On the shape and stability of a drop on a solid surface

The shape and stability of a liquid drop on a bare planar solid surface are analyzed by minimizing its total potential energy calculated microscopically. The solution of the obtained differential equation for the drop profile shows that there is a rapid variation of the angle between the tangent to the profile and the solid surface in the region near the leading edge. At the leading edge, this angle is equal to 180degrees and is independent of the interaction parameters and drop size. For a large droplet, the profile of which is close to a circular one everywhere except in the microscopically small region near the solid surface, a macroscopic contact angle theta(m) is introduced, which is identified as the experimentally measured contact angle. The following simple expression was derived for this angle: cos theta(m) = (a - 2)/2, where a depends on the microscopic parameters of the intermolecular interactions (see section III.D for details). For cylindrical droplets, an analytical criterion was found that connects the droplet stability to the parameters involved in the interaction potentials. Two different domains of stability were identified. In the first one, a liquid droplet is stable for any height, y(m), defined as the distance of its apex from the solid surface. The drop profile of large drops sufficiently far from the solid surface is close to circular with a rapid variation of curvature near the solid surface. In the second domain, the drop height y(m) is limited by a critical value y(m,c). If y(m) is close to but less than y(m,c), the drop has a planar shape. If y(m) > y(m,c), no drop can exist. Similar features were established numerically for axisymmetrical drops and compared to those of cylindrical drops.