the gravitational field. The Young angle is 180° here.

In the last part of this section, we show that the profile determined in the previous subsection from the Laplace equation and Young’s law indeed corresponds to a minimum in the free energy. A convenient method of proving this fact is that of functional differentiation. This derivation [11] of Young’s law and Laplace’s law in the presence of gravity is closely related to the derivation first outlined by Gibbs [4] and later given by Johnson [8] (see also Ref. 9).