Capillary instability of soft cylinders: Dynamical selection of nonlinear states

Surface tension plays a key role for phenomena involving liquid interfaces. A prime example is the Rayleigh-Plateau instability, causing a liquid jet to break into droplets in order to minimise the surface energy. Remarkably, a similar capillary instability was observed in soft solids. Here we reveal the intricate morphologies that can be encountered during the capillary collapse of an elastic cylinder, from minimisation of capillary and elastic energy. Subsequently, we show the dynamical selection of the wavelength, which also dictates the final nonlinear state. It is found that near the onset of instability, the shapes resemble a “cylinders-on-a-string” configuration, while as the solid gets softer “beads-on-a-string” are observed — in analogy to the breakup of viscoelastic liquids. Our analysis explains recent experimental and numerical observations, and highlights how surface tension can dictate the mechanics of solids - provided that the solids are sufficiently soft.