  The duality between deformations of elastic bodies and non-inertial flows in
viscous liquids has been a guiding principle in decades of research. However,
this duality is broken when a spheroidal or other doubly-curved liquid film is
suddenly forced out of mechanical equilibrium, as occurs e.g. when the pressure
inside a liquid bubble drops rapidly due to rupture or controlled evacuation.
In such cases the film may evolve through a non-inertial yet
geometrically-nonlinear surface dynamics, which has remained largely
unexplored. We reveal the driver of such dynamics as temporal variations in the
curvature of the evolving surface. Focusing on the prototypical example of a
floating bubble that undergoes rapid depressurization, we show that the bubble
surface evolves via a topological instability and a subsequent front
propagation, whereby a small planar zone nucleates and expands in the
spherically-shaped film, bringing about hoop compression and triggering
another, symmetry-breaking instability and radial wrinkles that grow in
amplitude and invade the flattening film. Our analysis reveals the dynamics as
a non-equilibrium branch of "Jellium" physics, whereby a rate-of-change of
surface curvature in a viscous film is akin to charge in an electrostatic
medium that comprises polarizable and conducting domains. We explain key
features underlying recent experiments and highlight a qualitative
inconsistency between the prediction of linear stability analysis and the
observed "wavelength" of surface wrinkles. Our analysis points to the existence
of a nonlinear curvature-driven mechanism for pattern selection in viscous
flows.
