Hamiltonian principle in the binary mixtures of Euler fluids with applications to the second sound phenomena

Henri Gouin; Tommaso Ruggeri

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2003)

  • Volume: 14, Issue: 1, page 69-83
  • ISSN: 1120-6330

Abstract

top
In the present paper we compare the theory of mixtures based on Rational Thermomechanics with the one obtained by Hamilton principle. We prove that the two theories coincide in the adiabatic case when the action is constructed with the intrinsic Lagrangian. In the complete thermodynamical case we show that we have also coincidence in the case of low temperature when the second sound phenomena arises for superfluid Helium and crystals.

How to cite

top

Gouin, Henri, and Ruggeri, Tommaso. "Hamiltonian principle in the binary mixtures of Euler fluids with applications to the second sound phenomena." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.1 (2003): 69-83. <http://eudml.org/doc/252333>.

@article{Gouin2003,
abstract = {In the present paper we compare the theory of mixtures based on Rational Thermomechanics with the one obtained by Hamilton principle. We prove that the two theories coincide in the adiabatic case when the action is constructed with the intrinsic Lagrangian. In the complete thermodynamical case we show that we have also coincidence in the case of low temperature when the second sound phenomena arises for superfluid Helium and crystals.},
author = {Gouin, Henri, Ruggeri, Tommaso},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Fluid mixtures; Superfluidity; Second sound; Hamiltonian principle; fluid mixtures; superfluidity; second sound},
language = {eng},
month = {3},
number = {1},
pages = {69-83},
publisher = {Accademia Nazionale dei Lincei},
title = {Hamiltonian principle in the binary mixtures of Euler fluids with applications to the second sound phenomena},
url = {http://eudml.org/doc/252333},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Gouin, Henri
AU - Ruggeri, Tommaso
TI - Hamiltonian principle in the binary mixtures of Euler fluids with applications to the second sound phenomena
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/3//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 1
SP - 69
EP - 83
AB - In the present paper we compare the theory of mixtures based on Rational Thermomechanics with the one obtained by Hamilton principle. We prove that the two theories coincide in the adiabatic case when the action is constructed with the intrinsic Lagrangian. In the complete thermodynamical case we show that we have also coincidence in the case of low temperature when the second sound phenomena arises for superfluid Helium and crystals.
LA - eng
KW - Fluid mixtures; Superfluidity; Second sound; Hamiltonian principle; fluid mixtures; superfluidity; second sound
UR - http://eudml.org/doc/252333
ER -

References

top
  1. TRUESDELL, C., Sulle basi della termomeccanica. Nota II. Atti Acc. Lincei Rend. fis., s. 8, v. 21, 1957, 158-166. Zbl0098.21002
  2. MÜLLER, I., A new approach to thermodynamics of simple mixtures. Zeitschrift für Naturforschung, 28a, 1973, 1801. 
  3. HUTTER, K. - MÜLLER, I., On mixtures of relativistic fluids. Helvetica physica Acta, 48, 1975, 675. 
  4. DREYER, W., Zur Thermodynamik von Helium II - Superfluides Helium mit und ohne Wirbellinien als binäre Mischung. Dissertation Technische Universität, Berlin1983. 
  5. MÜLLER, I., Thermodynamics. Pitman, New York1985. Zbl0637.73002
  6. LANDAU, L. - LIFCHSITZ, E., Mécanique des Fluides. Mir, Moscow1971, 418 pp. 
  7. PUTTERMAN, S., Super Fluid Hydrodynamics. Elsevier, New York1974. 
  8. RUGGERI, T., The binary mixtures of Euler fluids: A unified theory of second sound phenomena. In: B. STRAUGHAN - R. GREVE - H. EHRENTRAUT - Y. WANG (eds.), Continuum Mechanics and Applications in Geophysics and the Environment. Springer-Verlag, Berlin2001, 79 pp. MR1882568
  9. GAVRILYUK, S. - GOUIN, H. - PEREPECHKO, YU., Hyperbolic models of homogeneous two-fluid mixtures. Meccanica, 33, 1998, 161-175. Zbl0923.76335MR1626200DOI10.1023/A:1004354528016
  10. GOUIN, H. - GAVRILYUK, S., Hamilton’s principle and Rankine-Hugoniot conditions for general motions of mixtures. Meccanica, 34, 1999, 39-47. Zbl0947.76090MR1683706DOI10.1023/A:1004370127958
  11. GAVRILYUK, S. - GOUIN, H., A new form of governing equations of fluids arising from Hamilton’s principle. Int. J. Eng. Sci., 37 (12), 1999, 1485-1520. Zbl1210.76009MR1709736DOI10.1016/S0020-7225(98)00131-1
  12. GOUIN, H., Variational theory of mixtures in continuum mechanics. Eur. J. Mech. B/Fluids, 9, 1990, 469. Zbl0704.76001MR1075270
  13. MÜLLER, I. - RUGGERI, T., Rational Extended Thermodynamics. 2nd ed., Springer Tracts in Natural Philosophy, 37, Springer-Verlag, New York1998. Zbl0895.00005MR1632151DOI10.1007/978-1-4612-2210-1
  14. RUGGERI, T. - MURACCHINI, A. - SECCIA, L., A Continuum Approach to Phonon Gas and Shape Changes of Second Sound via Shock Waves Theory. Nuovo Cimento D, 16, 1994, 15. 
  15. RUGGERI, T. - MURACCHINI, A. - SECCIA, L., Shock Waves and Second Sound in a Rigid Heat Conductor: A Critical Temperature for NaF and Bi. Phys. Rev. Lett., 64, 1990, 2640. 
  16. RUGGERI, T. - MURACCHINI, A. - SECCIA, L., Second Sound and Characteristic Temperature in Solids. Phys. Rev. B, 54, 1996, 332-339. 
  17. RUGGERI, T. - MURACCHINI, A. - SECCIA, L., Second Sound Propagation in Superfluid Helium via Extended Thermodynamics. Lecture notes WASCOM 2001. MR1953413DOI10.1142/9789812777331_0044
  18. SERRIN, J., Mathematical principles of classical fluid mechanics. Encyclopedia of Physics, vol. VIII/I, Springer-Verlag, Berlin1959, 125-263. MR108116

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.