Universality of satellites in the breakup of a stretched fluid bridge

Abstract: As a fluid object breaks, it often leaves behind satellite fragments. Here we show that satellite formation can follow universal dynamics, leading to robust satellite sizes. Specifically, we consider the breakup of a slowly stretched fluid bridge, which we realize experimentally using a soap-film bubble suspended between two plates. Combining experiments and one-dimensional simulations, we show that a main satellite bubble always forms as the bridge breaks. We discover that the size of the bubble is highly reproducible and can be dramatically increased by stretching the bridge faster or increasing its volume. The satellite size is a simple function of two non-dimensional parameters: the normalized volume of the bridge and the Weber number, measuring inertia due to stretching as compared to surface tension. These observations can be explained by tracing the bridge evolution over a series of dynamical stages in which the bridge: (i) closely follows a sequence of equilibrium bridge configurations; (ii) stretches as it begins to breakup after reaching an unstable equilibrium; and (iii) follows a universal breakup solution. The last stage takes place over a finite region, the corresponding length scale determined by stretching during the previous stage. This length scale controls the satellite size, and the universality of the dynamics makes the system highly reproducible. This work suggests universal satellite formation dynamics may provide a route for understanding satellite bubble sizes in turbulent flows.