The shape of a sessile drop for small and large surface tension

Abstract

Asymptotic solutions for large and small surface tension are developed for the profile of a symmetric sessile drop. The problem for large surface tension (i.e., small Bond number) is a regular perturbation problem, where the solution may be written as a uniformly valid asymptotic expansion. The problem for small surface tension (i.e., large Bond number) is a singular perturbation problem with boundary-layer behaviour in the edge region. The solution is a matched asymptotic expansion, where some care is to be taken for the matching. The respective ranges of validity are established by comparing the asymptotic results with solutions obtained by numerical integration of the full equations.