Pattern formation on the surface of a bubble driven by an acoustic field

Maksimov, A.O. and Leighton, T.G. (2011) Pattern formation on the surface of a bubble driven by an acoustic field. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468 (2137), 57-75. (doi:10.1098/rspa.2011.0366).

Abstract

The final stable shape taken by a fluid–fluid interface when it experiences a growing
instability can be important in determining features as diverse as weather patterns in
the atmosphere and oceans, the growth of cell structures and viruses, and the dynamics
of planets and stars. An example which is accessible to laboratory study is that of an
air bubble driven by ultrasound when it becomes shape-unstable through a parametric
instability. Above the critical driving pressure threshold for shape oscillations, which is
minimal at the resonance of the breathing mode, regular patterns of surface waves are
observed on the bubble wall. The existing theoretical models, which take account only of
the interaction between the breathing and distortion modes, cannot explain the selection
of the regular pattern on the bubble wall. This paper proposes an explanation which is
based on the consideration of a three-wave resonant interaction between the distortion
modes. Using a Hamiltonian approach to nonlinear bubble oscillation, corrections to
the dynamical equations governing the evolution of the amplitudes of interacting surface
modes have been derived. Steady-state solutions of these equations describe the formation
of a regular structure. Our predictions are confirmed by images of patterns observed on
the bubble wall.

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Contributors

Author: T.G. Leighton

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