Wetting Effect on Torricelli's Law

This Letter presents an experimental study on the effect of wetting on the draining of a tank through an orifice set at its bottom. The investigation focuses on flows of liquids in the inertial regime through an orifice the size on the order of magnitude of the capillary length. The results show that although the flows always follow a Torricelli-like behavior, wetting strongly affects the speed of drainage. Surprisingly, this speed goes through a minimum as the outside surface of the tank bottom plate changes from hydrophilic to hydrophobic. The maximum effect in slowing down the flows (up to 20%) is obtained for a static wetting angle θ_{s} of about 60°. Experiments suggest that the effect of wetting on the exit flows, very likely, is related to the meniscus that forms at the hole's outlet. A simple model is proposed that estimates the variation of kinetic energy within the meniscus. This model captures the main features of the experimental observations, particularly the nonmonotonic variation of the speed of drainage as a function of θ_{s} with a minimum for a static wetting angle of about 60°.