Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics
Abstract
When 5 a liquid touches a solid surface, it spreads to minimize the system’s energy. The classic thin-film model describes the spreading as an interplay between gravity, capillarity and viscous forces, but cannot see an end to this process as it does not account for the nonhydrodynamic liquid–solid interactions. Even though these interactions are important only close to the contact line, where the liquid, solid and gas meet, they have macroscopic implications: in the partial-wetting regime, a liquid puddle ultimately stops spreading. We show that 10 by incorporating these intermolecular interactions, the free energy of the system at equilibrium can be cast in a Cahn–Hilliard framework with a height-dependent interfacial tension. Utilizing this free energy, we derive a mesoscopic thin-film model that describes statics and dynamics of liquid spreading in the partial-wetting regime. The height-dependence of the interfacial tension introduces a localized apparent slip in the contact-line region and leads to compactly-supported spreading states. In our model, the contact line dynamics emerge naturally as 15 part of the solution and are therefore nonlocally coupled to the bulk flow. Surprisingly, we find that even in the gravity-dominated regime, the dynamic contact angle follows the Cox–Voinov law.
- Authors:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Technical Univ. of Madrid, Madrid (Spain)
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
- OSTI Identifier:
- 1505719
- Alternate Identifier(s):
- OSTI ID: 1195696
- Grant/Contract Number:
- SC0003907
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 115; Journal Issue: 3; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Alizadeh Pahlavan, Amir, Cueto-Felgueroso, Luis, McKinley, Gareth H., and Juanes, Ruben. Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics. United States: N. p., 2015.
Web. doi:10.1103/physrevlett.115.034502.
Alizadeh Pahlavan, Amir, Cueto-Felgueroso, Luis, McKinley, Gareth H., & Juanes, Ruben. Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics. United States. doi:10.1103/physrevlett.115.034502.
Alizadeh Pahlavan, Amir, Cueto-Felgueroso, Luis, McKinley, Gareth H., and Juanes, Ruben. Fri .
"Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics". United States. doi:10.1103/physrevlett.115.034502. https://www.osti.gov/servlets/purl/1505719.
@article{osti_1505719,
title = {Thin Films in Partial Wetting: Internal Selection of Contact-Line Dynamics},
author = {Alizadeh Pahlavan, Amir and Cueto-Felgueroso, Luis and McKinley, Gareth H. and Juanes, Ruben},
abstractNote = {When 5 a liquid touches a solid surface, it spreads to minimize the system’s energy. The classic thin-film model describes the spreading as an interplay between gravity, capillarity and viscous forces, but cannot see an end to this process as it does not account for the nonhydrodynamic liquid–solid interactions. Even though these interactions are important only close to the contact line, where the liquid, solid and gas meet, they have macroscopic implications: in the partial-wetting regime, a liquid puddle ultimately stops spreading. We show that 10 by incorporating these intermolecular interactions, the free energy of the system at equilibrium can be cast in a Cahn–Hilliard framework with a height-dependent interfacial tension. Utilizing this free energy, we derive a mesoscopic thin-film model that describes statics and dynamics of liquid spreading in the partial-wetting regime. The height-dependence of the interfacial tension introduces a localized apparent slip in the contact-line region and leads to compactly-supported spreading states. In our model, the contact line dynamics emerge naturally as 15 part of the solution and are therefore nonlocally coupled to the bulk flow. Surprisingly, we find that even in the gravity-dominated regime, the dynamic contact angle follows the Cox–Voinov law.},
doi = {10.1103/physrevlett.115.034502},
journal = {Physical Review Letters},
number = 3,
volume = 115,
place = {United States},
year = {2015},
month = {7}
}
Web of Science
Figures / Tables:

Works referenced in this record:
Spreading of nonvolatile liquids in a continuum picture
journal, February 1991
- Brochard-Wyart, Francoise.; Di Meglio, Jean Marc.; Quere, David.
- Langmuir, Vol. 7, Issue 2
Equilibrium contact angles and film thicknesses in the apolar and polar systems: role of intermolecular interactions in coexistence of drops with thin films
journal, December 1993
- Sharma, Ashutosh
- Langmuir, Vol. 9, Issue 12
Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics
journal, August 2000
- Pismen, Len M.; Pomeau, Yves
- Physical Review E, Vol. 62, Issue 2
Disjoining pressure for nonuniform thin films
journal, December 2008
- Dai, Bing; Leal, L. Gary; Redondo, Antonio
- Physical Review E, Vol. 78, Issue 6
On the motion of a fluid-fluid interface along a solid surface
journal, August 1974
- Dussan V., Elizabeth B.; Davis, Stephen H.
- Journal of Fluid Mechanics, Vol. 65, Issue 1
Combining atomistic and continuum simulations of contact-line motion
journal, February 1999
- Hadjiconstantinou, Nicolas G.
- Physical Review E, Vol. 59, Issue 2
Theory of phase-ordering kinetics
journal, March 2002
- Bray, A. J.
- Advances in Physics, Vol. 51, Issue 2
Wetting and spreading
journal, May 2009
- Bonn, Daniel; Eggers, Jens; Indekeu, Joseph
- Reviews of Modern Physics, Vol. 81, Issue 2
Global models for moving contact lines
journal, December 2000
- Diez, Javier A.; Kondic, L.; Bertozzi, Andrea
- Physical Review E, Vol. 63, Issue 1
Slippery questions about complex fluids flowing past solids
journal, April 2003
- Granick, Steve; Zhu, Yingxi; Lee, Hyunjung
- Nature Materials, Vol. 2, Issue 4
The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface
journal, August 1982
- Huppert, Herbert E.
- Journal of Fluid Mechanics, Vol. 121, Issue -1
Precursor films in wetting phenomena
journal, May 2012
- Popescu, M. N.; Oshanin, G.; Dietrich, S.
- Journal of Physics: Condensed Matter, Vol. 24, Issue 24
Dewetting: Film Rupture by Nucleation in the Spinodal Regime
journal, June 2001
- Thiele, Uwe; Velarde, Manuel G.; Neuffer, Kai
- Physical Review Letters, Vol. 87, Issue 1
Power-Law Slip Profile of the Moving Contact Line in Two-Phase Immiscible Flows
journal, August 2004
- Qian, Tiezheng; Wang, Xiao-Ping; Sheng, Ping
- Physical Review Letters, Vol. 93, Issue 9
Spreading of a viscous drop due to gravity and capillarity on a horizontal or an inclined dry wall
journal, January 2002
- Reznik, S. N.; Yarin, A. L.
- Physics of Fluids, Vol. 14, Issue 1
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
book, January 2004
- de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David
A microscopic view on contact angle selection
journal, May 2008
- Snoeijer, Jacco H.; Andreotti, Bruno
- Physics of Fluids, Vol. 20, Issue 5
Spreading kinetics of liquid drops on solids
journal, September 1976
- Lopez, Jaime; Miller, Clarence A.; Ruckenstein, Eli
- Journal of Colloid and Interface Science, Vol. 56, Issue 3
An experimental investigation of the dynamic contact angle in liquid-liquid systems
journal, October 1991
- Fermigier, Marc; Jenffer, Patrice
- Journal of Colloid and Interface Science, Vol. 146, Issue 1
Dynamics of wetting: local contact angles
journal, March 1990
- Gennes, P. G. De; Hua, X.; Levinson, P.
- Journal of Fluid Mechanics, Vol. 212, Issue -1
Kinetic Slip Condition, van der Waals Forces, and Dynamic Contact Angle
journal, August 2001
- Pismen, Len M.; Rubinstein, Boris Y.
- Langmuir, Vol. 17, Issue 17
Hydrodynamic model of steady movement of a solid/liquid/fluid contact line
journal, January 1971
- Huh, Chun; Scriven, L. E.
- Journal of Colloid and Interface Science, Vol. 35, Issue 1
A slope-dependent disjoining pressure for non-zero contact angles
journal, January 1999
- Wu, Qingfang; Wong, Harris
- Journal of Fluid Mechanics, Vol. 506
Continuum models for the contact line problem
journal, October 2010
- Ren, Weiqing; Hu, Dan; E., Weinan
- Physics of Fluids, Vol. 22, Issue 10
Revisiting the Saffman-Taylor Experiment: Imbibition Patterns and Liquid-Entrainment Transitions
journal, July 2014
- Levaché, Bertrand; Bartolo, Denis
- Physical Review Letters, Vol. 113, Issue 4
Dewetting of Solid Surface: Analogy with Spinodal Decomposition
journal, March 1993
- Mitlin, Vladimir S.
- Journal of Colloid and Interface Science, Vol. 156, Issue 2
Nanofluidics, from bulk to interfaces
journal, January 2010
- Bocquet, Lydéric; Charlaix, Elisabeth
- Chem. Soc. Rev., Vol. 39, Issue 3
Three-Phase Contact Line Energetics from Nanoscale Liquid Surface Topographies
journal, August 2000
- Pompe, T.; Herminghaus, S.
- Physical Review Letters, Vol. 85, Issue 9
Critical phenomena in fluid invasion of porous media
journal, February 1991
- Martys, Nicos; Cieplak, Marek; Robbins, Mark O.
- Physical Review Letters, Vol. 66, Issue 8
Droplet Spreading: Partial Wetting Regime Revisited
journal, March 1999
- de Ruijter, M. J.; De Coninck, J.; Oshanin, G.
- Langmuir, Vol. 15, Issue 6
Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle
journal, January 1999
- Eggers, Jens; Stone, Howard A.
- Journal of Fluid Mechanics, Vol. 505
Water Slippage versus Contact Angle: A Quasiuniversal Relationship
journal, November 2008
- Huang, David M.; Sendner, Christian; Horinek, Dominik
- Physical Review Letters, Vol. 101, Issue 22
Surface-Tension-Driven Phenomena
journal, January 1969
- Levich, V. G.; Krylov, V. S.
- Annual Review of Fluid Mechanics, Vol. 1, Issue 1
Phase-Field Model of Long-Time Glasslike Relaxation in Binary Fluid Mixtures
journal, April 2011
- Benzi, R.; Sbragaglia, M.; Bernaschi, M.
- Physical Review Letters, Vol. 106, Issue 16
The atomic detail of a wetting/de-wetting flow
journal, May 2003
- Freund, Jonathan B.
- Physics of Fluids, Vol. 15, Issue 5
A variational approach to moving contact line hydrodynamics
journal, September 2006
- Qian, Tiezheng; Wang, Xiao-Ping; Sheng, Ping
- Journal of Fluid Mechanics, Vol. 564
Boundary slip in Newtonian liquids: a review of experimental studies
journal, October 2005
- Neto, Chiara; Evans, Drew R.; Bonaccurso, Elmar
- Reports on Progress in Physics, Vol. 68, Issue 12
Spreading of “heavy” droplets
journal, March 1992
- Redon, C.; Brochard-Wyart, F.; Hervet, H.
- Journal of Colloid and Interface Science, Vol. 149, Issue 2
Free Energy of a Nonuniform System. I. Interfacial Free Energy
journal, February 1958
- Cahn, John W.; Hilliard, John E.
- The Journal of Chemical Physics, Vol. 28, Issue 2
Macroscopic Phase-Field Model of Partial Wetting: Bubbles in a Capillary Tube
journal, April 2012
- Cueto-Felgueroso, Luis; Juanes, Ruben
- Physical Review Letters, Vol. 108, Issue 14
The moving contact line: the slip boundary condition
journal, October 1976
- Dussan V., E. B.
- Journal of Fluid Mechanics, Vol. 77, Issue 4
The origin of flow during wetting of solids
journal, September 1974
- Miller, C. A.; Ruckenstein, E.
- Journal of Colloid and Interface Science, Vol. 48, Issue 3
Theory of dynamic critical phenomena
journal, July 1977
- Hohenberg, P. C.; Halperin, B. I.
- Reviews of Modern Physics, Vol. 49, Issue 3
Dynamics of immiscible-fluid displacement in a capillary tube
journal, February 1990
- Zhou, Min-Yao; Sheng, Ping
- Physical Review Letters, Vol. 64, Issue 8
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
The influence of intermolecular forces on thin fluid layers
journal, April 1993
- Hocking, L. M.
- Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 4
The spreading of silicone oil drops on horizontal surfaces
journal, September 1979
- Tanner, L. H.
- Journal of Physics D: Applied Physics, Vol. 12, Issue 9
Spreading of droplets on a solid surface
journal, July 1993
- Brenner, Michael; Bertozzi, Andrea
- Physical Review Letters, Vol. 71, Issue 4
Microscopic and Macroscopic Structure of the Precursor Layer in Spreading Viscous Drops
journal, November 2003
- Kavehpour, H. Pirouz; Ovryn, Ben; McKinley, Gareth H.
- Physical Review Letters, Vol. 91, Issue 19
Thin Film Instability Induced by Long-Range Forces
journal, March 1999
- Reiter, Günter; Sharma, Ashutosh; Casoli, Alain
- Langmuir, Vol. 15, Issue 7
Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system
journal, August 2012
- Sibley, David N.; Savva, Nikos; Kalliadasis, Serafim
- Physics of Fluids, Vol. 24, Issue 8
Simulations of contact-line motion: Slip and the dynamic contact angle
journal, August 1989
- Thompson, Peter A.; Robbins, Mark O.
- Physical Review Letters, Vol. 63, Issue 7
Wetting: statics and dynamics
journal, July 1985
- de Gennes, P. G.
- Reviews of Modern Physics, Vol. 57, Issue 3, p. 827-863
The Spreading of a thin drop by Gravity and Capillarity
journal, January 1983
- Hocking, L. M.
- The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 36, Issue 1
Slip velocity during wetting of solids
journal, March 1977
- Ruckenstein, E.; Dunn, C. S.
- Journal of Colloid and Interface Science, Vol. 59, Issue 1
Dynamics and stability of thin liquid films
journal, August 2009
- Craster, R. V.; Matar, O. K.
- Reviews of Modern Physics, Vol. 81, Issue 3
The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow
journal, July 1986
- Cox, R. G.
- Journal of Fluid Mechanics, Vol. 168, Issue -1
Nonlocal Dynamics of Spontaneous Imbibition Fronts
journal, August 2002
- Geromichalos, Dimitrios; Mugele, Frieder; Herminghaus, Stephan
- Physical Review Letters, Vol. 89, Issue 10
Relationship of thin film stability and morphology to macroscopic parameters of wetting in the apolar and polar systems
journal, March 1993
- Sharma, Ashutosh
- Langmuir, Vol. 9, Issue 3
Moving Contact Lines: Scales, Regimes, and Dynamical Transitions
journal, January 2013
- Snoeijer, Jacco H.; Andreotti, Bruno
- Annual Review of Fluid Mechanics, Vol. 45, Issue 1
Molecular scale contact line hydrodynamics of immiscible flows
journal, July 2003
- Qian, Tiezheng; Wang, Xiao-Ping; Sheng, Ping
- Physical Review E, Vol. 68, Issue 1
Moving contact lines in liquid/liquid/solid systems
journal, March 1997
- Shikhmurzaev, Yulii D.
- Journal of Fluid Mechanics, Vol. 334
Boundary conditions for the moving contact line problem
journal, February 2007
- Ren, Weiqing; E., Weinan
- Physics of Fluids, Vol. 19, Issue 2
Equilibrium configurations of liquid droplets on solid surfaces under the influence of thin-film forces
journal, October 1999
- Yeh, E. K.; Newman, John; Radke, C. J.
- Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 156, Issue 1-3
Experiments on a spreading drop and its contact angle on a solid
journal, March 1988
- Chen, Jing-Den
- Journal of Colloid and Interface Science, Vol. 122, Issue 1
Dynamics of Liquid Spreading on Solid Surfaces
journal, January 1996
- Kalliadasis, Serafim; Chang, Hsueh-Chia
- Industrial & Engineering Chemistry Research, Vol. 35, Issue 9
A study of the advancing interface. I. Interface shape in liquid—gas systems
journal, February 1975
- Hoffman, Richard L.
- Journal of Colloid and Interface Science, Vol. 50, Issue 2
Dynamic Scaling of Growing Interfaces
journal, March 1986
- Kardar, Mehran; Parisi, Giorgio; Zhang, Yi-Cheng
- Physical Review Letters, Vol. 56, Issue 9
Dynamics of Nanoscale Precursor Film near a Moving Contact Line of Spreading Drops
journal, June 2011
- Hoang, A.; Kavehpour, H. P.
- Physical Review Letters, Vol. 106, Issue 25
Figures / Tables found in this record: