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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. R. Baker, D. I. Meiron, S. A. Orszag: Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477 (1982).
O. N. Boratav, P. H. Steen: Singular axisymmetric surfaces: pinchoff via inviscid dynamics. Preprint. To be submitted (2000).
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).
Y-J. Chen: Stability and breakup of capillary surfaces of revolution: Liquid and film bridges. Ph.D. Thesis. Cornell University (1997).
Y-J. Chen, P. H. Steen: Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245 (1997).
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).
S. A. Cryer, P. H. Steen: Collapse of the soap-film bridge: quasistatic description. J. Colloid Interface Sci. 154, 276 (1992).
R. F. Day, E. J. Hinch, J. R. Lister: Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80(4), 704 (1998).
E. B. Dussan: On the difference between a bounding surface and a material surface. J. Fluid. Mech. 75(4), 609-623 (1976).
J. Eggers: Universal pinching of 3D axisymmetric free surface flow. Phys. Rev. Lett. 71, 3458 (1993).
J. Eggers: Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865 (1997).
J. Eggers, T. F. Dupont: Drop formation in a one-dimensional approximation of the Navier-Stokes equation. J. Fluid Mech. 262, 205 (1994).
L. Euler: Opera Omnia (Orell Fussli), 24(1), 25 (1744).
D. M. Henderson: On the pinchoff of a pendant drop of a viscous liquid. Phys. Fluids 9, 3188 (1997).
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).
T. A. Kowalewski: On the separation of droplets from a liquid jet. Fluid Dyn. Res. 17 121 (1996).
E. Kreyzig: Differential Geometry. University of Toronto Press. Toronto (1959).
J. R. Lister, H. A. Stone: Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 10(11), 2758–2764 (1998).
M. S. Longuet-Higgins and E. D. Cokelet: The deformation of steep surface waves. Proc. Roy. Soc. London A 350, 1 (1976).
N. Mansour, T. S. Lundgren: Satellite formation in capillary jet breakup. Phys. Fluids A, 2, 1141 (1990).
D. T. Papageorgiou: Analytical description of the breakup of liquid jets. J. Fluid Mech. 301 109 (1995).
P. H. Steen, Y-J. Chen: Contacting and forming singularities: Distinguishing ex amples. Chaos. 9(1) (1999).
R. M. S. M. Schulkes: The evolution of capillary fountains. J. Fluid Mech. 261, 223 (1994).
R. M. S. M. Schulkes: The contraction of liquid filaments. J. Fluid Mech. 277, (1996).
X. D. Shi, M. P. Brenner, S. R. Nagel: A cascade of structure in a drop falling from a faucet. Science 265, 219 (1994).
G. I. Taylor, D. H. Michael: On making holes in a thin sheet of fluid. Proc. Roy. Soc. A 58, 625 (1973).
M. Tjahjadi, H. A. Stone, J. M. Ottino: Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243, 297 (1992).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-44512-9_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41475-9
Online ISBN: 978-3-540-44512-8
eBook Packages: Springer Book Archive