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The duality between deformations of elastic bodies and non-inertial flows inviscous liquids has been a guiding principle in decades of research. However,this duality is broken when a spheroidal or other doubly-curved liquid film issuddenly forced out of mechanical equilibrium, as occurs e.g. when the pressureinside a liquid bubble drops rapidly due to rupture or controlled evacuation.In such cases the film may evolve through a non-inertial yetgeometrically-nonlinear surface dynamics, which has remained largelyunexplored. We reveal the driver of such dynamics as temporal variations in thecurvature of the evolving surface. Focusing on the prototypical example of afloating bubble that undergoes rapid depressurization, we show that the bubblesurface evolves via a topological instability and a subsequent frontpropagation, whereby a small planar zone nucleates and expands in thespherically-shaped film, bringing about hoop compression and triggeringanother, symmetry-breaking instability and radial wrinkles that grow inamplitude and invade the flattening film. Our analysis reveals the dynamics asa non-equilibrium branch of "Jellium" physics, whereby a rate-of-change ofsurface curvature in a viscous film is akin to charge in an electrostaticmedium that comprises polarizable and conducting domains. We explain keyfeatures underlying recent experiments and highlight a qualitativeinconsistency between the prediction of linear stability analysis and theobserved "wavelength" of surface wrinkles. Our analysis points to the existenceof a nonlinear curvature-driven mechanism for pattern selection in viscousflows.

How viscous bubbles collapse: topological and symmetry-breaking instabilities in curvature-driven hydrodynamics