Research Papers: Multiphase Flows

A Generalized Equation for Scattering Cross Section of Spherical Gas Bubbles Oscillating in Liquids Under Acoustic Excitation

[+] Author and Article Information
Yuning Zhang

School of Engineering,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: zhangyn02@gmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 17, 2012; final manuscript received April 2, 2013; published online June 6, 2013. Assoc. Editor: John Abraham.

J. Fluids Eng 135(9), 091301 (Jun 06, 2013) (6 pages) Paper No: FE-12-1578; doi: 10.1115/1.4024128 History: Received November 17, 2012; Revised April 02, 2013

When irradiated by acoustic waves, gas bubbles can generate divergent spherical waves, which are frequently used to detect the sizes and number density of the gas bubbles. In this paper, a generalized equation for scattering cross section of spherical gas bubbles oscillating in liquids under acoustic excitation is proposed. Comparing with formulas in the literature, this generalized equation can improve the predictions of acoustical scattering cross section in the near-resonance region with high ambient pressure and above-resonance region.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Newhouse, V. L., and Shankar, P. M., 1984, “Bubble Size Measurement Using the Nonlinear Mixing of Two Frequencies,” J. Acoust. Soc. Am., 75, pp. 1473–1477. [CrossRef]
Vagle, S., and Farmer, D. M., 1992, “The Measurement of Bubble-Size Distributions by Acoustic Backscatter,” J. Atmos. Oceanic Technol., 9, pp. 630–644. [CrossRef]
Sutin, A. M., Yoon, S. W., Kim, E. J., and Didenkulov, I. N., 1998, “Nonlinear Acoustic Method for Bubble Density Measurements in Water,” J. Acoust. Soc. Am., 103, pp. 2377–2384. [CrossRef]
Lentz, W. J., Atchley, A. A., and Gaitan, D. F., 1995, “Mie Scattering From a Sonoluminescing Air Bubble in Water,” Appl. Opt., 34, pp. 2648–2654. [CrossRef]
Brenner, M. P., Hilgenfeldt, S., and Lohse, D., 2002, “Single-Bubble Sonoluminescence,” Rev. Mod. Phys., 74, pp. 425–484. [CrossRef]
ter Haar, G. R., and Daniels, S., 1981, “Evidence for Ultrasonically Induced Cavitation In Vivo,” Phys. Med. Biol., 26, pp. 1145–1149. [CrossRef]
ter Haar, G., Daniels, S., Eastaugh, K. C., and Hill, C. R., 1982, “Ultrasonically Induced Cavitation In Vivo,” Br. J. Cancer Suppl., 5, pp. 151–155.
Coussios, C. C., and Roy, R. A., 2008, “Applications of Acoustics and Cavitation to Noninvasive Therapy and Drug Delivery,” Annu. Rev. Fluid Mech., 40, pp. 395–420. [CrossRef]
Rubissow, G. J., and Mackay, R. S., 1971, “Ultrasonic Imaging of In Vivo Bubbles in Decompression Sickness,” Ultrasonics, 9, pp. 225–234. [CrossRef]
Jepson, P. D., Arbelo, M., Deaville, R., Patterson, I. A. P., Castro, P., Baker, J. R., Degollada, E., Ross, H. M., Herráez, P., Pocknell, A. M., Rodríguez, F., Howie, F. E., Espinosa, A., Reid, R. J., Jaber, J. R., Martin, V., Cunningham, A. A., and Fernández, A., 2003, “Gas-Bubble Lesions in Stranded Cetaceans,” Nature, 425, pp. 575–576. [CrossRef]
Cox, T. M., Ragen, T. J., Read, A. J., Vos, E., Baird, R. W., Balcomb, K., Barlow, J., Caldwell, J., Cranford, T., Crum, L., D'Amico, A., D'Spain, G., Fernandez, A., Finneran, J., Gentry, R., Gerth, W., Gulland, F., Hildebrand, J., Houser, D., Hullar, T., Jepson, P. D., Ketten, D., Macleod, C. D., Miller, P., Moore, S., Mountain, D., Palka, D., Ponganis, P., Rommel, S., Rowles, T., Taylor, B., Tyack, P., Wartzok, D., Gisiner, R., Mead, J., Llowry, L., and Benner, L., 2006, “Understanding the Impacts of Anthropogenic Sound On Beaked Whales,” J. Cetacean Res. Manage., 7, pp. 77–187.
Crum, L. A., Bailey, M. R., Guan, J., Hilmo, P. R., Kargl, S. G., Matula, T. J., and Sapozhnikov, O. A., 2005, “Monitoring Bubble Growth in Supersaturated Blood and Tissue Ex Vivo and the Relevance to Marine Mammal Bioeffects,” ARLO, 6, pp. 214–220. [CrossRef]
Medwin, H., and Clay, C. S., 1998, Fundamentals of Acoustical Oceanography, Academic Press, NY.
Judd, A. G., 2003, “The Global Importance and Context of Methane Escape from the Seabed,” Geo-Mar. Lett., 23, pp. 147–154. [CrossRef]
Leifer, I., and Tang, D., 2007, “The Acoustic Signature of Marine Seep Bubbles,” J. Acoust. Soc. Am., 121, pp. el35–el40. [CrossRef]
Leifer, I., Roberts, D., Margolis, J., and Kinnaman, F., 2006, “In Situ Sensing of Methane Emissions from Natural Marine Hydrocarbon Seeps: A Potential Remote Sensing Technology,” Earth Planet. Sci. Lett., 245, pp. 509–522. [CrossRef]
Spitzer, L.Jr., 1943, “Acoustic Properties of Gas Bubbles in A Liquid,” OSRD Report No. 1705, Division of War Research, Columbia University, New York.
Wildt, R., 1946, “Acoustic Theory of Bubbles,” Physics of Sound in the Sea, Vol. 8, NDRC Summary Technical Report Div. 6, Washington, D.C., pp. 460–477.
Andreeva, I. B., 1964, “Scattering of Sound by Air Bladders of Fish in Deep Sound Scattering Ocean Layers,” Sov. Phys. Acoust., 10, pp. 17–20.
Weston, D. E., 1967, “Sound Propagation in the Presence of Bladder Fish,” Underwater Acoustics NATO Advanced Study Institute Series, Vol. II, V. M.Albers, ed., Plenum, New York, pp. 55–88.
Medwin, H., 1977, “Counting Bubbles Acoustically: A Review,” Ultrasonics, 15, pp. 7–13. [CrossRef]
Thuraisingham, R. A., 1997, “New Expressions of Acoustic Cross-Sections of a Single Bubble in the Monopole Bubble Theory,” Ultrasonics, 35, pp. 407–409. [CrossRef]
Ainslie, M. A., and Leighton, T. G., 2009, “Near Resonant Bubble Acoustic Cross-Section Corrections, Including Examples from Oceanography, Volcanology, and Biomedical Ultrasound,” J. Acoust. Soc. Am., 126, pp. 2163–2175. [CrossRef]
Anderson, A. L., and Hampton, L. D., 1980, “Acoustics of Gas-Bearing Sediments i. Background,” J. Acoust. Soc. Am., 67, pp. 1865–1889. [CrossRef]
Devin, C., 1959, “Survey of Thermal, Radiation, and Viscous Damping of Pulsating Air Bubbles in Water,” J. Acoust. Soc. Am., 31, pp. 1654–1667. [CrossRef]
Prosperetti, A., 1977, “Thermal Effects and Damping Mechanisms in the Forced Radial Oscillations of Gas Bubbles in Liquids,” J. Acoust. Soc. Am., 61, pp. 17–27. [CrossRef]
Zhang, Y., and Li, S. C., 2010, “Notes on Radial Oscillations of Gas Bubbles in Liquids: Thermal Effects,” J. Acoust. Soc. Am., 128, pp. 306–309. [CrossRef]
Zhang, Y., 2012, “Analysis of Radial Oscillations of Gas Bubbles in Newtonian or Viscoelastic Mediums under Acoustic Excitation,” Ph.D. thesis, University of Warwick, UK.
Keller, J. B., and Kolodner, I. I., 1956, “Damping of Underwater Explosion Bubble Oscillations,” J. Appl. Phys., 27, pp. 1152–1161. [CrossRef]
Keller, J. B., and Miksis, M., 1980, “Bubble Oscillations of Large Amplitude,” J. Acoust. Soc. Am., 68, pp. 628–633. [CrossRef]
Crandall, I. B., 1926, Theory of Vibrating Systems and Sound, D. Van Nostrand Company, NY, pp. 120–124.
Zhang, Y., 2013, “Heat Transfer Across Interfaces of Oscillating Gas Bubbles in Liquids Under Acoustic Excitation,” Int. Commun. Heat and Mass Transf., 43, pp. 1–7. [CrossRef]
van Wijngaarden, L., 1972, “One-Dimensional Flow of Liquids Containing Small Gas Bubbles,” Annu. Rev. Fluid Mech., 4, pp. 369–396. [CrossRef]
Johnson, R. W., The Handbook of Fluid Dynamics, CRC Press LLC and Springer-Verlag GmbH & Co. KG, Berlin, Appendix C.


Grahic Jump Location
Fig. 1

Comparisons of acoustical scattering cross section predicted by Eqs. (9), (11), and (30) (corresponding to dashed, dotted, solid lines, respectively) with ambient pressure of 1 atm, (ω = 107 s−1)

Grahic Jump Location
Fig. 2

Comparisons of acoustical scattering cross section predicted by Eqs. (9), (11), and (30) (corresponding to dashed, dotted, solid lines, respectively) with ambient pressure of 10 MPa, (ω = 107 s−1)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In