Skip to main content

Oscillation of Droplets and Bubbles

  • Chapter
  • First Online:
Handbook of Atomization and Sprays

Abstract

A liquid droplet may go through shape oscillation if it is forced out of its equilibrium spherical shape, while gas bubbles undergo both shape and volume oscillations because they are compressible. This can happen when droplets and bubbles are exposed to an external flow or an external force. Liquid droplet oscillation is observed during the atomization process when a liquid ligament is first separated from a larger mass or when two droplets are collided. Droplet oscillations may change the rate of heat and mass transport. Bubble oscillations are important in cavitation problems, effervescent atomizers and flash atomization where large number of bubbles oscillate and interact with each other. This chapter provides the basic theory for the oscillation of liquid droplet and gas bubbles.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 469.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 599.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 599.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. J. W. S. Rayleigh, On the capillary phenomena of jets, Proc. R. Soc. Lond. 29, 71, 1879.

    Article  Google Scholar 

  2. F.H. Busse, J. Fluid Mech. 142, 1, 1984.

    Article  MATH  Google Scholar 

  3. H. Lamb, Hydrodynamics, 6th ed. Cambridge University Press, Cambridge, 1932.

    MATH  Google Scholar 

  4. S. Chandrasekhar, The oscillations of a viscous liquid globe, Proc. Lond. Math. Soc. 9, 141 1959.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. H. Reid, The oscillations of a viscous liquid drop, Q. Appl. Math. 18, 86, 1960.

    Google Scholar 

  6. A. Prosperetti, Free oscillations of drops and bubbles: the initial-value problem, J. Fluid Mech. 100, 333, 1980.

    Article  MATH  Google Scholar 

  7. J. A. Tsamopoulos and R. A. Brown, Nonlinear oscillations of inviscid drops and bubbles, J. Fluid Mech. 127, 519, 1983.

    Article  MATH  Google Scholar 

  8. G. B. Foote, A numerical method for studying simple drop behavior: simple oscillation, J. Comput. Phys. 11, 507, 1973.

    Article  Google Scholar 

  9. C. T. Alonso, The Dynamics of Colliding and Oscillating Drops, in Proceedings of the International Colloquium on Drops and Bubbles, edited by D. J. Collins, M. S. Plesset, and M. M. Saffren, Jet Propulsion Laboratory, 1974.

    Google Scholar 

  10. T. S. Lundgren and N. N. Mansour, Oscillations of drops in zero gravity with weak viscous effects, J. Fluid Mech. 194, 479, 1991.

    Article  MathSciNet  Google Scholar 

  11. T. W. Patzek, R. E. Benner, Jr., O. A. Basaran, and L. E. Scriven, Nonlinear oscillations of inviscid free drops, J. Comput. Phys. 97, 489 1991.

    Article  MATH  Google Scholar 

  12. O. A. Basaran, Nonlinear oscillations of viscous liquid drops, J. Fluid Mech. 241, 169, 1992.

    Article  MATH  Google Scholar 

  13. E. Trinh and T. G. Wang, Large-amplitude free and driven drop shape oscillations: experimental observations, J. Fluid Mech. 122, 315, 1982.

    Article  Google Scholar 

  14. E. Becker, W. J. Hiller, and T. A. Kowalewski, Experimental and theoretical investigation of large amplitude oscillations of liquid droplets, J. Fluid Mech. 231, 180, 1991.

    Article  Google Scholar 

  15. E. Becker, W. J. Hiller, and T. A. Kowalewski, Nonlinear dynamics of viscous droplets, J. Fluid Mech. 258, 191, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  16. F. Mashayek and N. Ashgriz, Nonlinear oscillation of liquid drops With internal circulation, Phys. Fluids 10(5), 1071–1082, May 1998.

    Article  Google Scholar 

  17. C. A. Miller and L. E. Scriven, The oscillations of a fluid droplet immersed in another fluid, J. Fluid Mech. 32, 417, 1968.

    Article  Google Scholar 

  18. P. L. Marston, Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses: theory, J. Acoust. Soc. Am. 67, 15, 1980.

    Article  MATH  Google Scholar 

  19. A. Prosperetti, Normal-mode analysis for the oscillations of a viscous liquid drop immersed in another liquid, J. Me´c. 19, 142, 1980.

    MathSciNet  Google Scholar 

  20. O. A. Basaran, T. C. Scott, and C. H. Byers, Drop oscillations in liquid-liquid systems, AIChE. J. 35, 1263, 1989.

    Article  Google Scholar 

  21. E. Trinh, A. Zwern, and T. G. Wang, An experimental study of small amplitude drop oscillations in immiscible liquid systems, J. Fluid Mech. 115, 453, 1982.

    Article  Google Scholar 

  22. O. A. Basaran and D. W. Depaoli, Nonlinear oscillations of pendant drops, Phys. Fluids 6, 2923, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  23. D. W. DePaoli, J. Q. Feng, O. A. Basaran, and T. C. Scott, Hysteresis in forced oscillations of pendant drops, Phys. Fluids 7, 1181, 1995.

    Article  Google Scholar 

  24. J. A. Tsamopoulos and R. A. Brown, Resonant oscillations of inviscid charged drops, J. Fluid Mech. 147, 373, 1984.

    Article  MATH  Google Scholar 

  25. E. H. Trinh, R. G. Holt, and D. B. Thiessen, The dynamics of ultrasonically levitated drops in an electric field, Phys. Fluids 8, 43, 1996.

    Article  Google Scholar 

  26. T. Shi and R. E. Apfel, Oscillatiaons of a deformed liquid drop in an acoustic field, Phys. Fluids 7(7), 1545, 1995.

    Article  MATH  Google Scholar 

  27. E. H. Trinh, D. B. Thiessen, and R. G. Holt, Driven and freely decaying nonlinear shape oscillations of drops and bubbles immersed in a liquid, experimental results, J. Fluid Mech. 364, 253, 1998.

    Article  MATH  Google Scholar 

  28. N.J. Holter and W.R. Glasscock, Vibrations of evaporating liquid drops, J. Acoust. Soc. Am. 24, 682, 1952.

    Article  Google Scholar 

  29. K. Adachi and R. Takaki, Vibration of a flattened drop. I. Observation, J. Phys. Soc. Jpn. 53, 4184, 1984.

    Article  Google Scholar 

  30. K. Adachi and R. Takaki, Vibration of a flattened drop. II. Normal mode analysis, J. Phys. Soc. Jpn. 54, 2462, 1985.

    Article  Google Scholar 

  31. N. Yoshiyasu, K. Matsuda, and R. Takaki, Self-induced vibration of a water drop placed on an oscillating plate, J. Phys. Soc. Jpn. 65, 2068, 1996.

    Article  Google Scholar 

  32. A. J. James, B. Vukasinovic, M. K. Smith, and A. Glezer, Vibration–induced drop atomization and bursting, J. Fluid Mech. 476, 1, 2003.

    MATH  Google Scholar 

  33. L. Rayleigh, The pressure developed in a liquid during the collapse of a spherical cavity, Phil. Mag. 34, 94, 1917.

    Google Scholar 

  34. M. S. Plesset and T. P. Mitchell, On the stability of the spherical shape of a vapor cavity in a liquid, Q. Appl. Math. 13, 419, 1955.

    MathSciNet  Google Scholar 

  35. A. I. Eller, Force on a bubble in a standing acoustic wave, J. Acoust. Soc. Am. 43, 170, 1968.

    Article  Google Scholar 

  36. V. F. K. Bjerknes, Fields of Force. Columbia University Press, New York, 1906.

    Google Scholar 

  37. A. Prosperetti, Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids, J. Acoust. Soc. Am. 61, 17, 1977.

    Article  Google Scholar 

  38. A. Prosperetti, Bubble phenomena in sound fields: part one, Ultrasonics 22, 69, 1984.

    Article  Google Scholar 

  39. A. Prosperetti, Bubble phenomena in sound fields: part two, Ultrasonics 22, 115, 1984.

    Article  Google Scholar 

  40. T. Barbat, N. Ashgriz, and C. Liu, Dynamics of two interacting bubbles in an acoustic field, J. Fluid Mech. 389, 137, 1999.

    Article  MATH  Google Scholar 

  41. T. Barbat and N. Ashgriz, Planner dynamics of two interacting bubbles in an acoustic field, Appl. Math. Comput. 157, 775, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  42. A. I. Eller and L. A. Crum, Instability of the motion of a pulsating bubble in a sound field, J. Acoust. Soc. Am. 47, 762, 1970.

    Article  Google Scholar 

  43. C. C. Mei and X. Zhou, Parametric resonance of a spherical bubble, J. Fluid Mech. 229, 26, 1991.

    Article  Google Scholar 

  44. A. A. Doinikov, Translational motion of a bubble undergoing shape oscillations, J. Fluid Mech. 501, 1, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  45. T. B. Benjamin and A. T. Ellis, Self-propulsion of asymmetrically vibrating bubbles, J. Fluid Mech. 212, 65, 1990.

    Article  MATH  Google Scholar 

  46. I. Sh. Akhatov and S. I. Konovalova, Regular and chaotic dynamics of a spherical bubble, J. Appl. Math. Mech., 69, 575, 2005.

    Article  MathSciNet  Google Scholar 

  47. T. Watanabe and Y. Kukita, Translational and radial motions of a bubble in an acoustic standing wave field, Phys. Fluids A. 5, 2682, 1993.

    Article  Google Scholar 

  48. M. Movassat, N. Ashgriz, and M. Bussmann, Bubble dynamics under forced oscillation in microgravity environment, in Proceedings of ASME International Mechanical Engineering Congress and Exposition, November 2009, Lake Buena Vista, FL.

    Google Scholar 

  49. H. N. Yoshikawa, F. Zoueshtigh, H. Caps, P. Kurowski, and P. Petitjeans, Bubble splitting in oscillatory flows on ground and in reduced gravity, Eur. Phys. J. E. 31, 191, 2010.

    Article  Google Scholar 

  50. M. Movassat, N. Ashgriz, and M. Bussmann, Three-dimensional numerical simulation of bubble interaction under forced vibration, Presented in COSPAR Meeting, July 2010, Bremen, Germany.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Ashgriz .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer US

About this chapter

Cite this chapter

Ashgriz, N., Movassat, M. (2011). Oscillation of Droplets and Bubbles. In: Ashgriz, N. (eds) Handbook of Atomization and Sprays. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7264-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-7264-4_5

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-7263-7

  • Online ISBN: 978-1-4419-7264-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics