A note on the sessile drop (Q1104830)

The problem considered is that of a drop of liquid resting on a plane, where the angle of contact between the drop surface and the plane is not assumed to be constant. With no assumption on the contact angle, it is shown that the drop surface, when considered from \(z_ 0/2\) to \(z_ 0\), is a graph (here \(z_ 0\) is the maximum height of the drop). When the contact angle is assumed to lie in the interval [0, \(\pi\) /2], the entire drop surface is shown to be a graph. These results also hold in zero gravity, thus applying to surfaces of constant mean curvature.