New analytical solutions for static two-dimensional droplets under the effects of long- and short-range molecular forces

Abstract

We report new analytical solutions for the thickness profile of partially wetting two-dimensional droplets. The model includes the effects of capillarity and both short- and long-range molecular forces. We analyze the dependence of the maximum thickness, the contact angle, and the cross-sectional area on the height of the nanometric precursor film that surrounds the droplet. We found asymptotic expressions for the thickness profile and for the contact angles for large and small droplets. The results are compared to those obtained previously for polar liquids. The analytical solutions found here are useful to assess the validity of the hypothesis and the semi-analytical solutions proposed in the literature. In addition, these solutions enable the inference of information about the molecular potential from the measured steady profiles.