Gravitational effect on the equilibrium contact angles of sessile droplets: Theory and simulations

Abstract

This study extends the investigation of the wetting phenomenon to larger droplets on a smooth solid substrate, where gravitational effects become significant. We examine three distinct droplet geometries: a spherical cap, an oblate spheroidal cap, and a pancake shape, and we observe that the approximated droplet shape depends on the droplet size and the interfacial tensions. For small droplets on a smooth solid substrate, the droplet shape is assumed to be a spherical cap. However, as the droplet size increases, the equilibrium shape of the droplet becomes deformed due to the effect of gravity. The actual equilibrium contact angles, here referred to as microscopic contact angles, are determined by Young’s law and are independent of droplet size or axisymmetric shape. Macroscopic contact angles are obtained by approximating the droplet shape with a geometric model and minimizing the free energy without assuming the validity of Young’s law. We extend this concept to larger droplets and systematically compare these macroscopic angles with the microscopic ones. Our results demonstrate a correlation between the macroscopic contact angle and droplet size, with significant deviations from Young’s law, increasing with droplet size. These findings are consistent with the Allen–Cahn model. Furthermore, we highlight the impact of the chosen measurement method on the accuracy of the contact angle, which varies with droplet size. In addition, the contact angle hysteresis—caused by varying liquid–solid and solid–gas interfacial tensions, which describes an intermolecular rearrangement of the liquid and gas species in an adsorption layer on the microscopic scale—is also influenced by the droplet size.