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When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension.
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Updated: Feb 23, 2026

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
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Augmented Gibbs-Tolman Model for Surface Tension.

Sukesh Tumram1, K Kesava Rao1, M S Ananth2

  • 1Department of Chemical Engineering, Indian Institute of Science , Bangalore 560012, India.

Langmuir : the ACS Journal of Surfaces and Colloids
|September 2, 2017
PubMed
Summary

This study refines the Gibbs-Tolman model for liquid-vapor systems, improving surface tension predictions for pure liquids and mixtures using an augmented model. The new model shows excellent data correlation, though a negative length parameter remains unexplained.

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Area of Science:

  • Thermodynamics
  • Interfacial phenomena
  • Physical chemistry

Background:

  • The Gibbs-Tolman (GT) model describes liquid-vapor interfaces using a 'surface of tension'.
  • Tolman's work provided expressions for surface tension (σ) and surface location based on pressure profiles.
  • Previous models accounted for interfacial properties but lacked detailed density gradient considerations.

Purpose of the Study:

  • To augment the Gibbs-Tolman model to incorporate density gradients in the interfacial transition zone.
  • To develop and validate a 4-parameter augmented Gibbs-Tolman (AGT) model for predicting surface tension.
  • To address fundamental concerns regarding the Gibbs-Tolman approach and analyze model parameter behavior.

Main Methods:

  • Applied the Gibbs-Tolman model in conjunction with the Lee and Kesler equation of state.
  • Developed an augmented Gibbs-Tolman (AGT) model incorporating density gradient effects.
  • Correlated experimental surface tension data for 152 pure liquids and 57 liquid mixtures.

Main Results:

  • The GT model achieved an absolute average deviation (AAD) of 4.91% for pure liquids and 4.2% for mixtures.
  • The AGT model significantly improved accuracy, yielding AADs of 2.02% for pure liquids and 3.0% for mixtures.
  • Analysis revealed a persistently negative length parameter in the model, the physical origin of which requires further investigation.

Conclusions:

  • The augmented Gibbs-Tolman (AGT) model provides a highly accurate correlation for surface tension in liquid-vapor systems.
  • The AGT model effectively accounts for density gradients, enhancing predictive capabilities over the original GT model.
  • Despite excellent performance, the interpretation of a negative model parameter warrants further theoretical and experimental exploration.