  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.
