FIG. 8 Liquid droplet on a solid substrate in a gravitational field.

In the following, we first derive the shape equations used by Bashforth and Adams [29] to calculate (numerically) the shape of the liquid droplet. After having rewritten the shape equations somewhat, we then supply a schematic program to solve the shape equations numerically using the Runge-Kutta method. Finally, in this section, we show from a functional minimization of the free energy that the profile thus determined from the Laplace equation and Young’s law corresponds to a minimum in the free energy [11].