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Title: Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids

Abstract

Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. Here, for sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of anmore » inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid’s viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance each other while capillary force remains negligible, in accordance with the results of Vaynblat, Lister, and Witelski.« less

Authors:
 [1];  [1];  [2];  [1];  [1]
+ Show Author Affiliations
  1. Purdue Univ., West Lafayette, IN (United States). School of Chemical Engineering
  2. Pfizer Worldwide R&D, Groton, CT (United States)
Publication Date:
Research Org.:
Purdue Univ., West Lafayette, IN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1467878
Alternate Identifier(s):
OSTI ID: 1319950
Grant/Contract Number:  
FG02-96ER14641
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 28; Journal Issue: 9; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 36 MATERIALS SCIENCE; 42 ENGINEERING

Citation Formats

Thete, Sumeet Suresh, Anthony, Christopher, Doshi, Pankaj, Harris, Michael T., and Basaran, Osman A. Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids. United States: N. p., 2016. Web. doi:10.1063/1.4961549.
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Thete, Sumeet Suresh, Anthony, Christopher, Doshi, Pankaj, Harris, Michael T., & Basaran, Osman A. Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids. United States. https://doi.org/10.1063/1.4961549
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Thete, Sumeet Suresh, Anthony, Christopher, Doshi, Pankaj, Harris, Michael T., and Basaran, Osman A. Tue . "Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids". United States. https://doi.org/10.1063/1.4961549. https://www.osti.gov/servlets/purl/1467878.
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@article{osti_1467878,
title = {Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids},
author = {Thete, Sumeet Suresh and Anthony, Christopher and Doshi, Pankaj and Harris, Michael T. and Basaran, Osman A.},
abstractNote = {Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. Here, for sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of an inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid’s viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance each other while capillary force remains negligible, in accordance with the results of Vaynblat, Lister, and Witelski.},
doi = {10.1063/1.4961549},
journal = {Physics of Fluids},
number = 9,
volume = 28,
place = {United States},
year = {Tue Sep 06 00:00:00 EDT 2016},
month = {Tue Sep 06 00:00:00 EDT 2016}
}
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https://doi.org/10.1063/1.4961549
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    Works referencing / citing this record:

    Self-similar rupture of thin films of power-law fluids on a substrate
    journal, August 2017

    • Garg, Vishrut; Kamat, Pritish M.; Anthony, Christopher R.
    • Journal of Fluid Mechanics, Vol. 826
    • DOI: 10.1017/jfm.2017.446

    A new experimental method based on volume measurement for determining axial scaling during breakup of drops and liquid threads
    journal, August 2018

    • Wagoner, Brayden W.; Thete, Sumeet S.; Basaran, Osman A.
    • Physics of Fluids, Vol. 30, Issue 8
    • DOI: 10.1063/1.5030330

    Effect of polymer-coated gold nanoparticle stabilizers on drop coalescence
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    Surface rheological measurements of isolated food foam systems
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