Contact line stability at edges: Comments on Gibbs’s inequalities

Abstract

In his discussion of contact line equilibrium for a system comprising two liquids and a solid, Gibbs [Scientific Papers (Dover, New York, 1961), Vol. 1, p. 326] used an argument that resulted in two inequalities he claimed to be applicable when the three-phase contact line coincides with an edge on the solid surface. A simple counterexample is given that shows Gibbs’s inequalities lack universal applicability. A serious objection to Gibbs’s argument is noted and his discussion is altered to remove the objectionable feature. This leads to modified inequalities, which surprisingly are known and have been attributed to Gibbs by recent authors.