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Gaseous mixture flow between two parallel plates in the whole range of the gas rarefaction

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  • Naris, S
  • Valougeorgis, D
  • Kalempa, D
  • Sharipov, F

Abstract

The flow of binary gaseous mixtures between two parallel plates driven by gradients of pressure, temperature and concentration is studied, based on the McCormack model of the Boltzmann equation. The coupled kinetic equations are solved numerically by the discrete velocity method. The mass flow, the heat flux and the diffusion flux, which are the mixture quantities of practical importance, are expressed in terms of the so-called thermodynamic fluxes. The latter are written in a form that allows us to verify the Onsager–Casimir reciprocity relations. In addition, analytical expressions for these quantities are derived in the limit case of the hydrodynamic regime. Thus, the numerical solution together with these expressions provides the solution in the whole range of the gas rarefaction. The influence of the intermolecular interaction potential is also investigated by comparing the results for the rigid sphere model with those for a realistic potential. Numerical results are presented for two binary mixtures of noble gases (Ne–Ar and He–Xe) for various values of the molar concentrations.

Suggested Citation

  • Naris, S & Valougeorgis, D & Kalempa, D & Sharipov, F, 2004. "Gaseous mixture flow between two parallel plates in the whole range of the gas rarefaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 294-318.
    • Handle: RePEc:eee:phsmap:v:336:y:2004:i:3:p:294-318
    DOI: 10.1016/j.physa.2003.12.047
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. Sharipov, Felix, 1994. "Onsager-Casimir reciprocity relations for open gaseous systems at arbitrary rarefraction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(3), pages 457-485.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    4. Sharipov, Felix, 1994. "Onsager-Casimir reciprocity relations for open gaseous systems at arbitrary rarefaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(3), pages 437-456.
    5. Sharipov, Felix, 1994. "Onsager-Casimir reciprocity relations for open gaseous systems at arbitrary rarefaction III. Theory and its application for gaseous mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(3), pages 457-476.
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    Cited by:

    1. Zhdanov, V.M. & Zaznoba, V.A., 2021. "Non-equilibrium phenomena in gas mixture flow through a plane channel in near-continuum regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Sharipov, Felix & Cumin, Liliana M. Gramani & Kalempa, Denize, 2007. "Heat flux between parallel plates through a binary gaseous mixture over the whole range of the Knudsen number," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 183-193.
    3. Sharipov, Felix, 2012. "Reciprocal relations based on the non-stationary Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 1972-1983.
    4. Sharipov, Felix, 2010. "The reciprocal relations between cross phenomena in boundless gaseous systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3743-3760.

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