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Stefan-Maxwell relations for ambipolar diffusion in a two-temperature plasma with application to the problem of an ion-sonic wave

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Abstract

The Stefan-Maxwell relations, in which the concentration gradients are expressed in terms of linear combinations of the diffusion velocities of the components and the thermodynamic parameter gradients, are derived for a partially ionized quasineutral multicomponent two-temperature gas mixture. It is shown that a component of the diffusion driving force proportional to ▿ln(T e /T h ), where T e is the electron temperature and T h is the gas temperature, can develop in the two-temperature mixtures. A generalization of the Fick law for the diffusion ion flow which contains the new thermal diffusion force is obtained for a three-component plasma. Under the assumption that the charged components have no effect on the shock wave structure, for linear approximations of the gas density and temperature profiles in this zone approximate mass ion concentration distributions in a shock wave propagating through weakly ionized argon and ahead of its front are analytically obtained under the condition that the electron temperature is much higher than the gas temperature. Analytic distributions of the ambipolar electric field E a and the ratio E a /n in the ion-sonic wave (extended zone ahead of the shock wave front in the non-isothermal plasma) are obtained.

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References

  1. J.O. Hirschfelder, Ch.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids (John Wiley and Sons, New York, Chapman and Hall, London, 1954; Inostr. Lit., Moscow, 1961).

    MATH  Google Scholar 

  2. A.F. Kolesnikov and G.A. Tirskii, “Hydrodynamic Equations for Partially Ionized Multicomponent Gas Mixtures with Transport Coefficients in the Higher Approximations,” in: Molecular Gas Dynamics (Nauka, Moscow, 1982) [in Russian], pp. 20–44.

    Google Scholar 

  3. A.F. Kolesnikov, “Equations of Motion of a Multicomponent Partially Ionized Two-Temperature Gas Mixture in an Electromagnetic Field with Transport Coefficients in the Higher Approximations,” Report of Institute of Mechanics of the Lomonosov Moscow State University No. 1556 (Moscow University Press, Moscow, 1974) [in Russian].

    Google Scholar 

  4. A.F. Kolesnikov, “Stefan-Maxwell Relations for Multicomponent Ambipolar Diffusion and Thermal-Baro Diffusion Effects in Two-Temperature Plasmas,” AIAA Paper 2000-2570 (2000).

    Google Scholar 

  5. A.F. Kolesnikov, “General Formulation of the Multicomponent Plasma Transport Equations,” in: D. Fletcher, J.-M. Charbonnier, G.S.R. Sarma, and T. Magin (Eds.), Physico-Chemical Models for High-Enthalpy and Plasma Flows. VKI Lecture Series 2002-07 (The von Karman Institute, 2002).

    Google Scholar 

  6. A.F. Kolesnikov, “General Formulation of Multicomponent Plasmas Transport Equations with Ambipolar Approach for Weakly Ionized Gases,” AIAA Paper 2003-1055 (2003).

    Google Scholar 

  7. J.H. Ferziger and H.G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland Publishing Company, Amsterdam-London, 1972; Mir, Moscow, 1976).

    Google Scholar 

  8. O.N. Suslov and G.A. Tirskii, “Definition, Properties, and Calculation of Ambipolar Diffusion Coefficients in the Laminar Multicomponent Ionized Boundary Layer,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 60–72 (1970).

    Google Scholar 

  9. R.F. Avramenko, A.A. Rukhadze, and S.F. Teselkin, “Shock Wave Structure in Weakly Ionized Nonisothermal Plasma,” Pis’ma v Zh. Eksp. Teor. Fiz. 34, 485–488 (1981).

    Google Scholar 

  10. A.F. Kolesnikov, “Mechanism of the Ion Baro-Thermal-Diffusion Pumping in Weakly Ionized Shock Layer,” AIAA Paper 2001-2871 (2001).

    Google Scholar 

  11. Ya.B. Zel’dovich and Yu.P. Raizer, Physics of Shock Waves and High-Temperature Gasdynamic Phenomena (Fizmatgiz, Moscow, 1963) [in Russian].

    Google Scholar 

  12. M.N. Kogan, Rarefied Gas Dynamics (Nauka, Moscow, 1967) [in Russian].

    Google Scholar 

  13. R.S. Devoto, “Transport Coefficients of Ionized Argon,” The Phys. Fluids. 16, No. 5, 616–623 (1973).

    Article  ADS  Google Scholar 

  14. Yu.P. Raizer, Physics of Gas Discharge (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, Moscow, 119526, Russia

    A. F. Kolesnikov

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  1. A. F. Kolesnikov
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Correspondence to A. F. Kolesnikov.

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Original Russian Text © A.F. Kolesnikov, 2015, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2015, Vol. 50, No. 1, pp. 170–181.

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Kolesnikov, A.F. Stefan-Maxwell relations for ambipolar diffusion in a two-temperature plasma with application to the problem of an ion-sonic wave. Fluid Dyn 50, 153–163 (2015). https://doi.org/10.1134/S0015462815010159

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  • DOI: https://doi.org/10.1134/S0015462815010159

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