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Non-equilibrium thermodynamics for surfaces; square gradient theory

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Abstract

We present a systematic procedure to describe fluid-fluid interfaces of multi-component systems out of equilibrium in a clear macroscopic context on a basis of non-equilibrium thermodynamics. The macroscopic description uses, as Gibbs did for equilibrium interfaces, excess densities. Comparing it with the local description which is based on the non-equilibrium square gradient theory, we show that two descriptions are consistent. This implies that out of equilibrium one can still use interfacial excess densities as if they are functions only of the local temperature and chemical potentials. This justifies that the surface is a separate thermodynamic system and is in local equilibrium.

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References

  1. G. Fang, C.A. Ward, Phys. Rev. E 59, 417 (1999)

    Article  ADS  Google Scholar 

  2. V.K. Badam, V. Kumar, F. Durst, K. Danov, Exp. Thermal Fluid Sci. 32, 276 (2007)

    Article  Google Scholar 

  3. J.S. Rowlinson, J. Stat. Phys. 20, 197 (1979), translation of J.D. van derWaals, Verh.-K. Ned. Akad.Wet., Afd. Natuurkd., Eerste Reeks 1, 8 (1893)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 28, 258 (1958)

    Article  ADS  Google Scholar 

  5. A.J.M. Yang, P.D. Fleming, J.H. Gibbs, J. Chem. Phys. 64, 3732 (1976)

    Article  ADS  Google Scholar 

  6. E. Johannessen, D. Bedeaux, Physica A 330, 354 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. K.S. Glavatskiy, D. Bedeaux, Phys. Rev. E 77, 061101, 1 (2008)

    Article  ADS  Google Scholar 

  8. K.S. Glavatskiy, D. Bedeaux, Phys. Rev. E 79, 021608, 1 (2009)

    Article  ADS  Google Scholar 

  9. K.S. Glavatskiy, D. Bedeaux, J. Chem. Phys. 133, 144709 (2010)

    Article  ADS  Google Scholar 

  10. K.S. Glavatskiy, D. Bedeaux, J. Chem. Phys. 133, 234501 (2010)

    Article  ADS  Google Scholar 

  11. K.S. Glavatskiy, Springer Thesis Book Series, Multi-component interfacial transport as described by the square gradient model; evaporation and condensation (Springer, Berlin, 2011)

  12. S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (Dover, London, 1984)

  13. S. Kjelstrup, D. Bedeaux, Non-Equilibrium Thermodynamics of Heterogeneous Systems, Series on Advances in Statistical Mechanics (2008)

  14. A. Røsjorde, D.W. Fossmo, S. Kjelstrup, D. Bedeaux, B. Hafskjold, J. Colloid Interf. Sci. 232, 178 (2000)

    Article  Google Scholar 

  15. J. Xu, S. Kjelstrup, D. Bedeaux, Phys. Chem. Chem. Phys. 8, 2017 (2006)

    Article  Google Scholar 

  16. S. Kjelstrup, D. Bedeaux, I. Inzoli, J-M. Simon, Energy 33, 1185 (2008)

    Article  Google Scholar 

  17. R. Taylor, R. Krishna, Multicomponent Mass Transfer (Wiley, New York, 1993)

  18. B. Hafskjold, Computer Simulations of Thermal Diffusion in Binary Fluid Mixtures, in Thermal non-equilibrium Phenomena in Fluid Mixtures, edited by W. Kohler, S. Wiegand (Springer, 2002)

  19. A. Røsjorde, S. Kjelstrup, D. Bedeaux, B. Hafskjold, J. Colloid Interf. Sci. 240, 355 (2001)

    Article  Google Scholar 

  20. G.D.C. Kuiken, Thermodynamics for Irreversible Processes (Wiley, Chichester, 1994)

  21. S. Kjelstrup, D. Bedeaux, Elements of Irreversible Thermodynamics for Engineers, Int. Centre of Applied Thermodynamics (Instanbul, Turkey, 2001)

  22. D. Bedeaux, A.M. Albano, P. Mazur, Physica A 82, 438 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  23. D. Bedeaux, Adv. Chem. Phys. 64, 47 (1986)

    Article  Google Scholar 

  24. A.M. Albano, D. Bedeaux, Physica A 147, 407 (1987)

    Article  ADS  Google Scholar 

  25. D. Bedeaux, S. Kjelstrup, Proceed. of ECOS 2003 (Copenhagen, 2003)

  26. J.W. Gibbs, The Scientific Papers of J.W. Gibbs (Dover, London, 1961)

  27. Y.P. Pao, Phys. Fluids 14, 306, 1340 (1971)

    MathSciNet  Google Scholar 

  28. J.W. Cipolla Jr., H. Lang, S.K. Loyalka, J. Chem. Phys. 61, 69 (1974)

    Article  ADS  Google Scholar 

  29. D. Bedeaux, L.F.J. Hermans, T. Ytrehus, Physica A 169, 263 (1990)

    Article  ADS  Google Scholar 

  30. D. Bedeaux, J.A.M. Smit, L.F.J. Hermans, T. Ytrehus, Physica A 182, 388 (1992)

    Article  ADS  Google Scholar 

  31. S. Kjelstrup, G. de Koeijer, Chem. Eng. Sci. 58, 1147 (2003)

    Article  Google Scholar 

  32. M.L. Olivier, Development of a non-equilibrium Mass and Heat Transfer Computation in Multiphase Hydrocarbon Mixtures, PhD thesis 134 (NTNU Trondheim, Norway, 2002)

  33. L.J.T.M. Kempers, J. Chem. Phys. 90, 6541 (1989)

    Article  ADS  Google Scholar 

  34. R. Haase, Thermodynamics of Irreversible Processes (Dover, London, 1990)

  35. S. Kjelstrup, T. Tsuruta, D. Bedeaux, J. Colloid Interface Sci. 256, 451 (2002)

    Article  Google Scholar 

  36. J. Ge, S. Kjelstrup, D. Bedeaux, J.-M. Simon, B. Rousseau, Phys., Rev. E 75, 061604 (2007)

    Article  ADS  Google Scholar 

  37. I. Inzoli, S. Kjelstrup, D. Bedeaux, J.-M. Simon, Chem. Eng. Sci. 66, 4533 (2011)

    Article  Google Scholar 

  38. L.V. van der Ham, R. Bock, S. Kjelstrup, Chem. Eng. Sci. 65, 2236 (2010)

    Article  Google Scholar 

  39. K. Glavatskiy, J.G. Pharoah, S. Kjelstrup, J. Memb. Sci. 431, 96 (2013)

    Article  Google Scholar 

  40. K. Glavatskiy, D. Reguera, D. Bedeaux, JCP (submitted)

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Glavatskiy, K., Bedeaux, D. Non-equilibrium thermodynamics for surfaces; square gradient theory. Eur. Phys. J. Spec. Top. 222, 161–175 (2013). https://doi.org/10.1140/epjst/e2013-01833-0

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