The teapot effect: sheet-forming flows with deflection, wetting and hysteresis

Abstract

The flow of a two-dimensional viscous film falling from the edge of an inclined plane exhibits a distinctive set of phenomena which, in various combinations, have been referred to as the teapot effect. This paper makes plain that three basic mechanisms are at the root of these phenomena: deflection of the liquid sheet by hydrodynamic forces, contact-angle hysteresis, and multiple steady states that give rise to a purely hydrodynamic hysteresis. The evidence is drawn from Galerkin/finite-element analysis of the Navier-Stokes system, matched to a one-dimensional asymptotic approximation of the sheet flow downstream, and is corroborated experimentally by flow visualization and measurements of free-surface profiles and contact line position. The results indicate that the Gibbs inequality condition quantifies the inhibiting effect of sharp edges on spreading of static contact lines, even in the presence of flow nearby. The branchings, turning points, and isolas of families of solutions in parameter space explain abrupt flow transitions observed experimentally, and illuminate the stability of predicted flow states.