Coupled Transport of Heat and Mass. Theory and Applications

  • S. Kjelstrup Ratkje
  • B. Hafskjold
Part of the Understanding Chemical Reactivity book series (UCRE, volume 18)


One natural and two technical processes with coupled transport of heat and mass are reviewed. The processes are frost heave, freeze concentration of juice, and salt transport in carbon cathode bottoms in the aluminium electrolysis cell. Recent non-equilibrium molecular dynamics simulation results have been used to establish molecular mechanisms of coupled heat and mass transport in liquids. Linear flux-force relationships have been found for extremely large temperature gradients. Use of linear irreversible thermodynamics is therefore Justified for all three practical cases considered here. Two criteria for local equilibrium are reviewed. In particular, local equilibrium was obtained in a liquid or dense gas with a temperature gradient if \( l|\vec \nabla T| \leqslant \delta {\rm T} < 0.05{\rm T}\), where l is the dimension of the local control volume, \( \vec \nabla T\) is the temperature gradient, and δT is the temperature fluctuation in the control volume. This criterion is fulfilled for the subcooled solution in the process of freeze concentration. The energy transported by water moving from a subsurface water table to an ice lens in clay capillaries during frost heave is mainly the enthalpy of freezing of water, lending support to the description of frost heave as a transport process. Similarly, the separation of salts in the cathode bottom of the aluminium electrolysis cell and the formation of salt lenses (bottom heave) can be understood as a way the system reacts to a temperature gradient in order to transport energy (heat) as effectively as possible. Computer simulations have confirmed the validity of the Onsager reciprocal relations (ORR) in liquids. The application of the ORR for average phenomenological coefficients across interfaces in the systems is discussed.


Heat Flux Local Equilibrium Enthalpy Flux Carbon Cathode Couple Transport 
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  1. 1.
    Førland, K.S., Førland, T. and Ratkje, S.K. (1994) Irreversible Thermodynamics. Theory and Applications, 2. repr. Wiley, Chichester.Google Scholar
  2. 2.
    Ratkje, S.K. and Flesland, O. (1995) J. Food Engng. 25, 553–567.CrossRefGoogle Scholar
  3. 3.
    Nygård, I. and Ratkje, S.K. (1994) Light Metals, Proceed. TMS Ann. Meeting, San Fransico, p.457–461.Google Scholar
  4. 4.
    Bomhorst, W.J. and Hatsopolulos, G.N. (1967) J. Applied Mechanics 840–-Google Scholar
  5. 5.
    Kincaid, J.M., Li, X., and Hafskjold, B. (1992) Fluid Phase Equil. 76, 113–121CrossRefGoogle Scholar
  6. 6.
    Hafskjold, B., Ikeshoji, T., and Ratkje, S.K. (1993) Molec. Phys. 80,1389–1412.CrossRefADSGoogle Scholar
  7. 7.
    Ikeshoji, T. and Hafskjold, B. (1994) Molec. Phys. 81,251–261.CrossRefADSGoogle Scholar
  8. 8.
    Kincaid, J.M. and Hafskjold, B. (1994) Molec. Phys. 82,1099–1114.CrossRefADSGoogle Scholar
  9. 9.
    Hafskjold, B. and Ratkje, S.K. (1995) J. Stat. Phys. 78,463–494.CrossRefzbMATHADSGoogle Scholar
  10. 10.
    Takashi, T., Ohrai, T., Yamamoto, H., and Okamoto, J. (1980) The 2nd. Int. Symp. on Ground Freezing, Trondheim, p. 713–725.Google Scholar
  11. 11.
    Tsuneto, T. (1994) J. Phys. Soc. Japan 63,2231–2234.CrossRefADSGoogle Scholar
  12. 12.
    Huige, N.J.J. (1972) Nucleation and growth of ice crystals from water and sugar solutions in continuous stirred tank crystallizers, Ph.D. thesis, Eindhoven University of Technology, Netherlands.Google Scholar
  13. 13.
    Heldman, D.R. (1992) Food Freezing, in Handbook of Food Engineering, ed. by D.R. Heldman and D.B. Lund, Marcel Dekker, New York.Google Scholar
  14. 14.
    Sørlie, M. and Øye, H.A. (1989) Cathodes in Aluminium Electrolysis, Aluminium Verlag,GmbH, Düsseldorf.Google Scholar
  15. 15.
    Richter, J. and Prüser, U. (1977) Ber. Bunsenges. Phys. Chem. 81,508–514.Google Scholar
  16. 16.
    Lundén, A. and Olsson, J.E. (1968) Z. Naturforsch. 23a,2045–2052.Google Scholar
  17. 17.
    Grimstvedt, A., Ratkje, S.K. and Førland, T. (1994) J. Electrochem. Soc. 141 (1994), 1236–1241.CrossRefGoogle Scholar
  18. 18.
    Siljan, O.J. (1990) Sodium aluminium fluoride attack on alumino-silicate refractories, thesis, Institute of Inorganic Chemistry, The Norwegian Institute of Technology, University of Trondheim, Norway.Google Scholar
  19. 19.
    Evans, D.J. and Morriss, G.P. (1990) Statistical mechanics of nonequilibrium liquids. Academic Press, London.zbMATHGoogle Scholar
  20. 20.
    Cummings, P.P and Evans, D.J. (1992) Ind. Eng. Chem. 31,1237–1252.CrossRefGoogle Scholar
  21. 21.
    MacGowan, D. and Evans, D.J. (1986) Phys. Rev. A 34,2133–2142. See also Evans, D.J. and MacGowan, D. (1987) Phys. Rev. A 36,948-950.CrossRefADSGoogle Scholar
  22. 22.
    Gillan, M.J. (1987) J. Phys. C: Solid State Phys. 20,521–538.ADSCrossRefGoogle Scholar
  23. 23.
    Paolini, G.V. and Ciccotti, G. (1987) Phys. Rev. A 35,5156–5166.CrossRefADSGoogle Scholar
  24. 24.
    Vogelsang, R., Hoheisel, C., Paolini, G.V., and Ciccotti, G. (1987) Phys. Rev. A 36, 3964–3974.CrossRefADSGoogle Scholar
  25. 25.
    Holian, B.L. and Evans, D.J. (1983) J. Chem. Phys. 78,5147–5150.CrossRefADSGoogle Scholar
  26. 26.
    Ashurst, W.T. and Hoover, W.G. (1975) Phys. Rev. A 11,658–678.CrossRefADSGoogle Scholar
  27. 27.
    Kreuzer, H.J. (1981) Nonequilibrium Thermodynamics and its Statistical Foundations., Clarendon, OxfordGoogle Scholar
  28. 28.
    Tenenbaum, A., Ciccotti, G., and Gallico, R. (1982) Phys. Rev. A 25,2778–2787.CrossRefADSGoogle Scholar
  29. 29.
    Haile, J.M. (1992) Molecular dynamics simulations. Elementory methods, John Wiley & Sons, New York.Google Scholar
  30. 30.
    Goodisman, J. (1987) Electrochemistry: Theoretical Foundations, Wiley-Interscience, New YorkGoogle Scholar
  31. 31.
    Legros, J.C., Goemare, P., and Platten, J.K. (1985) Phys. Rev. A 32,1903–1905.CrossRefADSGoogle Scholar
  32. 32.
    Kincaid, J.M., Cohen, E.G.D., and Lopez de Haro. M. (1987) J. Chem. Phys. 86,963–974.CrossRefADSGoogle Scholar
  33. 33.
    Bresme, F., Hafskjold, B., and Wold, I. (1996) J. Phys. Chem. (in press)Google Scholar
  34. 34.
    Tondeur, D. and Kvaalen, E. (1987) Ind. Eng. Chem. Res. 26,56–65.CrossRefGoogle Scholar
  35. 35.
    Ratkje, S.K., Sauar, E., Hansen, E.M., Lien, K.M., and Hafskjold, B. (1995) Ind. Eng. Chem. Res. 34,3001–3007.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • S. Kjelstrup Ratkje
    • 1
  • B. Hafskjold
    • 1
  1. 1.Department of Physical Chemistry, Norwegian Institute of TechnologyUniversity of TrondheimTrondheimNorway

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