RSS feeds
РусскийEnglish
Issue 10, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1998

 / 

April

←  →

Reviews of topical problems


Non-equilibrium thermodynamics and kinetic theory of rarefied gases

 a,  b
a Moscow State Engineering Physics Institute (State University), Kashirskoe shosse 31, Moscow, 115409, Russian Federation
b Institute of Physical Chemistry, Russian Academy of Sciences, Leninsky prosp. 31, Moscow, 119991, Russian Federation

The relation between the non-equilibrium thermodynamics and kinetic theory of rarefied gases is discussed. The phenomenological equations of generalized non-equilibrium thermodynamics are formulated using the fundamental relations of kinetic theory. Using the approach developed, the non-equilibrium thermodynamics of a multicomponent gas mixture are formulated for the moment method and Burnett approximation and the boundary conditions including the slip and jump effects are derived for slightly rarefied gases. An application to transport processes in discontinuous systems and gas flows over solid bodies is also made.

Fulltext pdf (455 KB)
Fulltext is also available at DOI: 10.1070/PU1998v041n04ABEH000383
PACS: 05.70.Ln
DOI: 10.1070/PU1998v041n04ABEH000383
URL: https://ufn.ru/en/articles/1998/4/b/
000074653300002
Citation: Zhdanov V M, Roldugin V I "Non-equilibrium thermodynamics and kinetic theory of rarefied gases" Phys. Usp. 41 349–378 (1998)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Жданов В М, Ролдугин В И «Неравновесная термодинамика и кинетическая теория разреженных газов» УФН 168 407–438 (1998); DOI: 10.3367/UFNr.0168.199804b.0407

References (156) ↓ Cited by (44) Similar articles (20)

  1. Chapman S, Cowling T Mathematical Theory of Non-Uniform Gases (Cambridge: Cambridge Univ. Press, 1952) [Translated into Russian (Moscow: Inostrannaya Literatura, 1960)]
  2. Grad H Commun. Pure Appl. Math. 2 331 (1949)
  3. De Groot S R, Mazur P Nonequilibrium Thermodynamics (Amsterdam: North-Holland, 1962) [Translated into Russian (Moscow: Mir, 1964)]
  4. Müller I Z. Phys. 198 329 (1967)
  5. Müller I, Ruggery T Extended Thermodynamics (New York: Springer-Verlag, 1992)
  6. Lebon G Bull. Acad. R. Soc. Belg. 64 456 (1978)
  7. Jou D, Casas-Vazquez J, Lebon G Rep. Prog. Phys. 51 1105 (1988)
  8. Jou D, Casas-Vazquez J, Lebon G Extended Irreversible Thermodynamics (Berlin, New York: Springer, 1993)
  9. Eu B C Kinetic Theory and Irreversible Thermodynamics (New York: Wiley, 1992)
  10. Prigogine I Physica 15 272 (1949)
  11. McLennan J A Phys. Rev. A 10 1272 (1974)
  12. Grad H "Principles of the kinetic theory of gases", in Thermodynamik der Gase (Handbuch der Physik, Bd. 12, Ed. S Flugge, Berlin: Springer-Verlag, 1958) p. 205
  13. Fox R F, Uhlenbeck G E Phys. Fluids 13 2881 (1970)
  14. Wang Chang C S, Uhlenbeck G E, in Studies in Statistical Mechanics Vol. 5 (Eds J de Boer, G E Uhlenbeck, Amsterdam: North Holland, 1970)
  15. Waldmann L "Transportercheinungen in Gasen von mittlerem Druck", in Thermodynamik der Gase (Handbuch der Physik, Bd. 12, Ed. S Flugge, Berlin: Springer-Verlag, 1958) p. 295
  16. Wang Chang C S, Uhlenbeck G E Project M999 (University of Michigan, 1952)
  17. Onsager L Phys. Rev. 37 405; 38 2265 (1931)
  18. Casimir H B G Rev. Mod. Phys. 17 343 (1945)
  19. Keizer J Statistical Thermodynamics of Nonequilibrium Processes (New York, Berlin: Springer-Verlag, 1987) [Translated into Russian (Moscow: Mir, 1990)]
  20. Zhdanov V, Kagan Yu, Sazykin A Zh. Eksp. Teor. Fiz. 42 857 (1962) [Sov. Phys. JETP 15 596 (1962)]
  21. Waldmann L, Vestner H Physica A 80 523 (1975)
  22. Roldughin V I Dokl. Akad. Nauk SSSR 263 606 (1982) [Sov. Phys. Dokl. 27 244 (1982)]
  23. Roldughin V I J. Non-Equilib. Thermodyn. 9 71 (1984)
  24. Kuscer I Physica A 133 397 (1985)
  25. Hubmer G F, Titulaer U M J. Stat. Phys. 50 913 (1988)
  26. Zhdanov V M, Roldughin V I Zh. Eksp. Teor. Fiz. 109 1267 (1996) [JETP 82 683 (1996)]
  27. Velasko R M, Garcia-Colin L S J. Stat. Phys. 69 217 (1992)
  28. Klimontovich Yu L Teor. Mat. Fiz. 92 312 (1992)
  29. Klimontovich Yu L Neravnovesnaya Statisticheskaya Termodinamika Otkrytykh Sistem (Nonequilibrium Statistical Thermodynamics of Open Systems, Moscow: Yanus, 1995)
  30. Klimontovich Yu L Usp. Fiz. Nauk 167 23 (1997) [Phys. Usp. 40 21 (1997)]
  31. Waldmann L Z. Naturforsch. A 22 1269 (1967)
  32. Vestner H, Kübel M, Waldmann L Nuovo Cimento B 25 405 (1975)
  33. Vestner H,Waldmann L Physica A 86 303 (1977)
  34. Roldughin V I J. Non-Equilib. Thermodyn. 16 13 (1991)
  35. Roldughin V I J. Non-Equilib. Thermodyn. 16 285 (1991)
  36. Kuscer I, in Rarefied Gas Dynamics (Weinheim: VCH, 1991) p. 1311
  37. Kramers H A Nuovo Cimento Suppl. 6 297 (1949)
  38. McCourt F R W et al. Non-Equilibrium Phenomena in Polyatomic Gases Vol. 1, 2 (Oxford: Clarendon Press, 1990, 1991)
  39. Kogan M N Dinamika Razrezhennogo Gaza (Rarefied Gas Dynamics, Moscow: Nauka, 1967) [Translated into English (New York: Plenum Press, 1969)]
  40. Cercignani C Theory and Application of Boltzmann Equation (Edinburgh, London: Scottish Academic Press, 1975) [Translated into Russian (Moscow: Mir, 1978)]
  41. Lifshitz E M, Pitaevskiî L P Fizicheskaya Kinetika (Physical Kinetics, Moscow: Nauka, 1979) [Translated into English (Oxford: Pergamon Press, 1981)]
  42. Grad H Phys. Fluids 6 147 (1963)
  43. Waldmann L Z. Naturforsch. A 32 521 (1977)
  44. Bakanov S P, Roldughin V I Prikl. Mat. Mekh. 41 651 (1977)
  45. Roldughin V I Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza (6) 157 (1983)
  46. Roldughin V I J. Non-Equilib. Thermodyn. 20 230 (1995)
  47. Landau L D, Lifshitz E M Gidrodinamika (Hydrodynamics, Moscow: Nauka, 1986) [Translated into English (Oxford: Pergamon Press, 1990)]
  48. Ferziger J H, Kaper H G Mathematical Theory of Transport Processes in Gases (Amsterdam: North-Holland, 1972) [Translated into Russian (Moscow: Mir, 1976)]
  49. Churaev N V, Sobolev V D, Somov A N J. Colloid Interface Sci. 97 524 (1984)
  50. Derjaguin B V, Churaev N V Langmuir 3 607 (1987)
  51. Sone Y, in Rarefied Gas Dynamics Vol. 1 (New York: Academic Press, 1969) p. 269
  52. Sone Y, in Rarefied Gas Dynamics Vol. 2 (Pisa: ETS, 1971) p. 737
  53. Sone Y, in Rarefied Gas Dynamics (Tokyo: Univ. of Tokyo Press, 1984) p. 71
  54. Sone Y, in Advances in Kinetic Theory and Continuum Mechanics (Berlin: Springer-Verlag, 1991) p. 19
  55. Sone Y, Aoki K Phys. Fluids 20 571 (1977)
  56. Aoki K, Inamuro T, Onishi Y J. Phys. Soc. Jpn. 47 663 (1979)
  57. Maxwell J C Philos. Trans. R. Soc. London Ser. B 170 231 (1879)
  58. Zhdanov V M Zh. Tekh. Fiz. 37 192 (1967) [Sov. Phys. Tech. Phys. 12 (1, 1967)]
  59. Zhdanov V M Zh. Eksp. Teor. Fiz. 53 2099 (1967)
  60. Loyalka S K Phys. Fluids 14 2291 (1971)
  61. Lang H, Loyalka S K Z. Naturforsch. A 27 1307 (1972)
  62. Cercignani C, Pagani C D Phys. Fluids 9 1167 (1966)
  63. Lang H Acta Mechanica 5 163 (1968)
  64. Deryagin B V, Bakanov S P Dokl. Akad. Nauk SSSR 141 384 (1961)
  65. Deryagin B V, Bakanov S P Dokl. Akad. Nauk SSSR 144 535 (1962) [Sov. Phys. Dokl. 7 420 (1962)]
  66. Brock J R J. Colloid Interface Sci. 20 570 (1965)
  67. Yalamov Yu I, Ivchenko I N Zh. Fiz. Khim. 43 2622 (1969)
  68. Bakanov S P, Deryagin B V, Roldughin V I Dokl. Akad. Nauk SSSR 227 329 (1976) [Sov. Phys. Dokl. 21 152 (1976)]
  69. Bakanov S P, Derjaguin B V, Roldughin V I J. Colloid Interface Sci. 60 172 (1977)
  70. Lang H Phys. Fluids 19 366 (1976)
  71. Zhdanov A A, Zaznoba V A Prikl. Mat. Mekh. 45 1063 (1981)
  72. Zhdanov V M, Roldughin V I Physica A 184 169 (1992)
  73. Bedeaux D, Albano A M, Mazur P Physica A 82 438 (1976)
  74. Kovac J Physica A 86 1 (1977)
  75. Kovac J Physica A 107 280 (1981)
  76. Wolff P A, Albano A M Physica A 98 491 (1979)
  77. Vodac F Physica A 93 244 (1978)
  78. Halbritter J, Waldmann L Physica A 104 1 (1980)
  79. Vestner H Z. Naturforsch. A 28 869 (1973)
  80. Vestner H Z. Naturforsch. A 28 1554 (1973)
  81. Waldmann L, Rubsamen R Z. Naturforsch. A 27 1025 (1972)
  82. Bertrand G, Prud’Homme R J. Non-Equilib. Thermodyn. 4 1 (1979)
  83. Bedeaux D Adv. Chem. Phys. 64 1027 (1977)
  84. Bakanov S P, Roldughin V I Kolloidn. Zh. 39 1027 (1977)
  85. Bakanov S P, Roldughin V I J. Colloid Interface Sci. 72 428 (1979)
  86. Kuscer I Surf. Sci. 25 225 (1971)
  87. Waldmann L, in Rarefied Gas Dynamics (New York: Academic Press, 1974) p. 431
  88. Waldmann L Phys. Lett. A 61 433 (1977)
  89. Vestner H, Waldmann L Z. Naturforsch. A 34 269 (1979)
  90. Waldmann L, Vestner H Physica A 99 1 (1979)
  91. Bakanov S P, Deryagin B V, Roldugin V I Usp. Fiz. Nauk 129 255 (1979) [Sov. Phys. Usp. 22 813 (1979)]
  92. Zhdanov V M, Roldughin V I Physica A 199 291 (1993)
  93. Zhdanov V M, Roldughin V I Zh. Eksp. Teor. Fiz. 105 321 (1994) [JETP 78 170 (1994)]
  94. Cipolla J W, Lang H, Loyalka S K J. Chem. Phys. 61 69 (1974)
  95. Rowlinson J S, Widom B Molecular Theory of Capillarity (Oxford: Clarendon Press, 1982) [Translated into Russian (Moscow: Mir, 1986)]
  96. Bakanov S P, Roldughin V I Prikl. Mat. Mekh. 60 761 (1996) [J. Appl. Math. Mech. 60 753 (1996)]
  97. Roldughin V I Kolloidn. Zh. 58 381 (1996)
  98. Pao Y Phys. Fluids 14 306 (1971)
  99. Aoki K, Cercignani C Phys. Fluids 26 1163 (1983)
  100. Ytrehus T Phys. Fluids 26 939 (1983)
  101. Cercignani C, Fiszdon W, Frezzotti A Phys. Fluids 28 3237 (1985)
  102. Sone Y, Ohwada T, Aoki K Phys. Fluids A 1 1398 (1989)
  103. Hermans L J F, Beenakker J J M Phys. Fluids 29 4231 (1986)
  104. Bedeaux D, Hermans L J F, Ytrehus T Physica A 169 263 (1990)
  105. Cercignani C, Sernagiotto F Phys. Fluids 9 40 (1966)
  106. Porodnov B T, Suetin P E Zh. Tekh. Fiz. 39 748 (1969)
  107. Loyalka S K J. Chem. Phys. 55 4497 (1971)
  108. Shendalman L H J. Chem. Phys. 51 2483 (1969)
  109. Zhdanov V M, Smirnova R V Zh. Prikl. Mekh. Tekh. Fiz. (5) 103 (1978)
  110. Zhdanov V M, Zaznoba V A Inzh. Fiz. Zh. 45 403 (1983)
  111. Chernyak V G Zh. Prikl. Mekh. Tekh. Fiz. (5) 50 (1978)
  112. Loyalka S K, Storvick T S, Lo S S J. Chem. Phys. 76 4157 (1982)
  113. Chernyak V G, Kalinin V V, Suetin P E Inzh.-Fiz. Zh. 37 91 (1979)
  114. Lang H Phys. Fluids 19 366 (1976)
  115. Ten Bosch B I M, Beenakker J J M, Kuscer I Physica A 123 443 (1984)
  116. Hirschfelder J O, Curtiss C F, Bird R B Molecular Theory of Gases and Liquids (New York: Wiley, 1954) [Translated into Russian (Moscow: Inostrannaya Literatura, 1961)]
  117. Breton J P Physica 50 365 (1970)
  118. Zhdanov V M Adv. Colloid Interface Sci. 66 1 (1996)
  119. Loyalka S K Phys. Fluids 14 2599 (1971)
  120. Zhdanov V M Zh. Prikl. Mekh. Tekh. Fiz. (2) 48 (1982)
  121. Kramers H A, Kistemaker J Physica 10 699 (1943)
  122. Happel J, Brenner H Low Reynolds Number Hydrodynamics(Englewood Cliffs, N.J.: Prentice Hall, 1965) [Translated into Russian (Moscow: Mir, 1976)]
  123. Landau L D, Lifshitz E M Њlectrodinamika Sploshnykh Sred (Electrodynamics of Continuous Media, Moscow: Nauka, 1980) [Translated into English (Oxford, New York: Pergamon, 1984)]
  124. Roldughin V I Kolloidn. Zh. 44 927 (1982)
  125. Roldughin V I Kolloidn. Zh. 45 1134 (1983)
  126. Waldmann L Z. Naturforsch. A 31 1029 (1976)
  127. Waldmann L Z. Naturforsch. A 31 1439 (1976)
  128. Waldmann L Z. Naturforsch. A 32 914 (1977)
  129. Freedlender O G, in Rarefied Gas Dynamics, Proc. 13 Int. Symp. Vol. 1 (New York: Plenum, 1985)
  130. Bishaev A M, Rykov V A Izv. Akad. Nauk SSSR MZhG (6) 140 (1983)
  131. Bishaev A M, Rykov V A Izv. Akad. Nauk SSSR MZhG (6) 106 (1984)
  132. Roldughin V I Kolloidn. Zh. 44 927 (1982)
  133. Sharipov F Physica A 203 437, 457; A 209 457 (1994)
  134. Mason E, Malinauskas A Transport in Porous Media: The Dusty-Gas Model (Amsterdam, New York: Elsevier, 1983) [Translated into Russian (Moscow: Mir, 1986)]
  135. Williams M M R, Loyalka S K Aerosol Science: Theory and Practice (New York: Pergamon Press, 1991)
  136. Talbot L, in Rarefied Gas Dynamics (New York: AIAA, 1981) p. 467
  137. Brock J R, in Aerosol Microphysics. I. Particle Interaction (Berlin: Springer-Verlag, 1980) p. 37
  138. Onishi Y J. Phys. Soc. Jpn. 43 1434 (1977)
  139. Beresnev S A, Chernyak V G, Suetin P E J. Fluid Mech. 176 295 (1987)
  140. Bakanov S P et al. J. Non-Equilib. Thermodyn. 8 75 (1983)
  141. Law W S, Loyalka S K Phys. Fluids 29 3886 (1986)
  142. Aoki K, Sone Y Phys. Fluids 30 2286 (1987)
  143. Beresnev S A, Chernyak V G, Fomyagin G A J. Fluid Mech. 219 405 (1990)
  144. Roldughin V I J. Non-Equilib. Thermodyn. 19 349 (1994)
  145. Bakanov S P, Roldughin V I Kolloidn. Zh. 42 1043 (1980)
  146. Derjaguin B V, Bakanov S P Kolloidn. Zh. 21 377 (1959)
  147. Deryagin B V, Bakanov S P Dokl. Akad. Nauk SSSR 147 139 (1962)
  148. Dukhin S S, Derjaguin B V Élektroforez (Electrophoresis, Moscow: Nauka, 1976)
  149. Derjaguin B V, Yalamov Yu I, in Topics in Current Aerosol Research (New York: Pergamon, 1972) p. 1
  150. Bakanov S P, Roldughin V I Kolloidn. Zh. 39 1027 (1977)
  151. Roldughin V I J. Non-Equilib. Thermodyn. 16 241 (1991)
  152. Brenner H Chem. Eng. Sci. 19 703 (1964)
  153. Brenner H Chem. Eng. Sci. 19 519 (1964)
  154. Velasco R M, Garcia-Colin L S Phys. Rev. A 44 4961 (1991)
  155. Velasco R M, Garcia-Colin L S J. Non-Equilib. Thermodyn. 20 1 (1995)
  156. Garcia-Colin L S Mol. Phys. 86 697 (1995)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions