaged fluxes and gradients of the corresponding thermodynamic quantities, are obtained. It is shown that the employed approach automatically ensures the validity of the reciprocal relations for the cross terms in the Onsager matrix. The results of calculations of the derived kinetic coefficients for several binary mixtures of noble gases (He-Ar, Ne-Ar, and He-Xe) are presented and compared with numerical data found by the discrete velocity method on the basis of the linearized Boltzmann equation with the McCormack model.