(677g) Characterizing the Curvature of Liquid-Vapor Interfaces and Its Effect on the Kelvin Equation Using Mean-Field Lattice Density Functional Theory

Characterizing the Curvature of Liquid-Vapor Interfaces and its Effect on the Kelvin Equation using Mean-field Lattice Density Functional Theory

Aaron J. Harrison, Stephen P. Beaudoin, David S. Corti

The Kelvin equation describes the relationship between the system saturation and the curvature of the liquid-vapor interface. It is extensively used to describe nucleation in supersaturated systems [1] , and capillarity in unsaturated systems [2]. However, when describing the curvature of a meniscus between two adhering surfaces, the Kelvin equation is an approximation [3–5] governed by the assumption of a pure-component, incompressible system with bulk properties. Hence, it is unclear how well the Kelvin equation describes the capillary forces between two surfaces, particularly when these surfaces are separated by nanoscale distances.

Using a two-dimensional lattice-gas model and mean-field density functional theory, the effect of meniscus curvature between hydrophilic surfaces on the prediction of the Kelvin equation has been studied. First, the dependence of the surface tension on the curvature of the liquid-vapor interface is established for critical bubbles forming within a bulk liquid. It is demonstrated that for a pure-component, bulk system the Kelvin equation properly describes the curvature of the interface at the Gibbs surface of tension, even for very small bubbles. Next, the system is modified to include parallel, hydrophilic surfaces in between which capillary bridges can form.  The curvature of these capillary bridges are quantified at differing saturation levels and compared to the Kelvin equation. The deviation from the Kelvin equation as the system approaches zero saturation is quantified as a function of the degree of hydrophilicity of the surfaces and the curvature of the interface. For these capillary bridges, it is found that the radius of curvature is not constant (i.e., the meniscus is not circular) and that agreement with the Kelvin equation decreases significantly as the system approaches zero saturation.  Therefore, the Kelvin equation best describes curvatures for pure-component systems or for capillary bridges that are near or at saturation.

[1]      A. W. Adamson and A. P. Gast, Physical Chemistry of Surfaces, 6th ed. New York: John Wiley & Sons, Inc., 1997.

[2]      J. N. Israelachvili, Intermolecular and Surface Forces, Third Edition, 3rd ed. Boston: Academic Press, 2011.

[3]      J. Melrose, “Model calculations for capillary condensation,” AIChE J., vol. 149, no. 1933, pp. 986–994, 1966.

[4]      S. Ono and S. Kondo, “Molecular Theory of Surface Tension in Liquids,” in Structure of Liquids / Struktur der Flüssigkeiten SE  - 2, vol. 3 / 10, Springer Berlin Heidelberg, 1960, pp. 134–280.

[5]      A. Shapiro and E. Stenby, “Kelvin equation for a non-ideal multicomponent mixture,” Fluid Phase Equilib., vol. 134, pp. 87–101, 1997.