Rippling instability of a collapsing Bubble
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Abstract
When a bubble of air rises to the top of a highly viscous liquid, it forms a
dome-shaped protuberance on the free surface. Unlike a soap bubble, it bursts
so slowly as to collapse under its own weight simultaneously, and folds into a
wavy structure. This rippling effect occurs for both elastic and viscous sheets,
and a theory for its onset is formulated. The growth of the corrugation is
governed by the competition between gravitational and bending (shearing)
forces and is exhibited for a range of densities, stiffnesses (viscosities), and
sizes—a result that arises less from dynamics than from geometry, suggesting
a wide validity. A quantitative expression for the number of ripples is presented,
together with experimental results that support the theoretical predictions.