Do all glasses empty when turned to the horizontal?

C. Rascón, A.O. Parry, D.G.A.L. Aarts
Universidad Carlos III de Madrid,

Keywords: capillarity, surface tension, contact angle, gravity, Young-Laplace equation


When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counter-intuitive behaviour. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping.