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Augmented Gibbs-Tolman Model for Surface Tension

Tumram, Sukesh and Rao, Kesava K and Ananth, MS (2017) Augmented Gibbs-Tolman Model for Surface Tension. In: LANGMUIR, 33 (42). pp. 11687-11697.

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Official URL: http://doi.org/10.1021/acs.langmuir.7b02041


Gibbs developed the thermodynamics of a liquid-vapor system by introducing the idea of a ``dividing surface'' a hypothetical surface that separates the system into two homogeneous phases. The area and curvatures of a conveniently chosen dividing surface, the ``surface of tension'', are used to account for the effects of the smooth variation of properties across the actual transition layer between the phases. Tolman (1948, 1949) considered a more detailed model of the interfacial region and obtained expressions for surface tension (sigma) and the location of the surface of tension. Based on qualitative arguments, Tolman's model introduced a surface of tension, such that the pressure (P) increases from its saturation value (P-sat) to a maximum value (P-max) as the surface is approached from the vapor side and decreases from (P-sat) to its minimum value (P-min) as the surface is approached from the liquid side. Assuming an exponential decay of (P) away from the surface, Tolman obtained an explicit expression for (sigma) in terms of P-sat, P-max, P-min, and two length scales. In the this work, the Gibbs-Tolman (GT) model is used along with the Lee and Kesler (1975) equation of state. The model is augmented to take into account the effect of the density gradient in the transition zone and a 4-parameter augmented model (AGT model) is proposed. The GT and AGT models are shown to fit the data for 152 pure liquids with an absolute average deviation (AAD) of 4.91% and 2.02%, respectively. The corresponding AAD values for 57 liquid mixtures are 4.2% and 3.0% respectively. Arguments are also presented to counter some of the fundamental concerns that have been raised about the GT approach. Although the model correlates the data very well, one of the length parameters turns out to be persistently negative, and the reason for this behavior is not clear.

Item Type: Journal Article
Publication: LANGMUIR
Additional Information: Copy right for this article belongs to the AMER CHEMICAL SOC, 1155 16TH ST, NW, WASHINGTON, DC 20036 USA
Department/Centre: Division of Mechanical Sciences > Chemical Engineering
Date Deposited: 24 Nov 2017 10:05
Last Modified: 21 Feb 2019 08:55
URI: http://eprints.iisc.ac.in/id/eprint/58318

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