Axisymmetric bubble collapse in a quiescent liquid pool. I. Theory and numerical simulations

Physics of Fluids

Volumn 20, Issue 11, 2008, Pages

  Gordillo, J M ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

VISCOSITY OF LIQUIDS;

BUBBLE COLLAPSE; BUBBLE PINCH-OFF; GAS PRESSURES; LOW-VISCOSITY LIQUIDS; MAXIMUM VELOCITY; QUIESCENT LIQUID; SYSTEM OF EQUATIONS; TIME EVOLUTIONS;

NUMERICAL MODELS;

EID: 57149084697     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3009297     Document Type: Article

References (42)

1. J. Eggers, "Universal pinching of 3D axisymmetric free-surface flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.71.3458 71, 3458 (1993).
2. Y. J. Chen and P. H. Steen, "Dynamics of inviscid capillary breakup: Collapse and pinchoff of a film bridge," J. Fluid Mech. JFLSA70022-112010.1017/S002211209700548X 341, 245 (1997).
3. R. F. Day, E. J. Hinch, and J. R. Lister, "Self-similar capillary pinchoff of an inviscid fluid," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.80.704 80, 704 (1998).
4. D. Leppinen and J. R. Lister, "Capillary pinch-off in inviscid fluids," Phys. Fluids PHFLE61070-663110.1063/1.1537237 15, 568 (2003).
5. J. C. Burton, J. E. Rutledge, and P. Taborek, "Fluid pinch-off dynamics at nanometer length scales," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.92.244505 92, 244505 (2004).
6. M. S. Longuet-Higgins, B. R. Kerman, and K. Lunde, "The release of air bubbles from an underwater nozzle," J. Fluid Mech. JFLSA70022-112010.1017/S0022112091000836 230, 365 (1991).
7. H. N. Oguz and A. Prosperetti, "Dynamics of bubble growth and detachment from a needle," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112093003015 257, 111 (1993).
8. D. Lohse, R. Bergmann, R. Mikkelsen, C. Zeilstra, D. van der Meer, M. Versluis, K. van der Weele, M. van der Hoef, and H. Kuipers, "Impact on soft sand: Void collapse and jet formation," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.93.198003 93, 198003 (2004).
9. A. M. Worthington, A Study of Splashes (Longman and Green, London, 1908).
10. R. Bergmann, D. van der Meer, M. Stijnman, M. Sandtke, A. Prosperetti, and D. Lohse, "Giant bubble pinchoff," Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.96.154505 96, 154505 (2006).
11. H. N. Oguz and A. Prosperetti, "Bubble entrainment by the impact of drops on liquid surfaces," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112090002890 219, 143 (1990).
12. D. Bartolo, C. Josserand, and D. Bonn, "Singular jets and bubbles in drop impact," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.96.124501 96, 124501 (2006).
13. R. Manasseh, G. Riboux, and F. Risso, "Sound generation on bubble coalescence following detachment," Int. J. Multiphase Flow IJMFBP0301-932210.1016/j.ijmultiphaseflow.2008.03.005 34, 938 (2008).
14. Clear evidence of the jets ejected as a consequence of bubble collapse can be found in R. Manasseh, S. Yoshida, and M. Rudman, "Bubble formation processes and bubble acoustic signals," Proceedings of the Third International Conference on Multiphase Flow, ICMF'98 Lyon, France, 1998, pp. 1-8.
15. J. M. Gordillo, A. Sevilla, and C. Martínez-Bazán, "Bubbling in a coflow at high Reynolds numbers," Phys. Fluids PHFLE61070-663110.1063/1.2747996 19, 077102 (2007).
16. S. T. Thoroddsen and A. Q. Shen, "Granular jets," Phys. Fluids PHFLE61070-663110.1063/1.1328359 13, 4 (2001).
17. S. T. Thoroddsen, T. G. Etoh, and K. Takehara, "Experiments on bubble pinch-off," Phys. Fluids PHFLE61070-663110.1063/1.2710269 19, 042101 (2007).
18. M. S. Longuet-Higgins, "Bubbles, breaking waves and hyperbolic jets at a free surface," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112083002645 127, 103 (1983).
19. J. M. Boulton-Stone and J. R. Blake, "Gas bubbles bursting at a free surface," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112093002216 254, 437 (1993).
20. L. Duchemin, S. Popinet, C. Josserand, and S. Zaleski, "Jet formation in bubbles bursting at a free surface," Int. J. Multiphase Flow IJMFBP0301-9322 14, 3000 (2002).
21. A. Antkowiak, N. Bremond, S. Le Dizes, and E. Villermaux, "Short-term dynamics of a density interface following an impact," J. Fluid Mech. JFLSA70022-112010.1017/S0022112007005058 577, 241 (2007).
22. S. T. Thoroddsen, T. G. Etoh, and K. Takehara, "Microjetting from wave focusing on oscillating drops," Phys. Fluids PHFLE61070-663110.1063/1.2718479 19, 052101 (2007).
23. A. Sierou and J. R. Lister, "Self-similar solutions for viscous capillary pinch-off," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112003006736 497, 381 (2003).
24. P. Doshi, I. Cohen, W. W. Zhang, M. Siegel, P. Howell, O. A. Basaran, and S. R. Nagel, "Persistence of memory in drop breakup: The breakdown of universality," Science SCIEAS0036-807510.1126/ science.1089272 302, 1185 (2003).
25. R. Suryo, P. Doshi, and O. A. Basaran, "Non-self-similar, linear dynamics during pinch-off of a hollow annular jet," Phys. Fluids PHFLE61070-663110.1063/1.1793631 16, 4177 (2004).
26. Keim et al. (Ref. 27) showed that slight azimuthal asymmetries initially introduced at the length scale of the bubble are convected toward the pinch-off region, producing a nonaxisymmetric breakup.
27. N. C. Keim, P. Moller, W. W. Zhang, and S. R. Nagel, "Breakup of air bubbles in water: Memory and breakdown of cylindrical symmetry," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.97.144503 97, 144503 (2006).
28. J. M. Gordillo, A. Sevilla, J. Rodríguez-Rodríguez, and C. Martínez-Bazán, "Axisymmetric bubble pinch-off at high Reynolds numbers," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.95.194501 95, 194501 (2005).
29. B. Dollet, W. van Hoeve, J.-P. Raven, P. Marmottant, and M. Versluis, "Role of the channel geometry on the bubble pinch-off in flow-focusing devices," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.100.034504 100, 034504 (2008).
30. J. Burton, R. Waldrep, and P. Taborek, "Scaling instabilities in bubble pinch-off," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.94.184502 94, 184502 (2005).
31. J. M. Gordillo and M. Pérez-Saborid, "Axisymmetric breakup of bubbles at high Reynolds numbers," J. Fluid Mech. JFLSA70022-112010.1017/S0022112006001388 562, 303 (2006).
32. J. Eggers, M. A. Fontelos, D. M. Leppinen, and J. Snoeijer, "Theory of the collapsing axisymmetric cavity," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.98.094502 98, 094502 (2007).
33. J. M. Gordillo and M. A. Fontelos, "Satellites in the inviscid breakup of bubbles," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.98.144503 98, 144503 (2007).
34. R. Bolaños-Jiménez, A. Sevilla, C. Martínez-Bazán, and J. M. Gordillo, "Axisymmetric bubble collapse in a quiescent liquid pool. II. Experimental study," Phys. Fluids PHFLE61070-663110.1063/1.3009298 20, 112104 (2008).
35. D. D. Joseph, "Potential flow of viscous fluids: Historical notes," Int. J. Multiphase Flow IJMFBP0301-932210.1016/ j.ijmultiphaseflow.2005.09.004 32, 285 (2006).
36. This is the viscous potential flow approach which is discussed at length in Ref. and references therein.
37. 2, the second term from the left (-1) represents the liquid convective acceleration.
38. A. Prosperetti, "Bubbles," Phys. Fluids PHFLE61070-663110.1063/ 1.1695308 16, 1852 (2004).
39. J. Rodríguez-Rodríguez, J. M. Gordillo, and C. Martínez-Bazán, "Breakup time and morphology of drops and bubbles in a high Reynolds number flow," J. Fluid Mech. JFLSA70022-112010.1017/S002211200500741X 548, 69 (2006).
40. R. Suryo, P. Doshi, and O. A. Basaran, "Nonlinear dynamics and breakup of compound jets," Phys. Fluids PHFLE61070-663110.1063/ 1.2245377 18, 082107 (2006).
41. g) → ∞.
42. num.