The interplay between inertia and surface tension in the breakup of a fluid bridge


  Anna Frishman  ,  Daniel Lecoanet  
Technion
Princeton University

The shape of the interface between two fluids in equilibrium is dictated by surface tension, as soap bubbles so beautifully demonstrate.
Similarly, a static fluid bridge, like the bridge that forms when a water droplet is held between two fingers, can only take a particular shape: one with a constant mean curvature equal to the pressure inside it. However, for long enough bridges with a given fluid volume, the mean curvature cannot be made constant and an equilibrium shape ceases to exist. Such long bridges can nonetheless be reached if the bridge is stretched, inducing a flow with pressure differences balanced by inertia. This interplay between surface tension and inertia always terminates in a non-linear processes of breakup of the bridge. We combine table-top experiments of a soap film bridge, numerical simulations and theoretical considerations to study the universal features of this breakup process. We find a new effect induced by inertia: in a symmetrically stretched bridge, which always breaks into three parts with a satellite bubble in the middle, the size of the middle bubble grows with inertia. The bubble size, as well as the process of the bubble formation, satisfy scaling laws, which can be reproduced and explained using a one dimensional fluid model in the limit of low inertia.