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Updated: May 11, 2026

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
Published on: August 30, 2019
Triezenberg-Zwanzig expression for the surface tension of a liquid drop
1Colloid and Interface Science, Leiden Institute of Chemistry, Gorlaeus Laboratories, P.O. Box 9502, 2300 RA Leiden, The Netherlands. e.blokhuis@chem.leidenuniv.nl
Abstract:
Formulas, analogous to the Triezenberg-Zwanzig expression for the surface tension of a planar interface, are presented for the Tolman length, the bending rigidity, and the rigidity constant associated with Gaussian curvature. These expressions feature the Ornstein-Zernike direct correlation function and are derived from considering the deformation of a liquid drop in the presence of an external field. This approach is in line with the original analysis by Yvon [in Proceedings of the IUPAP Symposium on Thermodynamics, Brussels, 1948]. It is shown that our expressions reduce to previous results from density functional theory when a mean-field approximation is made for the direct correlation function. We stress the importance of the form of the external field used and show how the values of the rigidity constants depend on it.
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