Equilibrium Shape of Droplets at the Wetted Surface in Strong Gravitational Fields

Abstract

In this work, we develop a novel model describing the equilibrium shape of sessile droplets on a wetted horizontal surface in a gravitational field. The model takes into account the intermolecular Lenard-Jones forces between solid and the liquid molecules using the standard disjoining pressure approximation. These forces lead to the formation of a thin, non-removable fluid layer covering the solid substrate. Balancing the disjoining pressure against the surface tension and the gravitational force we calculate the smooth shape of the surface of the liquid. We obtain a criterion when the gravitational forces are so large that they level the droplets completely. We show that, in the case of weak gravitational forces, the maximum height of the droplets is described by the classical Quincke formula.