Rippling Instability of a Collapsing Bubble
Rava da Silveira,
1
Sahraoui Chaïeb,
2
L. Mahadevan
2
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.
1 Department of Physics,
2 Department of Mechanical Engineering,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA.