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Line tension on approach to a wetting transition

Author

Listed:
  • Taylor, C.M.
  • Widom, B.

Abstract

The region of three-phase contact of a binary fluid system described by a model free energy functional is studied using a mean-field density-functional approach. A first order wetting transition is induced by varying a parameter that is the controlling field variable in the model. The surface tensions of the constituent two-phase interfaces are evaluated for a range of parameter values and used to locate the wetting transition. The behavior of the line tension upon approach to the wetting transition is then determined by numerical solution of the Euler–Lagrange equations for the full three-phase system at each value of the parameter. The line tension is found to converge to a finite value as the contact angle vanishes, with a derivative that is finite with respect to contact angle but divergent with respect to the field variable (parameter), apparently growing as the inverse square root of the difference between the field variable and its value at wetting. Except for a possible logarithmic factor, which could not be discerned at the present level of numerical precision, this would be in accord with the prediction from mean-field theory.

Suggested Citation

  • Taylor, C.M. & Widom, B., 2005. "Line tension on approach to a wetting transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(2), pages 492-504.
    • Handle: RePEc:eee:phsmap:v:358:y:2005:i:2:p:492-504
    DOI: 10.1016/j.physa.2005.03.043
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    References listed on IDEAS

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    1. Indekeu, J.O., 1992. "Line tension near the wetting transition: results from an interface displacement model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 183(4), pages 439-461.
    2. Blokhuis, Edgar M., 1994. "Line tension between two surface phases on a substrate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(3), pages 402-419.
    3. C. Bauer & S. Dietrich, 1999. "Quantitative study of laterally inhomogeneous wetting films," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 10(4), pages 767-779, June.
    4. Kerins, John & Boiteux, Michel, 1983. "Applications of Noether's theorem to inhomogeneous fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(2), pages 575-592.
    5. Dobbs, H.T. & Indekeu, J.O., 1993. "Line tension at wetting: interface displacement model beyond the gradient-squared approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 201(4), pages 457-481.
    Full references (including those not matched with items on IDEAS)

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