International Journal of Thermophysics

, Volume 29, Issue 1, pp 423–433 | Cite as

Simplified Gradient Theory Modeling of the Surface Tension for Binary Mixtures

  • H. Lin
  • Y. Y. Duan
  • J. T. Zhang


In this work, the gradient theory was combined with the volume translation Peng-Robinson and Soave Redlich-Kwong equations of state (VTPR and VTSRK EOSs) and the influence parameter correlation to predict the surface tension of binary mixtures. The density profiles of mixtures across the interface were assumed to be linearly distributed to simplify the gradient theory model. The only two inputs of the theory are the Helmholtz free-energy density of the homogeneous fluid and the influence parameter of the inhomogeneous fluid. The VTPR and VTSRK equations of state were applied to determine the Helmholtz free-energy density and the bulk properties. The influence parameter of the inhomogeneous fluid was calculated from a correlation published previously (Lin et al. Fluid Phase Equilib 254:75, 2007). The only adjustable coefficient of the simplified gradient theory was set equal to zero, which made the theory predictive. The surface tension predicted by this model shows good agreement with experimental data for binary non-polar and polar mixtures.


Equation of state Halogenated hydrocarbon Mixtures Simplified gradient theory Surface tension 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Weinaug C.F., Katz D.L. (1943). Ind. Eng. Chem. 35, 239CrossRefGoogle Scholar
  2. 2.
    Macleod D.B. (1923). Trans. Faraday Soc. 19, 38CrossRefGoogle Scholar
  3. 3.
    Sugden S. (1924). J. Chem. Soc. Trans. 125, 32CrossRefGoogle Scholar
  4. 4.
    Sugden S. (1924). J. Chem. Soc. Trans. 125: 1177CrossRefGoogle Scholar
  5. 5.
    Hugill J.A., van Welsenes A.J. (1986). Fluid Phase Equilib. 29, 383CrossRefGoogle Scholar
  6. 6.
    Rice P., Teja A.S. (1982). J. Colloid Interf. Sci. 86, 158CrossRefGoogle Scholar
  7. 7.
    Miqueu C., Broseta D., Satherley J., Mendiboure B., Lachaise J., Graciaa A. (2000). Fluid Phase Equilib. 172, 169CrossRefGoogle Scholar
  8. 8.
    Lin H., Y.Y. Duan, Prediction method for surface tension of HFC and HCFC refrigerants, in Proceedings of International Conference on Energy and the Environment, Shanghai, China (2003)Google Scholar
  9. 9.
    Toxvaerd S. (1972). J. Chem. Phys. 57: 4092CrossRefADSGoogle Scholar
  10. 10.
    Haile J.M., Gray C.G., Gubbins K.E. (1976). J. Chem. Phys. 64: 2569CrossRefADSGoogle Scholar
  11. 11.
    Teixeira P.I., Telo da Gama M.M. (1991). J. Phys.: Condens. Matter 3: 111CrossRefADSGoogle Scholar
  12. 12.
    Winkelmann J. (1994). Ber. Bunsenges. Phys. Chem. 98: 1308Google Scholar
  13. 13.
    Winkelmann J., Brodrecht U., Kreft I. (1994). Ber. Bunsenges. Phys. Chem. 98: 912Google Scholar
  14. 14.
    Fu D., Lu J.F., Liu J.C., Li Y.G. (2001). Chem. Eng. Sci. 56: 6989CrossRefGoogle Scholar
  15. 15.
    Lu J.F., Fu D., Liu J.C., Li Y.G., Fluid Phase Equilib. 194–197, 755 (2002)Google Scholar
  16. 16.
    Lin H., Gradient theory modeling and experimental investigation of the surface tension, Ph.D. thesis, Tsinghua University, Beijing, China, 2006Google Scholar
  17. 17.
    Cahn J.W., Hilliard J.E. (1958). J. Chem. Phys. 28, 258CrossRefADSGoogle Scholar
  18. 18.
    B.S. Carey, The gradient theory of fluid interface, Ph.D. thesis, University of Minnesota, Minnesota, 1979Google Scholar
  19. 19.
    Carey B.S., Scriven L.E., Davis H.T. (1978). AIChE J. 24: 1076CrossRefGoogle Scholar
  20. 20.
    Carey B.S., Scriven L.E., Davis H.T. (1980). AIChE J. 26, 705CrossRefGoogle Scholar
  21. 21.
    Carey B.S., Scriven L.E., Davis H.T. (1978). J. Chem. Phys. 68: 5040CrossRefADSGoogle Scholar
  22. 22.
    Davis H.T., Scriven L.E., Carey B.S., Application of gradient theory to fluid interfaces, Proceedings of 2nd International Conference on Phase Equilibria and Fluid Properties in the Chemical Industry, Dechema, Frankfurt (1980)Google Scholar
  23. 23.
    Lin H., Duan Y.Y. (2005). Fluid Phase Equilib. 233: 194CrossRefGoogle Scholar
  24. 24.
    Lin H., Duan Y.Y., Zhang T., Huang Z.M. (2006). Ind. Eng. Chem. Res. 45: 1829CrossRefGoogle Scholar
  25. 25.
    Zuo Y.X., Stenby E.H. (1996). J. Colloid Interf. Sci. 182, 126CrossRefGoogle Scholar
  26. 26.
    Zuo Y.X., Stenby E.H. (1996). J. Chem. Eng. Jpn. 29, 159CrossRefGoogle Scholar
  27. 27.
    Lin H., Duan Y.Y., Min Q. (2007). Fluid Phase Equilib. 254, 75CrossRefGoogle Scholar
  28. 28.
    Heide R. (1997). Int. J. Refrig. 20, 496CrossRefGoogle Scholar
  29. 29.
    Duan Y.Y., Lin H., Wang Z.W. (2003). J. Chem. Eng. Data 48: 1068CrossRefGoogle Scholar
  30. 30.
    Okada M., Shibata T., Sato Y., Higashi Y. (1999). Int. J. Thermophys. 20: 119CrossRefGoogle Scholar
  31. 31.
    Duan Y.Y., Lin H. (2003). Fluid Phase Equilib. 213, 89CrossRefGoogle Scholar
  32. 32.
    Lin H., Duan Y.Y. (2004). J. Chem. Eng. Data 49, 372CrossRefGoogle Scholar
  33. 33.
    Lin H., Duan Y.Y. (2003). Int. J. Thermophys. 24: 1495CrossRefGoogle Scholar
  34. 34.
    Lin H., Duan Y.Y. (2005). J. Chem. Eng. Data 50, 182CrossRefGoogle Scholar
  35. 35.
    Okada M., Arima T., Hattori M. (1988). J. Chem. Eng. Data 33, 399CrossRefGoogle Scholar
  36. 36.
    Holcomb C.D., Zollweg J.A. (1992). Fluid Phase Equilib. 75, 213CrossRefGoogle Scholar
  37. 37.
    Fuks S., Bellemans A. (1966). Physica 32, 594CrossRefADSGoogle Scholar
  38. 38.
    Sprow F.B., Prausnitz J.M. (1966). Trans. Faraday Soc. 62: 1105CrossRefGoogle Scholar
  39. 39.
    Blagoi Y.P. (1960). Ukr. Fiz. Zh. (Russ. Ed.) 5: 109Google Scholar
  40. 40.
    Saji Y., Okuda T. (1964). Adv. Cryo. Eng. 10: 209Google Scholar
  41. 41.
    Blagoi Y.P., Rudenko N.S. (1959). Lzv. Vyshch. Uchebn. Zav. Fiz. 2: 22Google Scholar
  42. 42.
    Morino Y. (1932). Bull. Inst. Phys. Chem. Res. Jpn. 11: 1018Google Scholar
  43. 43.
    Siskova M., Secova V. (1970). Collect. Czech. Chem. Commun. 35: 2702Google Scholar
  44. 44.
    Siskova M., Erdoes E. (1966). Collect. Czech. Chem. Commun. 31: 2327Google Scholar
  45. 45.
    Konobeev B.I., Lyapin V.V. (1970). Zh. Prikl. Khim. 43, 803Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Key Laboratory for Thermal Science and Power Engineering of MOE, Department of Thermal EngineeringTsinghua UniversityBeijingP.R. China
  2. 2.Division of Thermometry and Materials EvaluationNational Institute of MetrologyBeijingP.R. China

Personalised recommendations