Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T16:59:25.637Z Has data issue: false hasContentIssue false
  • English
  • Français

Thin films in partial wetting: stability, dewetting and coarsening

Published online by Cambridge University Press:  27 April 2018

A. Alizadeh Pahlavan Open the ORCID record for A. Alizadeh Pahlavan [Opens in a new window] ,
L. Cueto-Felgueroso Open the ORCID record for L. Cueto-Felgueroso [Opens in a new window] ,
A. E. Hosoi ,
G. H. McKinley Open the ORCID record for G. H. McKinley [Opens in a new window]  and
R. Juanes Open the ORCID record for R. Juanes [Opens in a new window]
A. Alizadeh Pahlavan
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
L. Cueto-Felgueroso
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
A. E. Hosoi
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
G. H. McKinley
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
R. Juanes*
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: juanes@mit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A uniform nanometric thin liquid film on a solid substrate can become unstable due to the action of van der Waals (vdW) forces. The instability leads to dewetting of the uniform film and the formation of drops. To minimize the total free energy of the system, these drops coarsen over time until one single drop remains. Here, using a thermodynamically consistent framework, we derive a new model for thin films in partial wetting with a free energy that resembles the Cahn–Hilliard form with a height-dependent surface tension that leads to a generalized disjoining pressure, and revisit the dewetting problem. Using both linear stability analysis and nonlinear simulations we show that the new model predicts a slightly smaller critical instability wavelength and a significantly (up to six-fold) faster growth rate than the classical model in the spinodal regime; this faster growth rate brings the theoretical predictions closer to published experimental observations. During coarsening at intermediate times, the dynamics become self-similar and model-independent; we therefore observe the same scalings in both the classical (with and without thermal noise) and new models. Both models also lead to a mean-field Lifshitz–Slyozov–Wagner (LSW)-type droplet-size distribution at intermediate times for small drop sizes. We, however, observe a skewed drop-size distribution for larger drops in the new model; while the tail of the distribution follows a Smoluchowski equation, it is not associated with a coalescence-dominated coarsening, calling into question the association made in some earlier experiments. Our observations point to the importance of the height dependence of surface tension in the early and late stages of dewetting of nanometric films and motivate new high-resolution experimental observations to guide the development of improved models of interfacial flows at the nanoscale.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 2018 , pp. 642 - 681
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amirfazli, A. & Neumann, A. W. 2004 Status of the three-phase line tension: a review. Adv. Colloid Interface Sci. 110 (3), 121–141.Google Scholar
Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139–165.CrossRefGoogle Scholar
Aranson, I. S. & Tsimring, L. S. 2006 Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78, 641–692.CrossRefGoogle Scholar
Arfken, G. B., Weber, H. J. & Harris, F. E.(Eds) 2013 Mathematical Methods for Physicists, 7th edn. Academic Press.Google Scholar
Barenblatt, G. I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Bauer, C. & Dietrich, S. 1999 Quantitative study of laterally inhomogeneous wetting films. Eur. Phys. J. B 10 (4), 767–779.CrossRefGoogle Scholar
Bäumchen, O., Fetzer, R., Klos, M., Lessel, M., Marquant, L., Hähl, H. & Jacobs, K. 2012 Slippage and nanorheology of thin liquid polymer films. J. Phys.: Condens. Matter 24 (32), 325102.Google Scholar
Bäumchen, O. & Jacobs, K. 2010 Slip effects in polymer thin films. J. Phys.: Condens. Matter 22 (3), 033102.Google Scholar
Bäumchen, O., Marquant, L., Blossey, R., Münch, A., Wagner, B. & Jacobs, K. 2014 Influence of slip on the Rayleigh–Plateau rim instability in dewetting viscous films. Phys. Rev. Lett. 113, 014501.CrossRefGoogle ScholarPubMed
Becker, J., Grun, G., Seemann, R., Mantz, H., Jacobs, K., Mecke, K. R. & Blossey, R. 2003 Complex dewetting scenarios captured by thin-film models. Nat. Mater. 2 (1), 59–63.Google Scholar
Belardinelli, D., Sbragaglia, M., Gross, M. & Andreotti, B. 2016 Thermal fluctuations of an interface near a contact line. Phys. Rev. E 94, 052803.Google Scholar
Benzi, R., Sbragaglia, M., Bernaschi, M. & Succi, S. 2011 Phase-field model of long-time glasslike relaxation in binary fluid mixtures. Phys. Rev. Lett. 106, 164501.Google Scholar
Bertozzi, A. L., Grün, G. & Witelski, T. P. 2001 Dewetting films: bifurcations and concentrations. Nonlinearity 14 (6), 1569–1592.Google Scholar
Bibette, J., Calderon, F. L. & Poulin, P. 1999 Emulsions: basic principles. Rep. Prog. Phys. 62 (6), 969–1033.CrossRefGoogle Scholar
Bischof, J., Scherer, D., Herminghaus, S. & Leiderer, P. 1996 Dewetting modes of thin metallic films: nucleation of holes and spinodal dewetting. Phys. Rev. Lett. 77, 1536–1539.Google Scholar
Blake, T. D. & Ruschak, K. J. 1979 A maximum speed of wetting. Nature 282 (5738), 489–491.Google Scholar
Blossey, R. 2012 Thin Liquid Films: Dewetting and Polymer Flow. Springer.CrossRefGoogle Scholar
Bocquet, L. & Charlaix, E. 2010 Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39, 1073–1095.CrossRefGoogle ScholarPubMed
Bocquet, L. & Tabeling, P. 2014 Physics and technological aspects of nanofluidics. Lab on a Chip 14, 3143–3158.CrossRefGoogle ScholarPubMed
Bollinne, C., Cuenot, S., Nysten, B. & Jonas, A. M. 2003 Spinodal-like dewetting of thermodynamically-stable thin polymer films. Eur. Phys. J. E 12 (3), 389–396.Google ScholarPubMed
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739–805.Google Scholar
Braun, R. J. 2012 Dynamics of the tear film. Annu. Rev. Fluid Mech. 44 (1), 267–297.Google Scholar
Bray, A. J. 2002 Theory of phase-ordering kinetics. Adv. Phys. 51 (2), 481–587.Google Scholar
Brenner, M. & Bertozzi, A. 1993 Spreading of droplets on a solid surface. Phys. Rev. Lett. 71, 593–596.CrossRefGoogle ScholarPubMed
Brochard-Wyart, F., Di Meglio, J. M., Quere, D. & de Gennes, P.-G. 1991 Spreading of nonvolatile liquids in a continuum picture. Langmuir 7 (2), 335–338.Google Scholar
Brochard-Wyart, F., Martin, P. & Redon, C. 1993 Liquid/liquid dewetting. Langmuir 9 (12), 3682–3690.Google Scholar
Cahn, J. W. 1961 On spinodal decomposition. Acta Metall. 9 (9), 795–801.Google Scholar
Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a nonuniform system. i. Interfacial free energy. J. Chem. Phys. 28 (2), 258–267.Google Scholar
Chen, J.-T., Zhang, M. & Russell, T. P. 2007 Instabilities in nanoporous media. Nano Lett. 7 (1), 183–187.Google Scholar
Chen, L., Yu, J. & Wang, H. 2014 Convex nanobending at a moving contact line: the missing mesoscopic link in dynamic wetting. ACS Nano 8 (11), 11493–11498.Google Scholar
Colin, A., Squires, T. M. & Bocquet, L. 2012 Soft matter principles of microfluidics. Soft Matt. 8, 10527–10529.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.Google Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.Google Scholar
Cueto-Felgueroso, L. & Juanes, R. 2012 Macroscopic phase-field model of partial wetting: bubbles in a capillary tube. Phys. Rev. Lett. 108, 144502.Google Scholar
Dai, B., Leal, L. G. & Redondo, A. 2008 Disjoining pressure for nonuniform thin films. Phys. Rev. E 78, 061602.Google Scholar
Davidovitch, B., Moro, E. & Stone, H. A. 2005 Spreading of viscous fluid drops on a solid substrate assisted by thermal fluctuations. Phys. Rev. Lett. 95, 244505.CrossRefGoogle ScholarPubMed
Deng, Y., Chen, L., Liu, Q., Yu, J. & Wang, H. 2016 Nanoscale view of dewetting and coating on partially wetted solids. J. Phys. Chem. Lett. 7 (10), 1763–1768.CrossRefGoogle ScholarPubMed
Diez, J. A., González, A. G. & Fernández, R. 2016 Metallic-thin-film instability with spatially correlated thermal noise. Phys. Rev. E 93, 013120.Google Scholar
Diez, J. A. & Kondic, L. 2007 On the breakup of fluid films of finite and infinite extent. Phys. Fluids 19 (7), 072107.CrossRefGoogle Scholar
Dzyaloshinskii, I. E., Lifshitz, E. M. & Pitaevskii, L. P. 1961 The general theory of van der Waals forces. Adv. Phys. 10 (38), 165–209.Google Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.Google Scholar
Fetzer, R., Jacobs, K., Münch, A., Wagner, B. & Witelski, T. P. 2005 New slip regimes and the shape of dewetting thin liquid films. Phys. Rev. Lett. 95, 127801.Google Scholar
Fetzer, R., Münch, A., Wagner, B., Rauscher, M. & Jacobs, K. 2007a Quantifying hydrodynamic slip: a comprehensive analysis of dewetting profiles. Langmuir 23 (21), 10559–10566.Google Scholar
Fetzer, R., Rauscher, M., Seemann, R., Jacobs, K. & Mecke, K. 2007b Thermal noise influences fluid flow in thin films during spinodal dewetting. Phys. Rev. Lett. 99, 114503.Google Scholar
Fowlkes, J. D., Kondic, L., Diez, J., Wu, Y. & Rack, P. D. 2011 Self-assembly versus directed assembly of nanoparticles via pulsed laser induced dewetting of patterned metal films. Nano Lett. 11 (6), 2478–2485.Google Scholar
Gates, B. D., Xu, Q., Stewart, M., Ryan, D., Willson, C. G. & Whitesides, G. M. 2005 New approaches to nanofabrication: molding, printing, and other techniques. Chem. Rev. 105 (4), 1171–1196.Google Scholar
Gau, H., Herminghaus, S., Lenz, P. & Lipowsky, R. 1999 Liquid morphologies on structured surfaces: from microchannels to microchips. Science 283 (5398), 46–49.Google Scholar
de Gennes, P.-G. 1980 Dynamics of fluctuations and spinodal decomposition in polymer blends. J. Chem. Phys. 72 (9), 4756–4763.Google Scholar
de Gennes, P.-G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.Google Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.CrossRefGoogle Scholar
Gentili, D., Foschi, G., Valle, F., Cavallini, M. & Biscarini, F. 2012 Applications of dewetting in micro and nanotechnology. Chem. Soc. Rev. 41, 4430–4443.Google Scholar
Geoghegan, M. & Krausch, G. 2003 Wetting at polymer surfaces and interfaces. Prog. Polym. Sci. 28 (2), 261–302.Google Scholar
Getta, T. & Dietrich, S. 1998 Line tension between fluid phases and a substrate. Phys. Rev. E 57, 655–671.Google Scholar
Giro, R., Bryant, P. W., Engel, M., Neumann, R. F. & Steiner, M. B. 2017 Adsorption energy as a metric for wettability at the nanoscale. Sci. Rep. 7 (46317).Google Scholar
Glasner, K. 2008 Ostwald ripening in thin film equations. SIAM J. Appl. Maths 69 (2), 473–493.Google Scholar
Glasner, K. B. & Witelski, T. P. 2005 Collision versus collapse of droplets in coarsening of dewetting thin films. Physica D 209 (1–4), 80–104.Google Scholar
Glasner, K. B. & Witelski, T. P. 2003 Coarsening dynamics of dewetting films. Phys. Rev. E 67, 016302.Google Scholar
Gogotsi, Y., Libera, J. A., Güvenç-Yazicioglu, A. & Megaridis, C. M. 2001 In situ multiphase fluid experiments in hydrothermal carbon nanotubes. Appl. Phys. Lett. 79 (7), 1021–1023.Google Scholar
Granick, S., Zhu, Y. & Lee, H. 2003 Slippery questions about complex fluids flowing past solids. Nat. Mater. 2 (4), 221–227.Google Scholar
Gratton, M. B.2008 coarsening of thin fluid films. PhD thesis, Department of Mathematics, Duke University.Google Scholar
Gratton, M. B. & Witelski, T. P. 2008 Coarsening of unstable thin films subject to gravity. Phys. Rev. E 77, 016301.Google Scholar
Gratton, M. B. & Witelski, T. P. 2009 Transient and self-similar dynamics in thin film coarsening. Physica D 238 (23–24), 2380–2394.Google Scholar
Green, P. F. 2003 Wetting and dynamics of structured liquid films. J. Polym. Sci. B 41 (19), 2219–2235.Google Scholar
Grün, G., Mecke, K. & Rauscher, M. 2006 Thin-film flow influenced by thermal noise. J. Stat. Phys. 122 (6), 1261–1291.Google Scholar
Gupta, A., Eral, H. B., Hatton, T. A. & Doyle, P. S. 2016 Nanoemulsions: formation, properties and applications. Soft Matt. 12, 2826–2841.Google Scholar
van Hameren, R., Schön, P., van Buul, A. M., Hoogboom, J., Lazarenko, S. V., Gerritsen, J. W., Engelkamp, H., Christianen, P. C. M., Heus, H. A., Maan, J. C., Rasing, T., Speller, S., Rowan, A. E., Elemans, J. A. A. W. & Nolte, R. J. M. 2006 Macroscopic hierarchical surface patterning of porphyrin trimers via self-assembly and dewetting. Science 314 (5804), 1433.Google Scholar
Hammoud, N. H., Trinh, P. H., Howell, P. D. & Stone, H. A. 2017 Influence of van der Waals forces on a bubble moving in a tube. Phys. Rev. Fluids 2, 063601.Google Scholar
Han, W. & Lin, Z. 2012 Learning from ‘coffee rings’: ordered structures enabled by controlled evaporative self-assembly. Angew. Chem. Intl Ed. Engl. 51 (7), 1534–1546.Google Scholar
Herminghaus, S., Jacobs, K., Mecke, K., Bischof, J., Fery, A., Ibn-Elhaj, M. & Schlagowski, S. 1998 Spinodal dewetting in liquid crystal and liquid metal films. Science 282 (5390), 916–919.Google Scholar
Herminghaus, S., Jacobs, K. & Seemann, R. 2001 The glass transition of thin polymer films: some questions, and a possible answer. Eur. Phys. J. E 5 (1), 531–538.Google Scholar
Herminghaus, S., Seemann, R. & Jacobs, K. 2002 Generic morphologies of viscoelastic dewetting fronts. Phys. Rev. Lett. 89, 056101.Google Scholar
Heslot, F., Cazabat, A. M., Levinson, P. & Fraysse, N. 1990 Experiments on wetting on the scale of nanometers: influence of the surface energy. Phys. Rev. Lett. 65, 599–602.Google Scholar
Higgins, A. M. & Jones, R. A. L. 2000 Anisotropic spinodal dewetting as a route to self-assembly of patterned surfaces. Nature 404 (6777), 476–478.Google Scholar
Hocking, L. M. 1993 The influence of intermolecular forces on thin fluid layers. Phys. Fluids A 5 (4), 793–799.Google Scholar
Hohenberg, P. C. & Halperin, B. I. 1977 Theory of dynamic critical phenomena. Rev. Mod. Phys. 49, 435–479.Google Scholar
Huang, J., Kim, F., Tao, A. R., Connor, S. & Yang, P. 2005 Spontaneous formation of nanoparticle stripe patterns through dewetting. Nat. Mater. 4 (12), 896–900.Google Scholar
Huang, J. Y., Lo, Y.-C., Niu, J. J., Kushima, A., Qian, X., Zhong, L., Mao, S. X. & Li, J. 2013 Nanowire liquid pumps. Nat. Nanotechnol. 8 (4), 277–281.Google Scholar
Huerre, A., Theodoly, O., Leshansky, A. M., Valignat, M.-P., Cantat, I. & Jullien, M.-C. 2015 Droplets in microchannels: dynamical properties of the lubrication film. Phys. Rev. Lett. 115, 064501.Google Scholar
Imhof, A. & Pine, D. J. 1997 Stability of nonaqueous emulsions. J. Colloid Interface Sci. 192 (2), 368–374.Google Scholar
Indeikina, A. & Chang, H.-C. 1999 A molecular theory for dynamic contact angles. In IUTAM Symposium on Non-linear Singularities in Deformation and Flow: Proceedings of the IUTAM Symposium held in Haifa, Israel 17–21 March 1997 (ed. Durban, D. & Pearson, J. R. A.), pp. 321–337. Springer.Google Scholar
Israelachvili, J. N. 2011 Intermolecular and Surface Forces. Academic Press.Google Scholar
Jacobs, K., Herminghaus, S. & Mecke, K. R. 1998 Thin liquid polymer films rupture via defects. Langmuir 14 (4), 965–969.Google Scholar
Kahlweit, M. 1975 Ostwald ripening of precipitates. Adv. Colloid Interface Sci. 5 (1), 1–35.CrossRefGoogle Scholar
Kardar, M., Parisi, G. & Zhang, Y.-C. 1986 Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892.Google Scholar
Keiser, L., Bense, H., Colinet, P., Bico, J. & Reyssat, E. 2017 Marangoni bursting: evaporation-induced emulsification of binary mixtures on a liquid layer. Phys. Rev. Lett. 118, 074504.Google Scholar
Keller, J. B. & Merchant, G. J. 1991 Flexural rigidity of a liquid surface. J. Stat. Phys. 63 (5–6), 1039–1051.Google Scholar
Kong, Y. L., Boulogne, F., Kim, H., Nunes, J., Feng, J. & Stone, H. A. 2015 Deposition of quantum dots in a capillary tube. Langmuir 31 (45), 12560–12566.Google Scholar
Kong, Y. L., Gupta, M. K., Johnson, B. N. & McAlpine, M. C. 2016 3D printed bionic nanodevices. Nano Today 11 (3), 330–350.Google Scholar
Kumar, S. 2015 Liquid transfer in printing processes: liquid bridges with moving contact lines. Annu. Rev. Fluid Mech. 47 (1), 67–94.Google Scholar
Kundan, A., Nguyen, T. T. T., Plawsky, J. L., Wayner, P. C., Chao, D. F. & Sicker, R. J. 2017 Condensation on highly superheated surfaces: unstable thin films in a wickless heat pipe. Phys. Rev. Lett. 118, 094501.Google Scholar
Langer, J. S. 1971 Theory of spinodal decomposition in alloys. Ann. Phys. 65 (1), 53–86.CrossRefGoogle Scholar
Lauga, E., Brenner, M. & Stone, H. 2007 Microfluidics: The No-Slip Boundary Condition. pp. 1219–1240. Springer.Google Scholar
Leal, L. G. 2004 Flow induced coalescence of drops in a viscous fluid. Phys. Fluids 16 (6), 1833–1851.Google Scholar
Li, J. 2016 Macroscopic model for head-on binary droplet collisions in a gaseous medium. Phys. Rev. Lett. 117, 214502.Google Scholar
Lifshitz, I. M. & Slyozov, V. V. 1961 The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19 (1), 35–50.Google Scholar
Limary, R. & Green, P. F. 2002 Late-stage coarsening of an unstable structured liquid film. Phys. Rev. E 66, 021601.Google Scholar
Limary, R. & Green, P. F. 2003 Dynamics of droplets on the surface of a structured fluid film: late-stage coarsening. Langmuir 19 (6), 2419–2424.Google Scholar
Liu, L. & Risbud, S. H. 1990 Quantum-dot size-distribution analysis and precipitation stages in semiconductor doped glasses. J. Appl. Phys. 68 (1), 28–32.Google Scholar
Lo, A. & Skodje, R. T. 2000 Kinetic and Monte Carlo models of thin film coarsening: cross over from diffusion-coalescence to Ostwald growth modes. J. Chem. Phys. 112 (4), 1966–1974.Google Scholar
Lohse, D. & Zhang, X. 2015 Surface nanobubbles and nanodroplets. Rev. Mod. Phys. 87, 981–1035.Google Scholar
Lopes, W. A. & Jaeger, H. M. 2001 Hierarchical self-assembly of metal nanostructures on diblock copolymer scaffolds. Nature 414 (6865), 735–738.Google Scholar
MacDowell, L. G., Benet, J. & Katcho, N. A. 2013 Capillary fluctuations and film-height-dependent surface tension of an adsorbed liquid film. Phys. Rev. Lett. 111, 047802.Google Scholar
MacDowell, L. G., Benet, J., Katcho, N. A. & Palanco, J. M. G. 2014 Disjoining pressure and the film-height-dependent surface tension of thin liquid films: new insight from capillary wave fluctuations. Adv. Colloid Interface Sci. 206, 150–171.Google Scholar
Mantz, H., Jacobs, K. & Mecke, K. 2008 Utilizing Minkowski functionals for image analysis: a marching square algorithm. J. Stat. Mech.: Theory Exp. 2008 (12), P12015.Google Scholar
Marchand, A., Weijs, J. H., Snoeijer, J. H. & Andreotti, B. 2011 Why is surface tension a force parallel to the interface? Am. J. Phys. 79 (10), 999–1008.Google Scholar
McGraw, J. D., Bäumchen, O., Klos, M., Haefner, S., Lessel, M., Backes, S. & Jacobs, K. 2014 Nanofluidics of thin polymer films: linking the slip boundary condition at solid–liquid interfaces to macroscopic pattern formation and microscopic interfacial properties. Adv. Colloid Interface Sci. 210, 13–20.Google Scholar
McGraw, J. D., Chan, T. S., Maurer, S., Salez, T., Benzaquen, M., Raphaël, E., Brinkmann, M. & Jacobs, K. 2016 Slip-mediated dewetting of polymer microdroplets. Proc. Natl Acad. Sci. USA 113 (5), 1168–1173.Google Scholar
McKeown, J. T., Wu, Y., Fowlkes, J. D., Rack, P. D. & Campbell, G. H. 2015 Simultaneous in-situ synthesis and characterization of co@cu core-shell nanoparticle arrays. Adv. Mater. 27 (6), 1060–1065.Google Scholar
Mecke, K. & Rauscher, M. 2005 On thermal fluctuations in thin film flow. J. Phys.: Condens. Matter 17 (45), S3515.Google Scholar
Mecke, K. R. 1998 Integral geometry in statistical physics. Intl J. Mod. Phys. B 12 (09), 861–899.Google Scholar
Meli, L. & Green, P. F. 2008 Aggregation and coarsening of ligand-stabilized gold nanoparticles in poly(methyl methacrylate) thin films. ACS Nano 2 (6), 1305–1312.CrossRefGoogle ScholarPubMed
Merchant, G. J. & Keller, J. B. 1992 Contact angles. Phys. Fluids A 4 (3), 477–485.CrossRefGoogle Scholar
Meredith, J. C., Smith, A. P., Karim, A. & Amis, E. J. 2000 Combinatorial materials science for polymer thin-film dewetting. Macromolecules 33 (26), 9747–9756.Google Scholar
Miller, C. A. & Ruckenstein, E. 1974 The origin of flow during wetting of solids. J. Colloid Interface Sci. 48 (3), 368–373.Google Scholar
Mitlin, V. S. 1993 Dewetting of solid surface: analogy with spinodal decomposition. J. Colloid Interface Sci. 156 (2), 491–497.Google Scholar
Molares, M. E. T., Balogh, A. G., Cornelius, T. W., Neumann, R. & Trautmann, C. 2004 Fragmentation of nanowires driven by Rayleigh instability. Appl. Phys. Lett. 85 (22), 5337–5339.Google Scholar
Mukherjee, R. & Sharma, A. 2015 Instability, self-organization and pattern formation in thin soft films. Soft Matt. 11, 8717–8740.Google Scholar
Nesic, S., Cuerno, R., Moro, E. & Kondic, L. 2015 Fully nonlinear dynamics of stochastic thin-film dewetting. Phys. Rev. E 92, 061002.Google Scholar
Neto, C., Evans, D. R., Bonaccurso, E., Butt, H.-J. & Craig, V. S. J. 2005 Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 68 (12), 2859.Google Scholar
Neto, C., Jacobs, K., Seemann, R., Blossey, R., Becker, J. & Grün, G. 2003 Satellite hole formation during dewetting: experiment and simulation. J. Phys.: Condens. Matter 15 (19), 3355–3366.Google Scholar
Nguyen, T. D., Fuentes-Cabrera, M., Fowlkes, J. D. & Rack, P. D. 2014 Coexistence of spinodal instability and thermal nucleation in thin-film rupture: insights from molecular levels. Phys. Rev. E 89, 032403.Google Scholar
Novick-Cohen, A. 1985 The nonlinear Cahn–Hilliard equation: transition from spinodal decomposition to nucleation behavior. J. Stat. Phys. 38 (3), 707–723.Google Scholar
Oron, A. 2000 Three-dimensional nonlinear dynamics of thin liquid films. Phys. Rev. Lett. 85, 2108–2111.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.Google Scholar
Ostwald, W. 1897 Studien über die Bildung und Umwandlung fester Körper: Übersättigung und Überkaltung. Z. Phys. Chem. 22, 289–330.Google Scholar
Otto, F., Rump, T. & Slepcev, D. 2006 Coarsening rates for a droplet model: rigorous upper bounds. SIAM J. Math. Anal. 38 (2), 503–529.CrossRefGoogle Scholar
Pahlavan, A. A., Cueto-Felgueroso, L., McKinley, G. H. & Juanes, R. 2015 Thin films in partial wetting: internal selection of contact-line dynamics. Phys. Rev. Lett. 115, 034502.Google Scholar
Pierre-Louis, O. 2016 Solid-state wetting at the nanoscale. Prog. Cryst. Growth Charact. Mater. 62 (2), 177–202.Google Scholar
Pokroy, B., Kang, S. H., Mahadevan, L. & Aizenberg, J. 2009 Self-organization of a mesoscale bristle into ordered, hierarchical helical assemblies. Science 323 (5911), 237–240.Google Scholar
Pompe, T. & Herminghaus, S. 2000 Three-phase contact line energetics from nanoscale liquid surface topographies. Phys. Rev. Lett. 85, 1930–1933.Google Scholar
Qian, B., Park, J. & Breuer, K. S. 2015 Large apparent slip at a moving contact line. Phys. Fluids 27 (9), 091703.Google Scholar
Qin, D., Xia, Y. & Whitesides, G. M. 2010 Soft lithography for micro- and nanoscale patterning. Nat. Protocols 5 (3), 491–502.Google Scholar
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31 (1), 347–384.Google Scholar
Rauscher, M. & Dietrich, S. 2008 Wetting phenomena in nanofluidics. Annu. Rev. Mater. Res. 38 (1), 143–172.Google Scholar
Reiter, G. 1992 Dewetting of thin polymer films. Phys. Rev. Lett. 68, 75–78.Google Scholar
Reiter, G. 1993 Unstable thin polymer films: rupture and dewetting processes. Langmuir 9 (5), 1344–1351.Google Scholar
Reiter, G., Hamieh, M., Damman, P., Sclavons, S., Gabriele, S., Vilmin, T. & Raphael, E. 2005 Residual stresses in thin polymer films cause rupture and dominate early stages of dewetting. Nat. Mater. 4 (10), 754–758.Google Scholar
Reiter, G. & Sharma, A. 2001 Auto-optimization of dewetting rates by rim instabilities in slipping polymer films. Phys. Rev. Lett. 87, 166103.Google Scholar
Reynolds, O. 1886 On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Phil. Trans. R. Soc. Lond. 177, 157–234.Google Scholar
Rowlinson, J. S. 1979 Translation of J. D. van der Waals’ ‘The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density’. J. Stat. Phys. 20 (2), 197–200.Google Scholar
Rowlinson, J. S. & Widom, B. 2013 Molecular Theory of Capillarity. Courier Corporation.Google Scholar
Ruckenstein, E. & Jain, R. K. 1974 Spontaneous rupture of thin liquid films. J. Chem. Soc. Faraday Trans. II 70, 132–147.Google Scholar
Ruschak, K. J. 1985 Coating flows. Annu. Rev. Fluid Mech. 17 (1), 65–89.Google Scholar
Schimmele, L., Napiorkowski, M. & Dietrich, S. 2007 Conceptual aspects of line tensions. J. Chem. Phys. 127 (16), 164715.Google Scholar
Schmidt, V., Wittemann, J. V. & Gösele, U. 2010 Growth, thermodynamics, and electrical properties of silicon nanowires. Chem. Rev. 110 (1), 361–388.Google Scholar
Schoch, R. B., Han, J. & Renaud, P. 2008 Transport phenomena in nanofluidics. Rev. Mod. Phys. 80, 839–883.Google Scholar
Seemann, R., Herminghaus, S. & Jacobs, K. 2001a Dewetting patterns and molecular forces: a reconciliation. Phys. Rev. Lett. 86, 5534–5537.Google Scholar
Seemann, R., Herminghaus, S. & Jacobs, K. 2001b Shape of a liquid front upon dewetting. Phys. Rev. Lett. 87, 196101.Google Scholar
Seemann, R., Herminghaus, S., Neto, C., Schlagowski, S., Podzimek, D., Konrad, R., Mantz, H. & Jacobs, K. 2005 Dynamics and structure formation in thin polymer melt films. J. Phys.: Condens. Matter 17 (9), S267.Google Scholar
Segalman, R. A. 2005 Patterning with block copolymer thin films. Mater. Sci. Engng 48 (6), 191–226.Google Scholar
Segalman, R. A. & Green, P. F. 1999 Dynamics of rims and the onset of spinodal dewetting at liquid/liquid interfaces. Macromolecules 32 (3), 801–807.Google Scholar
Shao-Horn, Y., Sheng, W. C., Chen, S., Ferreira, P. J., Holby, E. F. & Morgan, D. 2007 Instability of supported platinum nanoparticles in low-temperature fuel cells. Top. Catal. 46 (3), 285–305.Google Scholar
Sharma, A. 1993a Equilibrium contact angles and film thicknesses in the apolar and polar systems: role of intermolecular interactions in coexistence of drops with thin films. Langmuir 9 (12), 3580–3586.Google Scholar
Sharma, A. 1993b Relationship of thin film stability and morphology to macroscopic parameters of wetting in the apolar and polar systems. Langmuir 9 (3), 861–869.Google Scholar
Sharma, A. 2003 Many paths to dewetting of thin films: anatomy and physiology of surface instability. Eur. Phys. J. E 12 (3), 397–408.Google Scholar
Sharma, A. & Khanna, R. 1998 Pattern formation in unstable thin liquid films. Phys. Rev. Lett. 81, 3463–3466.Google Scholar
Sharma, A. & Reiter, G. 1996 Instability of thin polymer films on coated substrates: rupture, dewetting, and drop formation. J. Colloid Interface Sci. 178 (2), 383–399.Google Scholar
Sheludko, A. 1967 Thin liquid films. Adv. Colloid Interface Sci. 1 (4), 391–464.Google Scholar
Shikhmurzaev, Y. D. 1997 Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech. 334, 211–249.Google Scholar
Shikhmurzaev, Y. D. 2007 Capillary Flows with Forming Interfaces. CRC Press.Google Scholar
Sholl, D. S. & Skodje, R. T. 1996 Late-stage coarsening of adlayers by dynamic cluster coalescence. Physica A 231 (4), 631–647.Google Scholar
Sibley, D., Savva, N. & Kalliadasis, S. 2012 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. Phys. Fluids 24 (8), 082105.Google Scholar
Sibley, D. N., Nold, A., Savva, N. & Kalliadasis, S. 2015 A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading. J. Engng Maths 94 (1), 19–41.Google Scholar
Siggia, E. D. 1979 Late stages of spinodal decomposition in binary mixtures. Phys. Rev. A 20, 595–605.Google Scholar
Smoluchowski, M. V. 1917 Grundriß der Koagulationskinetik kolloider Lösungen. Colloid Polym. Sci. 21 (3), 98–104.Google Scholar
Snoeijer, J. H. & Andreotti, B. 2008 A microscopic view on contact angle selection. Phys. Fluids 20 (5), 057101.Google Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45 (1), 269–292.Google Scholar
Snoeijer, J. H. & Eggers, J. 2010 Asymptotic analysis of the dewetting rim. Phys. Rev. E 82, 056314.Google Scholar
Solans, C., Izquierdo, P., Nolla, J., Azemar, N. & Garcia-Celma, M. J. 2005 Nano-emulsions. Curr. Opin. Colloid Interface Sci. 10 (3–4), 102–110.Google Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977–1026.Google Scholar
Stange, T. G., Evans, D. F. & Hendrickson, W. A. 1997 Nucleation and growth of defects leading to dewetting of thin polymer films. Langmuir 13 (16), 4459–4465.Google Scholar
Starov, V. M. 2010 Surface forces action in a vicinity of three phase contact line and other current problems in kinetics of wetting and spreading. Adv. Colloid Interface Sci. 161 (1–2), 139–152.Google Scholar
Starov, V. M., Velarde, M. G. & Radke, C. J. 2007 Wetting and Spreading Dynamics. CRC Press.Google Scholar
Stenhammar, J., Tiribocchi, A., Allen, R. J., Marenduzzo, D. & Cates, M. E. 2013 Continuum theory of phase separation kinetics for active Brownian particles. Phys. Rev. Lett. 111, 145702.Google Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices. Annu. Rev. Fluid Mech. 36 (1), 381–411.Google Scholar
Talapin, D. V., Rogach, A. L., Haase, M. & Weller, H. 2001 Evolution of an ensemble of nanoparticles in a colloidal solution: theoretical study. J. Phys. Chem. B 105 (49), 12278–12285.Google Scholar
Tao, Y., Yeckel, A. & Derby, J. J. 2016 Steady-state and dynamic models for particle engulfment during solidification. J. Comput. Phys. 315, 238–263.Google Scholar
Taylor, P. 1998 Ostwald ripening in emulsions. Adv. Colloid Interface Sci. 75 (2), 107–163.Google Scholar
Thiele, U. 2014 Patterned deposition at moving contact lines. Adv. Colloid Interface Sci. 206, 399–413.Google Scholar
Thiele, U., Mertig, M. & Pompe, W. 1998 Dewetting of an evaporating thin liquid film: heterogeneous nucleation and surface instability. Phys. Rev. Lett. 80, 2869–2872.Google Scholar
Thiele, U., Velarde, M. G. & Neuffer, K. 2001a Dewetting: film rupture by nucleation in the spinodal regime. Phys. Rev. Lett. 87, 016104.Google Scholar
Thiele, U., Velarde, M. G., Neuffer, K. & Pomeau, Y. 2001b Film rupture in the diffuse interface model coupled to hydrodynamics. Phys. Rev. E 64, 031602.Google Scholar
Thompson, C. V. 1990 Grain growth in thin films. Annu. Rev. Mater. Sci. 20 (1), 245–268.Google Scholar
Thompson, C. V. 2012 Solid-state dewetting of thin films. Annu. Rev. Mater. Res. 42 (1), 399–434.Google Scholar
Voorhees, P. W. 1985 The theory of Ostwald ripening. J. Stat. Phys. 38 (1–2), 231–252.Google Scholar
Vrij, A. 1966 Possible mechanism for the spontaneous rupture of thin, free liquid films. Discuss. Faraday Soc. 42, 23–33.Google Scholar
Wagner, C. 1961 Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung). Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaft für physikalische Chemie 65 (7–8), 581–591.Google Scholar
Weijs, J. H., Marchand, A., Andreotti, B., Lohse, D. & Snoeijer, J. H. 2011 Origin of line tension for a Lennard-Jones nanodroplet. Phys. Fluids 23 (2), 022001.Google Scholar
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36 (1), 29–53.Google Scholar
Wijshoff, H. 2010 The dynamics of the piezo inkjet printhead operation. Phys. Rep. 491 (4–5), 77–177.Google Scholar
Williams, M. B. & Davis, S. H. 1982 Nonlinear theory of film rupture. J. Colloid Interface Sci. 90 (1), 220–228.Google Scholar
Willis, A. M. & Freund, J. B. 2009 Enhanced droplet spreading due to thermal fluctuations. J. Phys.: Condens. Matter 21 (46), 464128.Google Scholar
Wittkowski, R., Tiribocchi, A., Stenhammar, J., Allen, R. J., Marenduzzo, D. & Cates, M. E. 2014 Scalar 𝜙4 field theory for active-particle phase separation. Nat. Commun. 5, 4351.Google Scholar
Woehl, T. J., Park, C., Evans, J. E., Arslan, I., Ristenpart, W. D. & Browning, N. D. 2014 Direct observation of aggregative nanoparticle growth: kinetic modeling of the size distribution and growth rate. Nano Lett. 14 (1), 373–378.Google Scholar
Wu, L., Dong, Z., Kuang, M., Li, Y., Li, F., Jiang, L. & Song, Y. 2015 Printing patterned fine 3D structures by manipulating the three phase contact line. Adv. Funct. Mater. 25 (15), 2237–2242.Google Scholar
Wu, Q. & Wong, H. 2004 A slope-dependent disjoining pressure for non-zero contact angles. J. Fluid Mech. 506, 157–185.Google Scholar
Wyart, F. B. & Daillant, J. 1990 Drying of solids wetted by thin liquid films. Can. J. Phys. 68 (9), 1084–1088.Google Scholar
Xia, Y. & Whitesides, G. M. 1998 Soft lithography. Annu. Rev. Mater. Sci. 28 (1), 153–184.Google Scholar
Xie, R., Karim, A., Douglas, J. F., Han, C. C. & Weiss, R. A. 1998 Spinodal dewetting of thin polymer films. Phys. Rev. Lett. 81, 1251–1254.Google Scholar
Yamamoto, D., Nakajima, C., Shioi, A., Krafft, M. P. & Yoshikawa, K. 2015 The evolution of spatial ordering of oil drops fast spreading on a water surface. Nat. Commun. 6, 7189.Google Scholar
Yeh, E. K., Newman, J. & Radke, C. J. 1999 Equilibrium configurations of liquid droplets on solid surfaces under the influence of thin-film forces. Part I. Thermodynamics. Colloids Surf. A 156 (1–3), 137–144.Google Scholar
Yiantsios, S. G. & Davis, R. H. 1991 Close approach and deformation of two viscous drops due to gravity and van der Waals forces. J. Colloid Interface Sci. 144 (2), 412–433.Google Scholar
Young, T. 1805 An essay on the cohesion of fluids. Phil. Trans. R. Soc. Lond. 95, 65–87.Google Scholar
Yu, T. S., Bulović, V. & Hosoi, A. E. 2013 Coarsening and solidification via solvent-annealing in thin liquid films. J. Fluid Mech. 723, 69–90.Google Scholar
Zeng, H., Zhao, B., Tian, Y., Tirrell, M., Leal, L. G. & Israelachvili, J. N. 2007 Transient surface patterns during adhesion and coalescence of thin liquid films. Soft Matter 3, 88–93.Google Scholar