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Bubble Disconnection: Self-Similarity and Cascading Physics

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Part of the book series: Lecture Notes in Physics ((LNP,volume 566))

Abstract

Surface tension disconnects a capillary bubble from a capillary bridge while driving a surrounding inviscid flow. Spatial and temporal behavior is studied just prior to and just after disconnection, via computation and experiment. They are in agreement both before and after the event but anticipated self-similarity is observed only beforehand. Computation coincides with observation due to modeling that identifies the cascade of physics probed as decades of length scales are traversed.

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References

  1. G. R. Baker, D. I. Meiron, S. A. Orszag: Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477 (1982).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. O. N. Boratav, P. H. Steen: Singular axisymmetric surfaces: pinchoff via inviscid dynamics. Preprint. To be submitted (2000).

    Google Scholar 

  3. M. P. Brenner, J. Eggers, K. Joseph, S. R. Nagel, X. D. Shi: Breakdown of scaling in droplet fission at high Reynolds number. Phys. Fluids 9, 1573 (1997).

    Article  ADS  Google Scholar 

  4. Y-J. Chen: Stability and breakup of capillary surfaces of revolution: Liquid and film bridges. Ph.D. Thesis. Cornell University (1997).

    Google Scholar 

  5. Y-J. Chen, P. H. Steen: Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. I. Cohen, M. P. Brenner, J. Eggers, S. R. Nagel: Two fluid drop snap-off problem: Experiments and theory. Phys. Rev. Lett. 83(6), 1147 (1999).

    Article  ADS  Google Scholar 

  7. S. A. Cryer, P. H. Steen: Collapse of the soap-film bridge: quasistatic description. J. Colloid Interface Sci. 154, 276 (1992).

    Article  ADS  Google Scholar 

  8. R. F. Day, E. J. Hinch, J. R. Lister: Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80(4), 704 (1998).

    Article  ADS  Google Scholar 

  9. E. B. Dussan: On the difference between a bounding surface and a material surface. J. Fluid. Mech. 75(4), 609-623 (1976).

    Google Scholar 

  10. J. Eggers: Universal pinching of 3D axisymmetric free surface flow. Phys. Rev. Lett. 71, 3458 (1993).

    Article  ADS  Google Scholar 

  11. J. Eggers: Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865 (1997).

    Article  ADS  Google Scholar 

  12. J. Eggers, T. F. Dupont: Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech. 262, 205 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. L. Euler: Opera Omnia (Orell Fussli), 24(1), 25 (1744).

    Google Scholar 

  14. D. M. Henderson: On the pinchoff of a pendant drop of a viscous liquid. Phys. Fluids 9, 3188 (1997).

    Article  ADS  Google Scholar 

  15. T. Y. Hou, J. S. Lowengrub, M. J. Shelley: The long-time motion of vortex sheets with surface tension. Phys. Fluids 9(7), 1933 (1933).

    Article  ADS  MathSciNet  Google Scholar 

  16. T. A. Kowalewski: On the separation of droplets from a liquid jet. Fluid Dyn. Res. 17 121 (1996).

    Article  Google Scholar 

  17. E. Kreyzig: Differential Geometry. University of Toronto Press. Toronto (1959).

    Google Scholar 

  18. J. R. Lister, H. A. Stone: Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10(11), 2758–2764 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. M. S. Longuet-Higgins and E. D. Cokelet: The deformation of steep surface waves. Proc. Roy. Soc. London A 350, 1 (1976).

    Google Scholar 

  20. N. Mansour, T. S. Lundgren: Satellite formation in capillary jet breakup. Phys. Fluids A, 2, 1141 (1990).

    Article  ADS  Google Scholar 

  21. D. T. Papageorgiou: Analytical description of the breakup of liquid jets. J. Fluid Mech. 301 109 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. P. H. Steen, Y-J. Chen: Contacting and forming singularities: Distinguishing ex amples. Chaos. 9(1) (1999).

    Article  Google Scholar 

  23. R. M. S. M. Schulkes: The evolution of capillary fountains. J. Fluid Mech. 261, 223 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. R. M. S. M. Schulkes: The contraction of liquid filaments. J. Fluid Mech. 277, (1996).

    Google Scholar 

  25. X. D. Shi, M. P. Brenner, S. R. Nagel: A cascade of structure in a drop falling from a faucet. Science 265, 219 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  26. G. I. Taylor, D. H. Michael: On making holes in a thin sheet of fluid. Proc. Roy. Soc. A 58, 625 (1973).

    Google Scholar 

  27. M. Tjahjadi, H. A. Stone, J. M. Ottino: Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243, 297 (1992).

    Article  ADS  Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Boratav, O.N., Chen, YJ., Steen, P.H. (2001). Bubble Disconnection: Self-Similarity and Cascading Physics. In: Lumley, J.L. (eds) Fluid Mechanics and the Environment: Dynamical Approaches. Lecture Notes in Physics, vol 566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44512-9_2

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  • DOI: https://doi.org/10.1007/3-540-44512-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41475-9

  • Online ISBN: 978-3-540-44512-8

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