Skip to main content
Log in

Simplified Model for the Critical Thermal-Conductivity Enhancement in Molecular Fluids

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

This paper reviews the available information for the thermal-conductivity enhancement. This enhancement can be represented by a simplified solution of the mode-coupling theory of critical dynamics with two critical amplitudes and one cutoff wave number as fluid-specific parameters. Using corresponding states, these fluid-specific parameters are correlated in terms of their dependence on the acentric factor. A universal representation of the critical enhancement of the thermal conductivity for a large number of molecular fluids is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. J.V. Sengers, Int. J. Thermophys. 6, 203 (1985)

    Article  ADS  Google Scholar 

  2. M.L. Huber, R.A. Perkins, D.G. Friend, J.V. Sengers, M.J. Assael, I.N. Metaxa, K. Miyagawa, R. Hellmann, E. Vogel, J. Phys. Chem. Ref. Data 41, 033102 (2012)

    Google Scholar 

  3. J.V. Sengers, in Supercritical Fluids: Fundamentals for Application, ed. by E. Kiran, J.M.H. Levelt Sengers (Kluwer, Dordrecht, 1994), p. 231

    Google Scholar 

  4. E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Reference Fluid Thermodynamics and Transport Properties Database (REFPROP)—Version 9.0 (Office of Standards Reference Data, National Institute of Standards and Technology, Gaithersburg, MD, 2010)

  5. G.A. Olchowy, J.V. Sengers, Phys. Rev. Lett. 61, 15 (1988)

    Article  ADS  Google Scholar 

  6. G.A. Olchowy, J.V. Sengers, Int. J. Thermophys. 10, 417 (1989)

    Article  ADS  Google Scholar 

  7. R. Mostert, H.R. van den Berg, P.S. van der Gulik, J.V. Sengers, J. Chem. Phys. 92, 5454 (1990)

    Article  ADS  Google Scholar 

  8. R.A. Perkins, H.M. Roder, D.G. Friend, C.A. Nieto de Castro, Physica A 173, 332 (1991)

    Article  ADS  Google Scholar 

  9. J. Luettmer-Strathmann, J.V. Sengers, G.A. Olchowy, J. Chem. Phys. 103, 7482 (1995)

    Article  ADS  Google Scholar 

  10. S.B. Kiselev, V.D. Kulikov, Int. J. Thermophys. 15, 283 (1994)

    Article  ADS  Google Scholar 

  11. S.B. Kiselev, V.D. Kulikov, Int. J. Thermophys. 18, 1143 (1997)

    Article  ADS  Google Scholar 

  12. S.B. Kiselev, M.L. Huber, Fluid Phase Equilib. 142, 253 (1998)

    Article  Google Scholar 

  13. R. Folk, G. Moser, Phys. Rev. Lett. 75, 2706 (1995)

    Article  ADS  Google Scholar 

  14. J.V. Sengers, R.A. Perkins, M.L. Huber, D.G. Friend, Int. J. Thermophys. 30, 374 (2009)

    Article  ADS  Google Scholar 

  15. K. Kawasaki, Ann. Phys. 61, 1 (1970)

    Article  ADS  Google Scholar 

  16. K. Kawasaki, in Phase Transitions and Critical Phenomena, vol. 5a, ed. by C. Domb, M.S. Green (Academic Press, New York, 1976), p. 165

    Google Scholar 

  17. P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)

    Article  ADS  Google Scholar 

  18. V. Privman, P.C. Hohenberg, A. Ahorony, in Phase Transitions and Critical Phenomena, vol. 14, ed. by C. Domb, M.S. Green (Academic Press, New York, 1991), p. 1

    Google Scholar 

  19. H.C. Burstyn, J.V. Sengers, J.K. Bhattacharjee, R.A. Ferrell, Phys. Rev. A 28, 1567 (1983)

    Article  ADS  Google Scholar 

  20. G. Paladin, L. Peliti, J. Phys. Lett. (Paris) 43, 15 (1982)

    Article  Google Scholar 

  21. G. Paladin, L. Peliti, J. Phys. Lett. (Paris) 45, 289 (1984)

    Article  Google Scholar 

  22. J.K. Bhattacharjee, R.A. Ferrell, R.S. Basu, J.V. Sengers, Phys. Rev. A 24, 1469 (1981)

    Article  ADS  Google Scholar 

  23. H. Hao, R.A. Ferrell, J.K. Bhattacharjee, Phys. Rev. E 71, 021201 (2005)

    Article  ADS  Google Scholar 

  24. R.F. Berg, M.R. Moldover, G.A. Zimmerli, Phys. Rev. E 60, 4079 (1999)

    Article  ADS  Google Scholar 

  25. V. Vesovic, W.A. Wakeham, G.A. Olchowy, J.V. Sengers, J.T.R. Watson, J. Millat, J. Phys. Chem. Ref. Data 19, 763 (1990)

    Article  ADS  Google Scholar 

  26. V. Vesovic, W.A. Wakeham, J. Luettmer-Strathmann, J.V. Sengers, J. Millat, E. Vogel, M.J. Assael, J. Phys. Chem. Ref. Data 15, 33 (1994)

    Google Scholar 

  27. R.A. Perkins, D.G. Friend, H.M. Roder, C.A. Nieto de Castro, Int. J. Thermophys. 12, 965 (1991)

    Article  ADS  Google Scholar 

  28. B.W. Tiesinga, E.P. Sakonidou, H.R. van den Berg, J. Luettmer-Strathmann, J.V. Sengers, J. Chem. Phys. 101, 6944 (1994)

    Article  ADS  Google Scholar 

  29. E.P. Sakonidou, H.R. van den Berg, C.A. ten Seldam, J.V. Sengers, J. Chem. Phys. 105, 10535 (1996)

    Article  ADS  Google Scholar 

  30. K.N. Marsh, R.A. Perkins, M.L.V. Ramires, J. Chem. Eng. Data 47, 932 (2002)

    Article  Google Scholar 

  31. R.A. Perkins, M.L.V. Ramires, C.A. Nieto de Castro, L. Cusco, J. Chem. Eng. Data 47, 1263 (2002)

    Article  Google Scholar 

  32. R.A. Perkins, J. Chem. Eng. Data 47, 1272 (2002)

    Article  MathSciNet  Google Scholar 

  33. A. Laesecke, R.A. Perkins, C.A. Nieto de Castro, Fluid Phase Equilib. 80, 263 (1992)

    Article  Google Scholar 

  34. R. Krauss, J. Luettmer-Strathmann, J.V. Sengers, K. Stephan, Int. J. Thermophys. 14, 951 (1993)

    Article  ADS  Google Scholar 

  35. R. Krauss, V.C. Weiss, T.A. Edison, J.V. Sengers, K. Stephan, Int. J. Thermophys. 17, 731 (1996)

    Article  ADS  Google Scholar 

  36. S.B. Kiselev, J.F. Ely, Fluid Phase Equilib. 252, 57 (2007)

    Article  Google Scholar 

  37. S.B. Kiselev, R.A. Perkins, M.L. Huber, Int. J. Refrig. 22, 509 (1999)

    Article  Google Scholar 

  38. M.L. Huber, R.A. Perkins, A. Laesecke, D.G. Friend, J.V. Sengers, M.J. Assael, I.N. Metaxa, E. Vogel, R. Mareš, K. Miyagawa, J. Phys. Chem. Ref. Data 38, 101 (2009)

    Google Scholar 

  39. R.A. Ferrell, Phys. Rev. Lett. 24, 1169 (1970)

    Article  ADS  Google Scholar 

  40. M.E. Fisher, J. Math. Phys. 5, 944 (1964)

    Article  ADS  Google Scholar 

  41. M.H. Ernst, E.H. Hauge, J.M.J. van Leeuwen, Phys. Lett. A 34, 419 (1971)

    Article  ADS  Google Scholar 

  42. T.R. Kirkpatrick, D. Belitz, J.V. Sengers, J. Stat. Phys. 109, 373 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  43. M.A. Anisimov, S.B. Kiselev, J.V. Sengers, S. Tang, Physica A 188, 487 (1992)

    Article  ADS  Google Scholar 

  44. J.V. Sengers, J.M.H. Levelt Sengers, in Progress in Liquid Physics, ed. by C.A. Croxton (Wiley, New York, 1978), p. 103

    Google Scholar 

  45. A. Pelissetto, E. Vicari, Phys. Rep. 368, 549 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  46. J.V. Sengers, J.G. Shanks, J. Stat. Phys. 137, 857 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  47. M.E. Fisher, S.Y. Zinn, J. Phys. A 31, L629 (1998)

    Article  ADS  Google Scholar 

  48. H. Behnejad, J.V. Sengers, M.A. Anisimov, in Applied Thermodynamics, ed. by A.H. Goodwin, J.V. Sengers, C.J. Peters (IUPAC, RSC Publ., Cambridge, 2010), p. 321

    Chapter  Google Scholar 

  49. J.V. Sengers, J.M.H. Levelt Sengers, Ann. Rev. Phys. Chem. 37, 189 (1986)

    Article  ADS  Google Scholar 

  50. M. Ley-Koo, M.S. Green, Phys. Rev. A 23, 2650 (1981)

    Article  ADS  Google Scholar 

  51. D.G. Friend, H. Ingham, J.F. Ely, J. Phys. Chem. Ref. Data 20, 275 (1991)

    Article  ADS  Google Scholar 

  52. R.A. Perkins, A. Laesecke, M.L.V. Ramires, A. Gurova, L. Cusco, Experimental Thermal Conductivity Values for the IUPAC Round Robin Sample of 1,1,1,2-Tetrafluoroethane (R134a) (National Institute of Standards and Technology, Gaithersburg, MD, 2000)

    Google Scholar 

  53. M.L. Huber, A. Laesecke, R.A. Perkins, Ind. Eng. Chem. Res. 42, 3163 (2003)

    Article  Google Scholar 

  54. E.W. Lemmon, R.T. Jacobsen, Int. J. Thermophys. 25, 21 (2004)

    Article  ADS  Google Scholar 

  55. M.L. Huber, R.A. Perkins, Fluid Phase Equilib. 227, 47 (2005)

    Article  Google Scholar 

  56. R.A. Perkins, M.L. Huber, J. Chem. Eng. Data 51, 898 (2006)

    Article  Google Scholar 

  57. R.A. Perkins, U. Hammerschmidt, M.L. Huber, J. Chem. Eng. Data 53, 2120 (2008)

    Article  Google Scholar 

  58. M.J. Assael, J.A.M. Assael, M.L. Huber, R.A. Perkins, Y. Takata, J. Phys. Chem. Ref. Data 40, 033101 (2011)

    Article  ADS  Google Scholar 

  59. M.J. Assael, I.A. Koini, K.D. Antoniadis, M.L. Huber, I.M. Abdulagatov, R.A. Perkins, J. Phys. Chem. Ref. Data 41, 023104 (2012)

    Article  ADS  Google Scholar 

  60. M.J. Assael, S.K. Mylona, M.L. Huber, R.A. Perkins, J. Phys. Chem. Ref. Data 41, 023101 (2012)

    Article  ADS  Google Scholar 

  61. J.F. Ely, in Applied Thermodynamics, ed. by A.H. Goodwin, J.V. Sengers, C.J. Peters (IUPAC RSC Publ., Cambridge, 2010), p. 135

    Chapter  Google Scholar 

  62. M.A. Anisimov, F. Zhong, M. Barmatz, Low Temp. Phys. 137, 69 (2004)

    Article  ADS  Google Scholar 

  63. M.W. Pestak, M.H.W. Chan, Phys. Rev. B 30, 274 (1984)

    Article  ADS  Google Scholar 

  64. A. Rizi, A. Abbaci, J. Mol. Liq. 171, 64 (2012)

    Article  Google Scholar 

  65. B. Kovalchuk, Experimental Study of the Isochoric Heat Capacity of Argon in the Broad Parameters of State including the Critical Point, Ph.D. Thesis (Oil and Gas Research Institute of the Russian Academy of Sciences, Moscow, 1977)

  66. K.A. Gillis, I.I. Shinder, M.R. Moldover, Phys. Rev. E 70, 021201 (2004)

    Article  ADS  Google Scholar 

  67. H. Güttinger, D.S. Cannell, Phys. Rev. A 24, 3188 (1981)

    Article  ADS  Google Scholar 

  68. A. Kostrowicka Wyczalkowska, K.S. Abdulkadirova, M.A. Anisimov, J.V. Sengers, J. Chem. Phys. 113, 4985 (2000)

    Article  ADS  Google Scholar 

  69. M.A. Anisimov, J.V. Sengers, J.M.H. Levelt Sengers, in Aqueous Systems and Elevated Temperatures and Pressures, ed. by D.A. Palmer, R. Fernández-Prini, A.H. Harvey (Elsevier, Amsterdam, 2004), p. 29

    Chapter  Google Scholar 

  70. N.G. Polikhronidi, I.M. Abdulagatov, J.W. Magee, G.V. Stepanov, Int. J. Thermophys. 23, 745 (2002)

    Article  Google Scholar 

  71. P.C. Albright, T.J. Edwards, Z.Y. Chen, J.V. Sengers, J. Chem. Phys. 87, 1717 (1987)

    Article  ADS  Google Scholar 

  72. I.M. Abdulagatov, N.G. Polikhronidi, R.G. Batyrova, J. Chem. Thermodyn. 26, 1031 (1994)

    Article  Google Scholar 

  73. A. Kostrowicka Wyczalkowska, J.V. Sengers, J. Chem. Phys. 111, 1551 (1999)

    Article  ADS  Google Scholar 

  74. A. Haupt, J. Straub, Phys. Rev. E 59, 1795 (1999)

    Article  ADS  Google Scholar 

  75. S.B. Kiselev, J.C. Rainwater, Fluid Phase Equilib. 141, 129 (1997)

    Article  Google Scholar 

  76. T.A. Edison, J.V. Sengers, Int. J. Refrig. 22, 365 (1999)

    Article  Google Scholar 

  77. S.B. Kiselev, J.V. Sengers, Int. J. Thermophys. 14, 1 (1993)

    Article  ADS  Google Scholar 

  78. R.T. Jacobsen, M. Jahangiri, R.B. Stewart, R.D. McCarty, J.M.H. Levelt Sengers, H.J. White, J.V. Sengers, G.A. Olchowy, Ethylene (Ethene), International Thermodynamic Table of the Fluid State, vol. 10 (Blackwell Scientific, Oxford, 1988), pp. 67–77

    Google Scholar 

  79. A. Abbaci, A. Berrezeg, Int. J. Thermophys. 25, 739 (2004)

    Article  ADS  Google Scholar 

  80. J. Luettmer-Strathmann, S. Tang, J.V. Sengers, J. Chem. Phys. 97, 2705 (1992)

    Article  ADS  Google Scholar 

  81. A. Abbaci, J. Mol. Liq. 118, 31 (2005)

    Article  Google Scholar 

  82. A.V. Voronel, V.G. Gorbunova, V.A. Smirnov, N.G. Shamakov, V.V. Shekochikhina, Russ. J. Exp. Theor. Phys. 63, 965 (1972)

    Google Scholar 

  83. I.M. Abdulagatov, N.G. Polikhronidi, T.J. Bruno, R.G. Batyrova, G.V. Stepanov, Fluid Phase Equilib. 263, 71 (2008)

    Article  Google Scholar 

  84. S.B. Kiselev, J.F. Ely, I.M. Abdulagatov, A.R. Bazaev, J.W. Magee, Ind. Eng. Chem. Res. 41, 1000 (2002)

    Article  Google Scholar 

  85. S.B. Kiselev, Fluid Phase Equilib. 128, 1 (1997)

    Article  Google Scholar 

  86. K.I. Amirkhanov, B.G. Alibekov, D.I. Vikhrov, V.A. Mirskaya, Isochoric Heat Capacity and Other Caloric Properties of Hydrocarbons (Dagestan Center of the Russian Academy of Sciences, Makhachkala, 1981)

    Google Scholar 

  87. J.T. Wang, M.A. Anisimov, Phys. Rev. E 75, 051107 (2007)

    Article  ADS  Google Scholar 

  88. I.M. Abdulagatov, A.R. Bazaev, J.W. Magee, S.B. Kiselev, J.F. Ely, Ind. Eng. Chem. Res. 44, 1986 (2005)

    Google Scholar 

  89. S. Azzouz, A. Rizi, A. Acidi, A. Abbaci, St. Cerc. St. CIC BIA 11, 236 (2010)

    Google Scholar 

  90. N.G. Polikhronidi, I.M. Abdulagatov, R.G. Batyrova, Fluid Phase Equilib. 201, 269 (2002)

    Article  Google Scholar 

  91. S. Tang, G.X. Jin, J.V. Sengers, Int. J. Thermophys. 12, 515 (1991)

    Article  ADS  Google Scholar 

  92. S. Tang, G.X. Jin, J.V. Sengers, Int. J. Thermophys. 16, 1027 (1995)

    Article  ADS  Google Scholar 

  93. S.B. Kiselev, M.L. Huber, Int. J. Refrig. 21, 64 (1998)

    Article  Google Scholar 

  94. A. van Pelt, J.V. Sengers, J. Supercrit. Fluids 8, 81 (1995)

    Article  Google Scholar 

  95. R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, 4th edn. (McGraw Hill, New York, 1987), pp. 656–732

    Google Scholar 

  96. A.A. Gerasimov, Bull. Kaliningrad State University 3, 30 (2003)

    Google Scholar 

  97. Z.Y. Chen, A. Abbaci, S. Tang, J.V. Sengers, Phys. Rev. A 42, 4470 (1990)

    Article  ADS  Google Scholar 

  98. R. Tufeu, B. Le Neindre, Int. J. Thermophys. 8, 283 (1987)

    Article  ADS  Google Scholar 

  99. J.C. Nieuwoudt, B. Le Neindre, B. Tufeu, J.V. Sengers, J. Chem. Eng. Data 32, 1 (1987)

    Article  Google Scholar 

  100. P.M. Mathias, V.S. Parekh, E.J. Miller, Ind. Eng. Chem. Res. 41, 989 (2002)

    Article  Google Scholar 

  101. J. Luettmer-Strathmann, J.V. Sengers, J. Chem. Phys. 104, 3026 (1996)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We acknowledge stimulating discussions with Mikhail A. Anisimov and Allan H. Harvey. The support of Daniel G. Friend and of Michael Frenkel has also been much appreciated.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. A. Perkins.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perkins, R.A., Sengers, J.V., Abdulagatov, I.M. et al. Simplified Model for the Critical Thermal-Conductivity Enhancement in Molecular Fluids. Int J Thermophys 34, 191–212 (2013). https://doi.org/10.1007/s10765-013-1409-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-013-1409-z

Keywords

Navigation