Skip to main content
    • Aa
    • Aa

Mass transfer effects on linear wave propagation in diluted bubbly liquids

  • D. Fuster (a1) and F. Montel (a2)

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.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. A. Ainslie  & T. G. Leighton 2011 Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble. J. Acoust. Soc. Am. 130 (5), 31843208.

K. Ando , T. Colonius  & C. E. Brennen 2009 Improvement of acoustic theory of ultrasonic waves in dilute bubbly liquids. J. Acoust. Soc. Am. 126, 6974.

K. H. Ardron  & R. B. Duffey 1978 Acoustic wave propagation in a flowing liquid–vapour mixture. Intl J. Multiphase Flow 4 (3), 303322.

R. B. Chapman  & M. S. Plesset 1971 Thermal effects in the free oscillations of gas bubbles. Trans. ASME J. Basic Engng 93, 373376.

S. A. Cheyne , C. T. Stebbings  & R. A. Roy 1995 Phase velocity measurements in bubbly liquids using a fiber optic laser interferometer. J. Acoust. Soc. Am. 97 (3), 16211624.

K. W. Commander  & A. Prosperetti 1989 Linear pressure waves in bubbly liquids: comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732746.

C. Coste , C. Laroche  & S. Fauve 1990 Sound propagation in a liquid with vapour bubbles. Europhys. Lett. 11 (4), 343347.

D. Fuster , G. Hauke  & C. Dopazo 2010 Influence of accommodation coefficient on nonlinear bubble oscillations. J. Acoust. Soc. Am. 128, 510.

Y. Hao  & A. Prosperetti 1999 The dynamics of vapor bubbles in acoustic pressure fields. Phys. Fluids 11 (8), 20082019.

S. W. Kieffer 1977 Sound speed in liquid–gas mixtures: water–air and water–steam. J. Geophys. Res. 82 (20), 28952904.

G. T. Kuster  & M. N. Toksöz 1974 Velocity and attenuation of seismic waves in two-phase media: Part I. Theoretical formulations. Geophysics 39 (5), 587606.

L. D. Landau  & E. M. Lifshitz 1987 Fluid Mechanics. Pergamon.

V. Leroy , A. Strybulevych , J. H. Page  & M. G. Scanlon 2008 Sound velocity and attenuation in bubbly gels measured by transmission experiments. J. Acoust. Soc. Am. 123, 19311940.

R. C  Mecredy  & L. J. Hamilton 1972 The effects of nonequilibrium heat, mass and momentum transfer on two-phase sound speed. Intl J. Heat Mass Transfer 15 (1), 6172.

A. T. Preston , T. Colonius  & C. E. Brennen 2007 A reduced order model of diffusive effects on the dynamics of bubbles. Phys. Fluids 19, 123302,1-19.

A. Prosperetti 1977 Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids. J. Acoust. Soc. Am. 61, 1727.

A. Prosperetti 1982 A generalization of the Rayleigh–Plesset equation of bubble dynamics. Phys. Fluids 25 (3), 409410.

A. Prosperetti 2015 The speed of sound in a gas–vapor bubbly liquid. Interface Focus 20140024, doi:10.1098/rsfs.2015.0024.

A. Prosperetti , L. A. Crum  & K. W. Commander 1988 Nonlinear bubble dynamics. J. Acoust. Soc. Am. 83, 502514.

A. Prosperetti  & Y. Hao 2002 Vapor bubbles in flow and acoustic fields. Ann. N.Y. Acad Sci. 974 (1), 328347.

E. Silberman 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29 (8), 925933.

P. S. Wilson , R. A. Roy  & W. M. Carey 2005 Phase speed and attenuation in bubbly liquids inferred from impedance measurements near the individual bubble resonance frequency. J. Acoust. Soc. Am. 117 (4), 18951910.

D. Z. Zhang  & A. Prosperetti 1997 Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Intl J. Multiphase Flow 23, 425453.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 1
Total number of PDF views: 44 *
Loading metrics...

Abstract views

Total abstract views: 177 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th May 2017. This data will be updated every 24 hours.