Thermodynamic Analysis of Adsorption and Line-Tension Contributions to Contact Angles of Small Sessile Droplets

Relations for the contact angles of sessile liquid droplets with axially symmetric or cylindrical shapes and different equilibrium sizes have been considered using a general thermodynamic approach. For a multicomponent system comprising a liquid droplet, a vapor–gas medium, and a solid substrate, influence of dependence of the surface tension on the chemical potentials related to equilibrium droplet size (i.e., the effect of adsorption) and the effect of size-dependent line tension on the contact angles have been discussed. It has been shown that, for an axially symmetric sessile droplet, the effects of adsorption and line tension are, in the general case, comparable and manifest themselves already at the first order with respect to the droplet curvature. For a cylindrical droplet, the effect of adsorption is observed already in the first order with respect to the droplet curvature, while the influence of the line tension manifests itself only in the second order and is governed by the droplet-size dependence of the line tension.