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Extended thermodynamics of dense polyatomic gases: modeling of molecular energy exchange

  • Takashi Arima
  • Masaru Sugiyama
Article

Abstract

We revisit the extended thermodynamic (ET) theory of dense polyatomic gases developed in the paper (Arima et al. in Phys Rev Fluids 2:013401, 2017) from the viewpoint of the energy exchange between two subsystems: the subsystem with the kinetic and potential energies and the subsystem of the internal modes such as molecular rotation and vibration. We confirm that the system of balance equations derived from the viewpoint is completely the same as the previous one, but thereby we can obtain its complementary physical implications. We also point out a possible alternative procedure in the modeling method based on ET.

Keywords

Extended thermodynamics Dense polyatomic gas Molecular energy exchange Nonequilibrium temperature 

Mathematics Subject Classification

82C35 76N15 35Q35 35L60 

Notes

Acknowledgements

The present paper is dedicated to Professor Tommaso Ruggeri, our teacher and friend, on the occasion of his 70th birthday. We have learned extended thermodynamics deeply by stimulating discussions with him. This work was partially supported by JSPS KAKENHI Grant No. JP15K21452 (T.A.).

References

  1. 1.
    Müller, I., Ruggeri, T.: Extended Thermodynamics. Springer Tracts in Natural Philosophy, vol. 37, I edn. Springer, New York (1993)Google Scholar
  2. 2.
    Müller, I., Ruggeri, T.: Rational Extended Thermodynamics. Springer Tracts in Natural Philosophy, vol. 37, II edn. Springer, New York (1998)CrossRefGoogle Scholar
  3. 3.
    Ruggeri, T., Sugiyama, M.: Rational Extended Thermodynamics beyond the Monatomic Gas. Springer, Cham (2015). ISBN 978-3-319-13340-9CrossRefzbMATHGoogle Scholar
  4. 4.
    de Groot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. Dover, New York (1984)zbMATHGoogle Scholar
  5. 5.
    Liu, I.-S., Müller, I.: Extended thermodynamics of classical and degenerate ideal gases. Arch. Ration. Mech. Anal. 83, 285–332 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chapman, S., Cowling, T.G.: The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction and diffusion in gases. Cambridge University Press, Cambridge (1970)zbMATHGoogle Scholar
  7. 7.
    Grad, H.: On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2, 331–407 (1949)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Extended thermodynamics of dense gases. Contin. Mech. Thermodyn. 24, 271–292 (2011)CrossRefzbMATHGoogle Scholar
  9. 9.
    Arima, T., Sugiyama, M.: Characteristic features of extended thermodynamics of dense gases. Atti Accad. Pelorit. Pericol. 91(S1), A1–A15 (2013)MathSciNetGoogle Scholar
  10. 10.
    Ruggeri, T., Sugiyama, M.: Recent developments in extended thermodynamics of dense and rarefied polyatomic gases. Acta Applicandae Mathematicae 132, 527–548 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Arima, T., Mentrelli, A., Ruggeri, T.: Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments. Ann. Phys. 345, 111–140 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Arima, T., Mentrelli, A., Ruggeri, T.: Extended thermodynamics of rarefied polyatomic gases and characteristic velocities. Rend. Lincei Mat. Appl. 25, 275–291 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics. Contin. Mech. Thermodyn. 25, 727–737 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: beyond the Bethe–Teller theory. Phys. Rev. E 89, 013025 (2014)CrossRefGoogle Scholar
  15. 15.
    Arima, T., Taniguchi, S., Sugiyama, M.: Light scattering in rarefied polyatomic gases based on extended thermodynamics. In: Proceedings of The 34th Symposium on Ultrasonic Electronics, pp. 15–16 (2013)Google Scholar
  16. 16.
    Pavić, M., Ruggeri, T., Simić, S.: Maximum entropy principle for rarefied polyatomic gases. Phys. A 392, 1302–1317 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Bourgat, J.-F., Desvillettes, L., Le Tallec, P., Perthame, B.: Microreversible collisions for polyatomic gases. Eur. J. Mech. B/Fluids 13, 237–254 (1994)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Extended thermodynamics of real gases with dynamic pressure: an extension of Meixner’s theory. Phys. Lett. A 376, 2799–2803 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Arima, T., Ruggeri, T., Sugiyama, M., Taniguchi, S.: On the six-field model of fluids based on extended thermodynamics. Meccanica 49, 2181–2187 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Effect of dynamic pressure on the shock wave structure in a rarefied polyatomic gas. Phys. Fluids 26, 016103 (2014)CrossRefzbMATHGoogle Scholar
  21. 21.
    Meixner, J.: Absorption und dispersion des schalles in gasen mit chemisch reagierenden und anregbaren komponenten. I. Teil. Ann. Physik 43, 470–487 (1943)CrossRefGoogle Scholar
  22. 22.
    Meixner, J.: Allgemeine theorie der schallabsorption in gasen und flussigkeiten unter berucksichtigung der transporterscheinungen. Acoustica 2, 101–109 (1952)MathSciNetGoogle Scholar
  23. 23.
    Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics. Phys. Lett. A 377, 2136–2140 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Arima, T., Ruggeri, T., Sugiyama, M., Taniguchi, S.: Nonlinear extended thermodynamics of real gases with 6 fields. Int. J. Non Linear Mech. 72, 6–15 (2015)CrossRefzbMATHGoogle Scholar
  25. 25.
    Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Overshoot of the nonequilibrium temperature in the shock wave structure of a rarefied polyatomic gas subject to the dynamic pressure. Int. J. Non Linear Mech. 79, 66–75 (2016)CrossRefGoogle Scholar
  26. 26.
    Arima, T., Ruggeri, T., Sugiyama, M., Taniguchi, S.: Recent results on nonlinear extended thermodynamics of real gases with six fields. Ricerche Mat. 65, 263–277 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Recent results on nonlinear extended thermodynamics of real gases with six fields. Part II: shock wave structure. Ricerche Mat. 65, 279–288 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Ruggeri, T.: Non-linear maximum entropy principle for a polyatomic gas subject to the dynamic pressure. Bull. Inst. Math. Acad. Sin. 11, 1–22 (2016). (Special Issue in honor of Tai-Ping Liu 70 birthday)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Bisi, M., Ruggeri, T., Spiga, G.: Dynamical pressure in a polyatomic gas: interplay between kinetic theory and extended thermodynamic. Kinet. Relat. Mod. 11, 71–95 (2018)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Arima, T., Ruggeri, T., Sugiyama, M.: Rational extended thermodynamics of a rarefied gas with molecular relaxation processes. Phys. Rev. E 96, 042143 (2017)CrossRefGoogle Scholar
  31. 31.
    Arima, T., Ruggeri, T., Sugiyama, M.: Duality principle from rarefied to dense gas and extended thermodynamics with six fields. Phys. Rev. Fluids 2, 013401 (2017)CrossRefGoogle Scholar
  32. 32.
    Zhdanov, V.M.: The kinetic theory of a polyatomic gas. Sov. Phys. JETP 26, 1187–1191 (1968)Google Scholar
  33. 33.
    Tisza, L.: Supersonic absorption and Stokes’ viscosity relation. Phys. Rev. 61, 531–536 (1942)CrossRefGoogle Scholar
  34. 34.
    Landau, L.D., Lifshitz, E.M.: Statistical Physics. Pergamon, Oxford (1980)zbMATHGoogle Scholar
  35. 35.
    Ikenberry, E., Truesdell, C.: On the pressure and the flux of energy in a gas according to Maxwellfs kinetic theory. J. Ration. Mech. Anal. 5, 1–54 (1956)zbMATHGoogle Scholar
  36. 36.
    Arima, T., Sugiyama, M.: Nonequilibrium pressure and temperatures in extended thermodynamics of gases with six fields. Ricerche Mat. (submitted)Google Scholar

Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringKanagawa UniversityYokohamaJapan
  2. 2.Nagoya Institute of TechnologyNagoyaJapan

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