Skip to main content
Log in

Stability of a bubble expanding and translating through an inviscid liquid

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

A bubble expands adiabatically and translates in an incompressible and inviscid liquid. We investigate the number of equilibrium points of the bubble and the nature of stability of the bubble at these points. We find that there is only one equilibrium point and the bubble is stable there.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chakraborty B B, Effect of a viscous fluid flow past a spherical gas bubble on the growth of its radius,Proc. Ind. Acad, Sci. 100 (1990) 185–188

    Article  MATH  Google Scholar 

  2. Chakraborty B B and Khattar Dinesh, Stability of an expanding bubble in the Rayleigh model,Proc. Ind. Acad. Sci (Math. Sci) 109(4) (1999) 453–456

    MATH  Google Scholar 

  3. Chakraborty B B and Tuteja G S, Motion of an expanding gas bubble in a viscous liquid under gravity,Phys. Fluids A5(8) (1993) 1879–1882

    Google Scholar 

  4. Glendinning Paul, Stability, Instability and Chaos (Cambridge: Cambridge University Press) (1994)

    MATH  Google Scholar 

  5. Noltingk B E and Neppiras E A,Proc. Phys. Soc. London Sec. B63 (1950) 674–685;64 (1951) 1032–1038

    Article  Google Scholar 

  6. Plesset M S, The dynamics of cavitation bubbles,J. Appl. Mech. 16 (1949) 277

    Google Scholar 

  7. Poritsky H, The collapse or growth of a spherical bubble or cavity in a viscous fluid, Proceedings of the first U.S. National Congress on Applied Mechanics (ed) E. Sternberg (Am. Soc. Mech. Engg., New York, 1952) 813–821

  8. Rayleigh Lord, On the pressure developed in a liquid during the collapse of a spherical void,Philos. Mag. 34 (1917) 94

    Google Scholar 

  9. Turnbulll H W, Theory of Equations (London: Oliver and Boyd) (1957)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khattar, D., Chakraborty, B.B. Stability of a bubble expanding and translating through an inviscid liquid. Proc. Indian Acad. Sci. (Math. Sci.) 112, 361–365 (2002). https://doi.org/10.1007/BF02829760

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02829760

Keywords

Navigation