skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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]
  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) (SC-22)
OSTI Identifier:
1467878
Alternate Identifier(s):
OSTI ID: 1319950
Grant/Contract Number:  
FG02-96ER14641
Resource Type:
Journal Article: 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.
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. doi:10.1063/1.4961549.
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. doi:10.1063/1.4961549. https://www.osti.gov/servlets/purl/1467878.
@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},
issn = {1070-6631},
number = 9,
volume = 28,
place = {United States},
year = {2016},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Thin film rupture
journal, May 1996


Capillary breakup of a viscous thread surrounded by another viscous fluid
journal, November 1998

  • Lister, John R.; Stone, Howard A.
  • Physics of Fluids, Vol. 10, Issue 11
  • DOI: 10.1063/1.869799

Instability of a polymeric thread
journal, March 2014


Dynamics of the Tear Film
journal, January 2012


Computational and Experimental Analysis of Pinch-Off and Scaling
journal, April 2002


A numerical study of the asymptotic evolution and breakup of Newtonian and viscoelastic jets
journal, September 1995


Long-scale evolution of thin liquid films
journal, July 1997

  • Oron, Alexander; Davis, Stephen H.; Bankoff, S. George
  • Reviews of Modern Physics, Vol. 69, Issue 3
  • DOI: 10.1103/RevModPhys.69.931

How Liquids Spread on Solids
journal, May 1987

  • Teletzke, Gary F.; Ted Davis, H.; Scriven, L. E.
  • Chemical Engineering Communications, Vol. 55, Issue 1-6
  • DOI: 10.1080/00986448708911919

Theoretical modeling of microstructured liquids: a simple thermodynamic approach
journal, July 2004


Capillary breakup of a liquid bridge: identifying regimes and transitions
journal, May 2016


Rupture of thin viscous films by van der Waals forces: Evolution and self-similarity
journal, May 2001

  • Vaynblat, Dimitri; Lister, John R.; Witelski, Thomas P.
  • Physics of Fluids, Vol. 13, Issue 5
  • DOI: 10.1063/1.1359749

Free surface flows of polymer solutions with models based on the conformation tensor
journal, December 2002


Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges
journal, May 1999

  • Ambravaneswaran, Bala; Basaran, Osman A.
  • Physics of Fluids, Vol. 11, Issue 5
  • DOI: 10.1063/1.869972

Repeated Formation of Fluid Threads in Breakup of a Surfactant-Covered Jet
journal, February 2006


Coalescence of two equal-sized deformable drops in an axisymmetric flow
journal, October 2007

  • Yoon, Yosang; Baldessari, Fabio; Ceniceros, Hector D.
  • Physics of Fluids, Vol. 19, Issue 10
  • DOI: 10.1063/1.2772900

Self-Similar Capillary Pinchoff of an Inviscid Fluid
journal, January 1998


Self-similar pinch-off of power law fluids
journal, March 2004

  • Doshi, Pankaj; Basaran, Osman A.
  • Physics of Fluids, Vol. 16, Issue 3
  • DOI: 10.1063/1.1639015

Coating Flows
journal, January 2004


Can Surfactant Be Present at Pinch-Off of a Liquid Filament?
journal, January 2007


On the breakup of viscous liquid threads
journal, July 1995

  • Papageorgiou, Demetrios T.
  • Physics of Fluids, Vol. 7, Issue 7
  • DOI: 10.1063/1.868540

The effect of surfactant on the stability of a liquid thread
journal, May 2002


Coating flow theory by finite element and asymptotic analysis of the navier-stokes system
journal, March 1984

  • Kistler, S. F.; Scriven, L. E.
  • International Journal for Numerical Methods in Fluids, Vol. 4, Issue 3
  • DOI: 10.1002/fld.1650040302

Universal pinching of 3D axisymmetric free-surface flow
journal, November 1993


Plethora of transitions during breakup of liquid filaments
journal, March 2015

  • Castrejón-Pita, José Rafael; Castrejón-Pita, Alfonso Arturo; Thete, Sumeet Suresh
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 15
  • DOI: 10.1073/pnas.1418541112

Flow in Foams and Flowing Foams
journal, January 2013


Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge
journal, June 1997


Dynamics of viscoelastic liquid filaments: Low capillary number flows
journal, April 2008

  • Bhat, Pradeep P.; Basaran, Osman A.; Pasquali, Matteo
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 150, Issue 2-3
  • DOI: 10.1016/j.jnnfm.2007.10.021

Small-scale free surface flows with breakup: Drop formation and emerging applications
journal, September 2002


Symmetry and self-similarity in rupture and pinchoff: a geometric bifurcation
journal, June 2001

  • Vaynblat, Dimitri; Lister, John R.; Witelski, Thomas P.
  • European Journal of Applied Mathematics, Vol. 12, Issue 3
  • DOI: 10.1017/S0956792501004375

Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid
journal, September 1997


Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer
journal, February 2006

  • Liao, Ying-Chih; Franses, Elias I.; Basaran, Osman A.
  • Physics of Fluids, Vol. 18, Issue 2
  • DOI: 10.1063/1.2166657

Effect of Surface Tension Variations on the Pinch-Off Behavior of Small Fluid Drops in the Presence of Surfactants
journal, December 2009


Nonlinear dynamics and breakup of free-surface flows
journal, July 1997


Scaling in pinch-off of generalized Newtonian fluids
journal, July 2003

  • Doshi, Pankaj; Suryo, Ronald; Yildirim, Ozgur E.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 113, Issue 1
  • DOI: 10.1016/S0377-0257(03)00081-8

Inhibition of the Finite-Time Singularity during Droplet Fission of a Polymeric Fluid
journal, April 2001


Drop dynamics on the beads-on-string structure for viscoelastic jets: A numerical study
journal, April 2003

  • Li, Jie; Fontelos, Marco A.
  • Physics of Fluids, Vol. 15, Issue 4
  • DOI: 10.1063/1.1556291

Self-similar rupture of thin free films of power-law fluids
journal, August 2015

  • Thete, Sumeet Suresh; Anthony, Christopher; Basaran, Osman A.
  • Physical Review E, Vol. 92, Issue 2
  • DOI: 10.1103/PhysRevE.92.023014

Local dynamics during pinch-off of liquid threads of power law fluids: Scaling analysis and self-similarity
journal, October 2006


Drop formation - an overview
journal, June 2005


Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops
journal, August 2002

  • Ambravaneswaran, Bala; Wilkes, Edward D.; Basaran, Osman A.
  • Physics of Fluids, Vol. 14, Issue 8
  • DOI: 10.1063/1.1485077

Pinchoff and satellite formation in surfactant covered viscous threads
journal, April 2002

  • Craster, R. V.; Matar, O. K.; Papageorgiou, D. T.
  • Physics of Fluids, Vol. 14, Issue 4
  • DOI: 10.1063/1.1449893

Formation of beads-on-a-string structures during break-up of viscoelastic filaments
journal, June 2010

  • Bhat, Pradeep P.; Appathurai, Santosh; Harris, Michael T.
  • Nature Physics, Vol. 6, Issue 8
  • DOI: 10.1038/nphys1682

Nonlinear rupture of thin free liquid films
journal, April 1986

  • Prévost, Martine; Gallez, Dominique
  • The Journal of Chemical Physics, Vol. 84, Issue 7
  • DOI: 10.1063/1.450065

The beads-on-string structure of viscoelastic threads
journal, May 2006


Physics of liquid jets
journal, February 2008