Translation and oscillation of a bubble under axisymmetric deformation

Physics of Fluids

Volumn 18, Issue 7, 2006, Pages

  Shaw, Stephen J ^a  

^a CRANFIELD UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; FLOW INTERACTIONS; INCOMPRESSIBLE FLOW; OSCILLATIONS; POLYNOMIALS; SURFACE TENSION;

GAS BUBBLE; LEGENDRE POLYNOMIAL; SURFACE DEFORMATION;

BUBBLES (IN FLUIDS);

BUBBLES (IN FLUIDS); DEFORMATION; FLOW INTERACTIONS; INCOMPRESSIBLE FLOW; OSCILLATIONS; POLYNOMIALS; SURFACE TENSION;

EID: 33746694736     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2227047     Document Type: Article

References (35)

1. M. S. Plesset and A. Prosperetti, "Bubble dynamics and cavitation," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/ annurev.fl.09.010177.001045 9, 145 (1977).
2. Z. C. Feng and L. G. Leal, "Nonlinear bubble dynamics," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.29.1.201 29, 201 (1997).
3. Lord Rayleigh, "On the pressure developed in a liquid during the collapse of a spherical cavity," Philos. Mag. PHMAA40031-8086 34, 94 (1917).
4. M. S. Plesset, "The dynamics of cavitation bubbles," J. Appl. Mech. JAMCAV0021-8936 16, 277 (1949).
5. H. Lamb, Hydrodynamics, 4th ed. (Cambridge University Press, Cambridge, 1916).
6. J. A. Tsamopoulos and R. A. Brown, "Nonlinear oscillations of inviscid drops and bubbles," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112083002864 127, 519 (1983).
7. W. G. Penney and A. T. Price, "On the changing form of a nearly spherical submarine bubble," in Underwater Explosion Research, edited by G. K. Hartmann and E. G. Hill (Office of Naval Research, Washington, D.C., 1942), Vol. II, p. 145.
8. M. S. Plesset, "On the stability of fluid flows with spherical symmetry," J. Appl. Phys. JAPIAU0021-897910.1063/1.1721529 25, 96 (1954).
9. A. Prosperetti, "Viscous effects on perturbed spherical flows," Q. Appl. Mech. 34, 339 (1977).
10. W. A. H. J. Hermans, "On the instability of a translating gas bubble under the influence of a pressure step," Philips Res. Rep., Suppl. PRSSAM0554-0615 3 (1973).
11. T. B. Benjamin and A. T. Ellis, "Collapse of cavitation bubbles and pressures thereby produced against solid boundaries," Philos. Trans. R. Soc. London, Ser. A PTRMAD0962-8428 A260, 221 (1966).
12. A. J. Reddy and A. J. Szeri, "Shape stability of unsteadily translating bubbles," Phys. Fluids PHFLE61070-663110.1063/1.1483840 14, 2216 (2002).
13. M. S. Longuet-Higgins, "Monopole emission of sound by asymmetric bubble oscillations. Part 1. Normal modes," J. Fluid Mech. JFLSA70022-112010.1017/S0022112089001035 201, 525 (1989).
14. J. E. Ffowcs-Williams and Y. P. Guo, "On resonant nonlinear bubble oscillations," J. Fluid Mech. JFLSA70022-1120 224, 507 (1991).
15. M. S. Longuet-Higgins, "Resonance in nonlinear bubble oscillations," J. Fluid Mech. JFLSA70022-1120 224, 531 (1991).
16. S. M. Yang, Z. C. Feng, and L. G. Leal, "Nonlinear effects in the dynamics of shape and volume oscillations for a gas bubble in an external flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112093000515 247, 417 (1993).
17. Z. C. Feng and L. G. Leal, "On energy transfer in resonant bubble oscillations," Phys. Fluids A PFADEB0899-821310.1063/1.858630 5, 826 (1993).
18. N. K. McDougald and L. G. Leal, "Numerical study of the oscillations of a non-spherical bubble in an inviscid, incompressible liquid. Part I: Free oscillations from non-equilibrium initial conditions," Int. J. Multiphase Flow IJMFBP0301-932210.1016/ S0301-9322(98)00073-1 25, 887 (1999).
19. A. A. Doinikov, "Translational motion of a bubble undergoing shape oscillations," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112003006220 501, 1 (2004).
20. N. Gaines, "Magnetostriction oscillator producing intense audible sound and some effects obtained," Physics (N.Y.)PHYCA20092-8437 3, 209 (1932).
21. M. Strasberg and T. B. Benjamin, "Excitation of oscillations in the shape of pulsating gas bubbles; experimental work," J. Acoust. Soc. Am. JASMAN0001-4966 30, 697 (1958).
22. T. B. Benjamin and M. Strasberg, "Excitation of oscillations in the shape of pulsating gas bubbles; theoretical work," J. Acoust. Soc. Am. JASMAN0001-4966 30, 697 (1958).
23. A. I. Eller and L. A. Crum, "Instability of the motion of a pulsating bubble in a sound field," J. Acoust. Soc. Am. JASMAN0001-496610.1121/1.1911956 47, 762 (1970).
24. T. B. Benjamin and A. T. Ellis, "Self-propulsion of asymmetrically vibrating bubbles," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112090001860 212, 65 (1990).
25. P. G. Saffmann, "The self-propulsion of a deformable body in a perfect body," J. Fluid Mech. JFLSA70022-1120 28, 385 (1967).
26. T. B. Benjamin, "Hamiltonian theory for motions of bubbles in an infinite liquid," J. Fluid Mech. JFLSA70022-1120 181, 349 (1987).
27. C. C. Mei and X. Zhou, "Parametric resonance of a spherical bubble," J. Fluid Mech. JFLSA70022-1120 229, 29 (1991).
28. Z. C. Feng and L. G. Leal, "Translational instability of a bubble undergoing shape oscillations," Phys. Fluids PHFLE61070-663110.1063/ 1.868520 7, 1325 (1995).
29. J. Miles, "Nonlinear surface waves in closed basins," J. Fluid Mech. JFLSA70022-112010.1017/S002211207600030X 75, 419 (1976).
30. J. Miles, "On Hamilton's principle for surface waves," J. Fluid Mech. JFLSA70022-1120 83, 153 (1977).
31. D. M. Milder, "A note regarding 'On Hamilton's principle for surface waves'," J. Fluid Mech. JFLSA70022-1120 83, 159 (1977).
32. O. A. Basaran, "Nonlinear oscillations of viscous liquid drops," J. Fluid Mech. JFLSA70022-112010.1017/S002211209200199X 241, 169 (1992).
33. Y. Mao, L. A. Crum, and R. A. Roy, "Nonlinear coupling between the surface and volume modes of an oscillating bubble," J. Acoust. Soc. Am. JASMAN0001-4966 98, 2764 (1995).
34. R. G. Holt, J. Holzfuss, A. Judt, A. Philip, and S. Horsburgh, "Forced nonlinear oscillations of single air bubbles in water: Experimental results," Frontiers of Nonlinear Acoustics-12th ISNA (1990), p. 497.
35. K. Ohsaka, "An experimental study on resonance of oscillating air/ vapor bubbles in water using a two-frequency acoustic apparatus," Phys. Fluids PHFLE61070-663110.1063/1.1561613 15, 1189 (2003).