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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

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 598 - 621
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© 2015 Cambridge University Press 

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References

Ainslie, M. A. & Leighton, T. G. 2011 Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble. J. Acoust. Soc. Am. 130 (5), 3184–3208.Google Scholar
Ando, K., Colonius, T. & Brennen, C. E. 2009 Improvement of acoustic theory of ultrasonic waves in dilute bubbly liquids. J. Acoust. Soc. Am. 126, 69–74.Google Scholar
Ardron, K. H. & Duffey, R. B. 1978 Acoustic wave propagation in a flowing liquid–vapour mixture. Intl J. Multiphase Flow 4 (3), 303–322.Google Scholar
Chapman, R. B. & Plesset, M. S. 1971 Thermal effects in the free oscillations of gas bubbles. Trans. ASME J. Basic Engng 93, 373–376.Google Scholar
Cheyne, S. A., Stebbings, C. T. & Roy, R. A. 1995 Phase velocity measurements in bubbly liquids using a fiber optic laser interferometer. J. Acoust. Soc. Am. 97 (3), 1621–1624.Google Scholar
Commander, K. W. & Prosperetti, A. 1989 Linear pressure waves in bubbly liquids: comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732–746.Google Scholar
Coste, C., Laroche, C. & Fauve, S. 1990 Sound propagation in a liquid with vapour bubbles. Europhys. Lett. 11 (4), 343–347.CrossRefGoogle Scholar
Fuster, D. & Colonius, T. 2011 Modeling bubble clusters in compressible liquids. J. Fluid Mech. 688, 352–589.Google Scholar
Fuster, D., Conoir, J. M. & Colonius, T. 2014 Effect of direct bubble–bubble interactions on linear-wave propagation in bubbly liquids. Phys. Rev. E 90 (6), 063010.Google Scholar
Fuster, D., Hauke, G. & Dopazo, C. 2010 Influence of accommodation coefficient on nonlinear bubble oscillations. J. Acoust. Soc. Am. 128, 5–10.Google Scholar
Gumerov, N. A., Hsiao, C. T. & Goumilevski, A. G.2001 Determination of the accomodation coefficient using vapor/gas bubble dynamics in an acoustic field. Technical Report 1. California Institute of Technology, DYNAFLOW, Inc., Fulton, MD; see also URL http://gltrs.grc.nasa.gov/GLTRS (last viewed 9 May 2015).Google Scholar
Hao, Y. & Prosperetti, A. 1999 The dynamics of vapor bubbles in acoustic pressure fields. Phys. Fluids 11 (8), 2008–2019.Google Scholar
Hauke, G., Fuster, D. & Dopazo, C. 2007 Dynamics of a single cavitating and reacting bubble. Phys. Rev. E 75, 066310,1-14.Google ScholarPubMed
Hertz, H. 1982 Über die Verdunstug der Flüssigkeiten, Inbesondere des Quecksilbers im lufteren Räume [On the evaporation of fluids, especially of mercury, in vacuum spaces]. Ann. Phys. 17, 177–193.Google Scholar
Kieffer, S. W. 1977 Sound speed in liquid–gas mixtures: water–air and water–steam. J. Geophys. Res. 82 (20), 2895–2904.Google Scholar
Knudsen, M. 1915 Maximum rate of vaporization of mercury. Ann. Phys. 47, 697–705.Google Scholar
Kuster, G. T. & Toksöz, M. N. 1974 Velocity and attenuation of seismic waves in two-phase media: Part I. Theoretical formulations. Geophysics 39 (5), 587–606.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Leroy, V., Strybulevych, A., Page, J. H. & Scanlon, M. G. 2008 Sound velocity and attenuation in bubbly gels measured by transmission experiments. J. Acoust. Soc. Am. 123, 1931–1940.CrossRefGoogle ScholarPubMed
Lynnworth, L. C. 2013 Ultrasonic Measurements for Process Control: Theory, Techniques, Applications. Academic.Google Scholar
Mecredy, R. C  & Hamilton, L. J. 1972 The effects of nonequilibrium heat, mass and momentum transfer on two-phase sound speed. Intl J. Heat Mass Transfer 15 (1), 61–72.CrossRefGoogle Scholar
Preston, A. T., Colonius, T. & Brennen, C. E. 2007 A reduced order model of diffusive effects on the dynamics of bubbles. Phys. Fluids 19, 123302,1-19.Google Scholar
Prosperetti, A. 1977 Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids. J. Acoust. Soc. Am. 61, 17–27.CrossRefGoogle Scholar
Prosperetti, A. 1982 A generalization of the Rayleigh–Plesset equation of bubble dynamics. Phys. Fluids 25 (3), 409–410.CrossRefGoogle Scholar
Prosperetti, A. 2015 The speed of sound in a gas–vapor bubbly liquid. Interface Focus 20140024, doi:10.1098/rsfs.2015.0024.Google Scholar
Prosperetti, A., Crum, L. A. & Commander, K. W. 1988 Nonlinear bubble dynamics. J. Acoust. Soc. Am. 83, 502–514.Google Scholar
Prosperetti, A. & Hao, Y. 2002 Vapor bubbles in flow and acoustic fields. Ann. N.Y. Acad Sci. 974 (1), 328–347.Google Scholar
Sangani, A. S. 1991 A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids. J. Fluid Mech. 232, 221–284.Google Scholar
Saurel, R., Petitpas, F. & Abgrall, R. 2008 Modelling phase transition in metastable liquids: application to cavitating and flashing flows. J. Fluid Mech. 607, 313–350.Google Scholar
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29 (8), 925–933.Google Scholar
Van Wijngaarden, L. 1968 On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33 (3), 465–474.Google Scholar
Wilson, P. S., Roy, R. A. & Carey, W. M. 2005 Phase speed and attenuation in bubbly liquids inferred from impedance measurements near the individual bubble resonance frequency. J. Acoust. Soc. Am. 117 (4), 1895–1910.Google Scholar
Wood, A. B. 1930 A Textbook of Sound. G. Bell and Sons.Google Scholar
Yasui, K. 1997 Alternative model of single sonoluminiscence. Phys. Rev. E 56 (6), 6750–6760.Google Scholar
Zhang, D. Z. & Prosperetti, A. 1997 Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Intl J. Multiphase Flow 23, 425–453.CrossRefGoogle Scholar