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

Pattern formation on the surface of a bubble driven by an acoustic field
Pattern formation on the surface of a bubble driven by an acoustic field
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.
bubble, Faraday ripples, symmetry breaking, pattern formation
1364-5021
57-75
Maksimov, A.O.
2fc9c5f7-530b-4467-8c9d-320dc5a2942f
Leighton, T.G.
3e5262ce-1d7d-42eb-b013-fcc5c286bbae
Maksimov, A.O.
2fc9c5f7-530b-4467-8c9d-320dc5a2942f
Leighton, T.G.
3e5262ce-1d7d-42eb-b013-fcc5c286bbae

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, 468 (2137), 57-75. (doi:10.1098/rspa.2011.0366).

Record type: Article

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.

Full text not available from this repository.

More information

Published date: 17 August 2011
Keywords: bubble, Faraday ripples, symmetry breaking, pattern formation
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 204075
URI: http://eprints.soton.ac.uk/id/eprint/204075
ISSN: 1364-5021
PURE UUID: cb9aaf54-5601-4b55-92fa-eb75a87c3dd9
ORCID for T.G. Leighton: ORCID iD orcid.org/0000-0002-1649-8750

Catalogue record

Date deposited: 23 Nov 2011 15:24
Last modified: 17 Dec 2019 02:00

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