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The Rayleigh-Plesset equation in terms of volume with explicit shear losses

The Rayleigh-Plesset equation in terms of volume with explicit shear losses
The Rayleigh-Plesset equation in terms of volume with explicit shear losses
The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh–Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called ‘radius frame’). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh–Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the ‘radius frame’ Rayleigh–Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a ‘volume frame’ version of the Rayleigh–Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the ‘radius frame’ Rayleigh–Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.
cavitation, Rayleigh–Plesset, viscous damping, bubbles, parametric sonar, difference frequency
0041-624X
85-90
Leighton, T.G.
3e5262ce-1d7d-42eb-b013-fcc5c286bbae
Leighton, T.G.
3e5262ce-1d7d-42eb-b013-fcc5c286bbae

Leighton, T.G. (2008) The Rayleigh-Plesset equation in terms of volume with explicit shear losses. Ultrasonics, 48 (2), 85-90. (doi:10.1016/j.ultras.2007.10.004).

Record type: Article

Abstract

The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh–Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called ‘radius frame’). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh–Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the ‘radius frame’ Rayleigh–Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a ‘volume frame’ version of the Rayleigh–Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the ‘radius frame’ Rayleigh–Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.

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More information

Submitted date: 5 March 2007
Published date: April 2008
Keywords: cavitation, Rayleigh–Plesset, viscous damping, bubbles, parametric sonar, difference frequency

Identifiers

Local EPrints ID: 51040
URI: https://eprints.soton.ac.uk/id/eprint/51040
ISSN: 0041-624X
PURE UUID: c937fa9b-e762-4481-a796-8efdeaed712c
ORCID for T.G. Leighton: ORCID iD orcid.org/0000-0002-1649-8750

Catalogue record

Date deposited: 01 May 2008
Last modified: 07 Aug 2019 00:52

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Author: T.G. Leighton ORCID iD

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