Young's law with gravity

Abstract

The observation that Young's law for the contact angle of a liquid droplet on a substrate should continue to hold when the droplet is deformed by gravity is to some extent counter-intuitive, which has led to doubts and controversy in the literature. We show, in agreement with others, that Young's law holds in the presence of gravity. First, in a numerical illustration based on the classic tables by Bashforth and Adams, we see that the system's free energy for a fixed droplet volume is indeed at a minimum when, to within the numerical precision, the contact angle is as given by Young's law. We then give a transparent analytical derivation of Young's law by minimizing the free energy as a functional of the droplet shape with gravity included.