Plethora of transitions during breakup of liquid filaments
- Department of Engineering, University of Cambridge, Cambridge CB3 0FS, United Kingdom,
- Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom,
- School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283, and
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
Thinning and breakup of liquid filaments are central to dripping of leaky faucets, inkjet drop formation, and raindrop fragmentation. As the filament radius decreases, curvature and capillary pressure, both inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. As the neck radius vanishes, the governing equations become singular and the filament breaks. In slightly viscous liquids, thinning initially occurs in an inertial regime where inertial and capillary forces balance. By contrast, in highly viscous liquids, initial thinning occurs in a viscous regime where viscous and capillary forces balance. As the filament thins, viscous forces in the former case and inertial forces in the latter become important, and theory shows that the filament approaches breakup in the final inertial–viscous regime where all three forces balance. However, previous simulations and experiments reveal that transition from an initial to the final regime either occurs at a value of filament radius well below that predicted by theory or is not observed. In this paper, we perform new simulations and experiments, and show that a thinning filament unexpectedly passes through a number of intermediate transient regimes, thereby delaying onset of the inertial–viscous regime. Finally, the new findings have practical implications regarding formation of undesirable satellite droplets and also raise the question as to whether similar dynamical transitions arise in other free-surface flows such as coalescence that also exhibit singularities.
- Research Organization:
- Purdue Univ., West Lafayette, IN (United States); Univ. of Cambridge (United Kingdom)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Procter & Gamble (United States); Chevron Corporation (United States); Engineering and Physical Sciences Research Council (EPSRC); John Fell Oxford Univ. Press Research Fund (United Kingdom); Royal Society (United Kingdom)
- Contributing Organization:
- Univ. of Oxford (United Kingdom)
- Grant/Contract Number:
- FG02-96ER14641; EP/H018913/1
- OSTI ID:
- 1235161
- Alternate ID(s):
- OSTI ID: 1349047
- Journal Information:
- Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 112 Journal Issue: 15; ISSN 0027-8424
- Publisher:
- Proceedings of the National Academy of SciencesCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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