Drop Formation: From Dripping Faucets to Nanojets

We owe the ubiquitous presence of drops in daily life, science, and technology to surface tension. When a drop falls from a faucet, surface tension drives an increasingly rapid motion of the fluid neck down to a radius of molecular size. Because of the absence of any characteristic scale, one finds self-similar solutions of the equations of motion, independent of initial conditions. This universality imposes powerful constraints on the manner in which drops form. As a function of time the minimum radius follows different scaling regimes, all of which have by now been confirmed experimentally. Simplified asymptotic equations, along with adaptive numerical codes, allow the study of complex phenomena in the pinch region and have aided industrial applications such as nozzle design. On a scale of nanometers, thermal fluctuations take over as the dominant driving force, and once more change the character of the fluid motion.