Application of the variational calculus to wetting phenomena in chemical engineering

Abstract

The problem of determining the equilibrium shape of a wetting meniscus is proposed as a rich example of application of the variational method. The problem describes a common-place phenomena that is conceptually simple and physically tangible for undergraduate students. The proposal has the further appeal in that it illustrates how more abstract variational boundary equations can be implemented. It also represents a system that gives rise to both stable (minimum) and unstable (maximum) wetting profiles, and by utilizing these it leads to a criterion earmarking eventual existence limits of solutions of the variational equations.