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Mass transfer effects on linear wave propagation in diluted bubbly liquids

Published online by Cambridge University Press:  19 August 2015

D. Fuster  and
F. Montel
D. Fuster*
Affiliation:
Sorbonne Universités, UPMC Université Paris 06, CNRS UMR 7190, Institut Jean le Rond d’Alembert, 75005 Paris, France
F. Montel
Affiliation:
Total SA, CSTJF, Avenue Larribau, 64018 Pau, France
*
†Email address for correspondence: fuster@dalembert.upmc.fr
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Abstract

In this article we investigate the importance of mass transfer effects in the effective acoustic properties of diluted bubbly liquids. The classical theory for wave propagation in bubbly liquids for pure gas bubbles is extended to capture the influence of mass transfer on the effective phase speed and attenuation of the system. The vaporization flux is shown to be important for systems close to saturation conditions and at low frequencies. We derive a general expression for the transfer function that relates bubble radius and pressure changes, solving the linear version of the conservation equations inside, outside and at the bubble interface. Simplified expressions for various limiting situations are derived in order to get further insight about the validity of the common assumptions typically applied in bubble dynamic models. The relevance of the vapour content, the mass transfer flux across the interface and the effect of variations of the bubble interface temperature is discussed in terms of characteristic non-dimensional numbers. Finally we derive the various conditions that must be satisfied in order to reach the low-frequency limit solutions where the phase speed no longer depends on the forcing frequency.

JFM classification

Drops and Bubbles: Bubble dynamics Phase change: Condensation/evaporation Phase change: Phase change
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 598 - 621
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Copyright
© 2015 Cambridge University Press 

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