(551e) Modeling Surface Tension Using Gibbs'-Tolman Approach
AIChE Annual Meeting
Wednesday, November 16, 2022 - 4:30pm to 4:45pm
To understand the reasons for this anomaly, the Gibbs â Tolman model was modified removing the underlying assumption of zero curvature of the Gibbs dividing surface. An expression for Ï in terms of Psat, Pmin , Pmax and the model parameters Î»v and Î»l , the curvature of the Gibbs dividing surface (c) and the distance between the surface of discontinuity and the surface of tension (yt) is obtained. However, modeling the experimental surface tension values for various compounds, yielded parameters with poor confidence.
Later, a sensitivity analysis on the GT model showed that the length parameters turn positive for a certain range of Pminand Pmax depending on the compound, with Pmax being more sensitive than Pmin . In addition, the original paper by Tolman also  emphasizes that the model requires reliable estimates of Pminand Pmax . Thus, accurate experimental measurements or EoS estimates of Pminand Pmax are necessary for validating the GT model. However, an extensive search in the literature did not provide us any methods to obtain reliable values for the same.
Hence, we propose a rearrangement of terms in the GT model to regress for the more sensitive term (i.e., Pmax) along with the length parameters. The surface tension data for several compounds in the rearranged GT models using suitable EoS yields positive length parameters, as expected. We conclude that the origin of negative length parameters in the previous works was due to unreliable estimates of Pminand Pmax.
 Tumram S, Kesava Rao K, Ananth MS, Augmented Gibbs-Tolman Model for Surface Tension, Langmuir, 33, 11687 (2017
 Tolman RC, The Superficial Density of Matter at a Liquid-Vapor Boundary, Chem. Phys., 17, 118 (1949)