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Title: Plethora of transitions during breakup of liquid filaments

Abstract

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 practicalmore » 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.« less

Authors:
 [1];  [2];  [3];  [3];  [1];  [4];  [4];  [3]
  1. Univ. of Cambridge (United Kingdom). Dept. of Engineering
  2. Univ. of Oxford (United Kingdom). Dept. of Engineering Science
  3. Purdue Univ., West Lafayette, IN (United States). School of Chemical Engineering
  4. Univ. of Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics
Publication Date:
Research Org.:
Purdue Univ., West Lafayette, IN (United States); Univ. of Cambridge (United Kingdom)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); 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 Org.:
Univ. of Oxford (United Kingdom)
OSTI Identifier:
1235161
Alternate Identifier(s):
OSTI ID: 1349047
Grant/Contract Number:  
FG02-96ER14641; EP/H018913/1
Resource Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 112; Journal Issue: 15; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences, Washington, DC (United States)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; capillary; inertial; regimes; scaling; viscous

Citation Formats

Castrejón-Pita, José Rafael, Castrejón-Pita, Alfonso Arturo, Thete, Sumeet Suresh, Sambath, Krishnaraj, Hutchings, Ian M., Hinch, John, Lister, John R., and Basaran, Osman A. Plethora of transitions during breakup of liquid filaments. United States: N. p., 2015. Web. doi:10.1073/pnas.1418541112.
Castrejón-Pita, José Rafael, Castrejón-Pita, Alfonso Arturo, Thete, Sumeet Suresh, Sambath, Krishnaraj, Hutchings, Ian M., Hinch, John, Lister, John R., & Basaran, Osman A. Plethora of transitions during breakup of liquid filaments. United States. doi:10.1073/pnas.1418541112.
Castrejón-Pita, José Rafael, Castrejón-Pita, Alfonso Arturo, Thete, Sumeet Suresh, Sambath, Krishnaraj, Hutchings, Ian M., Hinch, John, Lister, John R., and Basaran, Osman A. Mon . "Plethora of transitions during breakup of liquid filaments". United States. doi:10.1073/pnas.1418541112.
@article{osti_1235161,
title = {Plethora of transitions during breakup of liquid filaments},
author = {Castrejón-Pita, José Rafael and Castrejón-Pita, Alfonso Arturo and Thete, Sumeet Suresh and Sambath, Krishnaraj and Hutchings, Ian M. and Hinch, John and Lister, John R. and Basaran, Osman A.},
abstractNote = {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.},
doi = {10.1073/pnas.1418541112},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 15,
volume = 112,
place = {United States},
year = {2015},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1418541112

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Cited by: 30 works
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    Restoring universality to the pinch-off of a bubble
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    • Pahlavan, Amir A.; Stone, Howard A.; McKinley, Gareth H.
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