Article pubs.acs.org/Langmuir
Rupture of Thin Liquid Films Induced by Impinging Air-Jets Christian W. J. Berendsen,† Jos C. H. Zeegers,† Geerit C. F. L. Kruis,‡ Michel Riepen,‡ and Anton A. Darhuber*,† †
Mesoscopic Transport Phenomena Group, Department of Applied Physics, Eindhoven University of Technology, Den Dolech 2, 5612AZ Eindhoven, The Netherlands ‡ ASML, De Run 6501, 5504DR Veldhoven, The Netherlands ABSTRACT: Thin liquid films on partially wetting substrates are subjected to laminar axisymmetric air-jets impinging at normal incidence. We measured the time at which film rupture occurs and dewetting commences as a function of diameter and Reynolds number of the air-jet. We developed numerical models for the air flow as well as the height evolution of the thin liquid film. The experimental results were compared with numerical simulations based on the lubrication approximation and a phenomenological expression for the disjoining pressure. We achieved quantitative agreement for the rupture times. We found that the film thickness profiles were highly sensitive to the presence of minute quantities of surface-active contaminants. or a surface forces apparatus (SFA).26,31,38 Scheludko,33 Bergeron and Radke,39 and Yaminsky et al.29 measured the disjoining pressure of free water films. The disjoining pressure in a liquid film between a solid surface and either a gas bubble or an immiscible liquid droplet was determined by evaluating the thickness34,40−47 or shape48,49 of the film as a function of hydrostatic or capillary pressure. Manor et al.50,51 developed a dynamic technique using a moving AFM cantilever with an attached bubble and documented the effect of surface impurities. Kim et al.52 determined Π(h) from the curvature of droplets in equilibrium with ultrathin films of fluoropolyethers. Metastable films on partially wetting substrates can undergo a dewetting instability35,53−61 upon nucleation of a dry-spot, which can be induced for example by means of a mechanical disturbance62,63 or an impinging air-jet.4,55,64 In this paper we present a detailed study of the rupture dynamics subjected to impinging air-jets by means of experiments and numerical simulations. We first evaluated the shear and pressure forces exerted on the nonvolatile liquid film by the impinging jet. Subsequently we measured the rupture times as a function of Reynolds number and diameter of the jet. We compared the experimental results to numerical simulations based on the lubrication approximation65 and an empirical model for the disjoining pressure introduced by Schwartz and Eley.66 Although the measurement of surface forces was not the primary focus of this study, we succeeded in identifying a set of parameters of the disjoining pressure isotherm that quantitatively reproduce the experimentally observed film rupture times. Despite the excellent agreement between experiments and simulations on the film rupture times, there initially was a significant discrepancy between measured and simulated dip profiles at low Reynolds numbers.
I. INTRODUCTION Thin liquid films with thicknesses in the micrometer range play a vital role in biology1,2 and technological applications such as coating processes3,4 or lubrication of bearings.5 In immersion lithography6−8 a water meniscus resides between the objective lens and the wafer to be exposed. At high scan speeds, a thin film of water is entrained on the photoresist coated wafer. Ideally this film needs to be removed before it can evaporate and induce temperature gradients that compromise the overlay accuracy of the lithography process. The motivation for this study is to destabilize liquid films in a controlled fashion as swiftly as possible. The interaction of gas flows with liquid films has been studied in diverse contexts. The impact of gas jets on deep liquid reservoirs was investigated by several authors,9−15 for instance in the context of steel making. High-speed planar gas jets have been applied for jet stripping,16−18 i.e., for the thinning or removal of liquid coatings. Derjaguin et al.19 introduced the so-called blow-off method for the measurement of effective viscosity in nm-thick liquid films. Scarpulla et al.20 applied this technique and measured the shear mobility in polymeric liquid films in the Ångström regime The flow of thin liquid films is influenced by the disjoining pressure Π.21 The magnitude of this internal pressure, a result of intermolecular and surface forces,22 strongly depends on the local thickness h of the thin liquid film. The disjoining pressure is composed of short-range and long-range, attractive and repulsive contributions, such as van der Waals23 and electric double-layer forces.22 Additional long-range interactions are still a subject of intense research.24−31 The film thickness and the shape of the disjoining pressure isotherm Π(h) determines if a liquid film is stable, metastable, or unstable.32−34 In the metastable thickness range, a finite amplitude disturbance can rupture the film.35 Attractive and repulsive disjoining pressure isotherms in thin liquid films between two solid bodies have been measured mechanically using an atomic force microscope (AFM)25,36,37 © 2012 American Chemical Society
Received: April 2, 2012 Revised: May 29, 2012 Published: June 6, 2012 9977
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The presence of surfactants in thin liquid films can have a strong impact on the film evolution. Surfactant concentration gradients can accelerate film rupture67−74 but can also stabilize thin liquid films.75−77 By accounting for the presence of a minute surfactant contamination, we also achieved excellent agreement between experimental and numerical results for the dip shape.
positioned at a stand-off distance H = 2 mm above the air−liquid interface. The air (Linde, N2/O2 mixture, oil-free, humidity level 620, the simulations overestimate the jet pressure maxima. This is most likely because, for higher Reynolds numbers, the needle length is too short to have a fully developed Poiseuille profile at the exit of the needle84,85[indicated by the asterisks in Figure 4d]. The measured jet pressure profiles generally are slightly wider than the calculated profiles for high ReD and narrower for high ReD [Figure 2b]. A possible reason for these small differences could be that the presence of the measurement hole breaks the axisymmetry of the flow. Examples of shear distributions, normalized with the average dynamic pressure, are shown in Figure 4c. The shear profiles have their maximum value closer to the stagnation point with increasing ReD and needle diameter. Figure 4d shows the numerically determined maximum value of the normalized shear stress as a function of Reynolds number for different D. B. The Thin Liquid Film. In a small-slope approximation,65 the time evolution of a thin liquid film of thickness h(r,t) on a solid surface under the influence of an impinging jet is given by ⎡⎛ ⎞⎤ ∂h 1 ∂ ⎢ ⎜ h2 h3 ∂p ⎟⎥ + τ− =0 r⎜ ∂t r ∂r ⎢⎣ ⎝ 2ηliq 3ηliq ∂r ⎟⎠⎥⎦
Figure 5. (a) Rupture time of a 3EG film on a PC substrate subjected to an impinging air-jet from a hollow needle with different diameters D. Experimental data are depicted as symbols, whereas the results of numerical simulations are shown as solid lines. (b) Shape of the disjoining pressure potential Π(h) given by eq 5, used for the calculation of the lines in panel a. The parameters are (n,m,h*) = (10,4,10 nm) and θ = 29°.
experimental and numerical results of rupture time trupture as a function of ReD for the different needle diameters. An increase in ReD strongly shortens the time needed to rupture the film. The black solid line segment represents a power law trupture ≈ ReD−3.8, which is a good approximation to the data set corresponding to D = 156 μm in the interval ReD ≤ 50. This exponent of −3.8 reflects the scaling of the stagnation pressure with ReD, Pstag ≈ Re3.8 D in this interval ReD ≤ 50. According to eq 3 the relevant time scale is inversely proportional to the scale of the driving force. We adjusted the parameters n, m, and h* in eq 5 to most accurately match the experimental results. The set of solid lines in Figure 5 correspond to (n,m,h*) = (10,4,10 nm). Interestingly, the value of m = 4 corresponds to the power of the retarded van der Waals interactions.23 Film rupture occurs when the minimum film thickness is in the range 50−300 nm, depending on ReD. This range is close to the values found in other experiments.29,45,76 Consequently, film rupture in our experiments is most sensitive to the disjoining pressure isotherm Π(h) in the film thickness range 50 - 500 nm. The disjoining pressure has a value of Π = 256 Pa at a film thickness h = 100 nm, as indicated in Figure 5b. This value is in the order of magnitude of repulsive forces measured in aqueous films29,67 and attractive forces measured between solid bodies in water.25 Figure 6 illustrates the sensitivity of trupture to changes in the parameters m, h*, h0, and θ. The rupture time is surprisingly insensitive to the initial film thickness for h0 > 500 nm [Figure 6a]. The contact angle θ primarily shifts the curve along the ordinate [Figure 6b]. In the case of a wetting film (θ = 0°) no rupture occurs, instead the film is thinned until the rupture criterion is fulfilled (min[h(r,trupture)] = 1.1h*). A change in the length scale h* does not seem to change the slope of the curve in Figure 6c but also induces a shift along the ordinate. The long-range attraction exponent m of the disjoining pressure Π has a more profound effect on the slope of the curve [Figure 6d]. For m < 4 the slope is lower than that of the measurement data points. From this we conclude that the agreement with experimental data is best if m = 4 or higher. The rupture time is quite insensitive to the short-range repulsion exponent n (data not shown)
(3)
where τ = τjet. The augmented pressure p≡−
γ ∂ ⎛ ∂h ⎞ ⎜r ⎟ + ρ gh − Π(h) + P jet liq r ∂r ⎝ ∂r ⎠
(4)
comprises contributions from capillary, hydrostatic and disjoining pressure as well as the jet pressure Pjet obtained from the air-jet simulations. For the disjoining pressure Π(h), we use a phenomenological model66 Π(h) = γ(1 − cos θ )
n ⎛ h* ⎞m⎤ (n − 1)(m − 1) ⎡⎛ h* ⎞ ⎜ ⎟ ⎜ ⎟ ⎥ − ⎢ ⎝ h ⎠ ⎦ (n − m)h* ⎣⎝ h ⎠
(5)
in which h*, m, and n are parameters determining the shape of Π(h) and θ = 29° is used as the contact angle. As an initial condition we consider a flat film of thickness h0 = 4.9 μm. The radius of the computational domain is 2 cm with mesh element size of 1 μm in the vicinity of r = 0 and 10 μm for r > 2 mm. Simulations were performed using the finite element software COMSOL 3.5a.
IV. RESULTS AND DISCUSSION A. Rupture Time and Disjoining Pressure Parameters. When the thin liquid film is subjected to the air-jet, a dip forms in the film that deepens and widens as a function of time. At some instant the film ruptures and one or more dry spots appear as shown in Figure 3. After rupture the dry spots grow with a dewetting speed of Vd ≈ 200 μm/s. For each needle diameter and flow rate, we recorded the time between the start of the air-jet pulse and the moment of film rupture. In the numerical simulations we define the rupture time trupture as the time, at which the minimum film thickness reaches the threshold value min[h(r,trupture)] = 1.1h*. Figure 5 shows the 9980
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first rupture point, as indicated by the dashed yellow lines in Figure 8a−d. Figure 8e represents the time-dependence I(r,t) of the same experiment. After 40s the height evolution of the thin liquid film changes character, where an off-center minimum (dimple) starts to form. This nonmonotonic evolution of the height profile becomes visible in this representation as 'angel wings,' indicated in green dotted lines. Film rupture occurs around t = 120 s very close to the position of this minimum. This effect occurs in experiments for low Reynolds numbers, independently of the needle diameter, as shown in Figure 8f. However, the numerical simulations presented in the previous section do not reproduce this off-center film rupture. In the numerical simulations, rupture always occurs close to the stagnation point of the impinging jet. D. Dip Shape. This discrepancy between the experimental and numerical results is illustrated in more detail in Figure 9, where we plotted the width of the dip Ddip as a function of ReD. We define the dip width Ddip as the diameter of the area where a flatter height profile (lower interference fringe density) transits into a steeper slope (higher fringe density), as indicated in Figure 8c,e. In the numerically simulated height profile h(r,trupture) this position corresponds to the location of maximum curvature in the region r > D, i.e., outside the impingement zone. Our numerical model correctly reproduces the trend in Ddip at the time of rupture at for high ReD, but deviates significantly for low ReD. The experimental data appear to increase monotonically as a function of ReD within experimental scatter. The numerical simulations (dashed lines), however, predict a nonmonotonic dependence of Ddip on ReD, with a minimum at ReD ≈ 200−300. This discrepancy indicates that our model disregards an effect that is relevant in our experiments. E. Influence of Surfactant Contamination. To investigate whether a surfactant contamination can explain the difference in dip shape and rupture location between experiments and simulations for low Reynolds numbers, we consider the presence of an insoluble surfactant in our numerical simulations. Equation 3 is now coupled to a convection/diffusion equation for the insoluble surfactant
Figure 6. Rupture time vs ReD for D = 208 μm and different parameters values. The red circles are the experimental data, the solid lines numerical results that illustrate the sensitivity of the results to changes in (a) the initial film thickness h0, (b) the liquid−solid contact angle θ, (c) the precursor thickness h*, and (d) the exponent m.
B. Number of Dry-Spots. Figure 3 illustrates that jets with lower Reynolds number induce film rupture at a single location. The resulting surface is “dry” and free from residual droplets. In the case of jets with high Reynolds number, several rupture events occur before the dewetting is complete. This leads to a pattern of residual droplets on the surface, arranged in a polygonal pattern.56 Figure 7 shows the number of dry spots N
Figure 7. Number of nucleated dry spots N due to air-jet impingement as a function of ReD. The experimental data are represented by the symbols. The dotted line represents a power law fit (N − 1) ≈ ReD2, which serves as a guide to the eye. The vertical lines represent WeD = 1.
⎡⎛ ⎞⎤ ∂Γ ∂Γ 1 ∂ ⎢ ⎜ hτ h2 ∂p + Γ − DS ⎟⎟⎥ = 0 r⎜ Γ − ∂t ∂r ⎠⎥⎦ r ∂r ⎢⎣ ⎝ ηliq 2ηliq ∂r
Here Γ is the surfactant surface concentration and DS = 5 × 10−10m2/s is the surface diffusion coefficient. The surface shear stress τ now consists of the air-jet induced shear τjet and the gradient of surface tension
that nucleate before dewetting is complete as a function of ReD. The dotted line represents a power law (N − 1) ≈ ReD2, that was fitted to the data. The transition from N = 1 to N > 1 occurs around the position where the Weber number of the impinging jet WeD ≡
τ = τjet +
ρgas v ̅ 2D γ
(7)
∂γ ∂r
(8)
The surface tension is linked to the surfactant surface concentration through a so-called equation of state. Since we do not know the equation of state for the contaminant, we assume a generic functional dependence
(6)
is around unity (as indicated by the vertical lines in Figure 7). C. Rupture Location. For Reynolds numbers above ReD ≈ 70 the first dry spots nucleate in the impingement zone of the air-jet (Figure 3). The same behavior is observed in the thin film simulations. However, in experiments at very low Reynolds number ReD ≲ 70 we observed that the dry spot appeared at the perimeter of the dip. Figure 8a−d presents an example. We extracted a radial cross-section I(r,t) from each recorded frame, that includes the center of the dip (r = 0) and the position of the
γ(Γ) = γmin + Δγ exp−A Γ
2
(9)
where we set A = 0.5 m4/μL2, γmin = 27 mN/m, and Δγ = 18.4 mN/m. A similar expression with different parameter values was found for oleic acid on glycerol in earlier work.86 We assume an initial surfactant concentration of Γ0 = 0.105 μL/m2, which means that the surface tension reduction γ(Γ0) − γ(0) = 9981
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Figure 8. For low Reynolds numbers, film rupture does not occur in the jet impingement zone, but at the dip perimeter. (a−d) A series of micrographs for D = 208 μm at ReD = 49 and a film thickness h0 = 4.9 μm. The red dashed circle indicates the nozzle exit size. (e) Radial crosssection I(r,t) along the yellow dashed line shown in panels a−d as a function of time. The dewetting speed Vd can be extracted from the slope of the contact line. (f) Nondimensional rupture position as a function of Reynolds number.
Figure 9. Width of the dip Ddip in the liquid film at the time of film rupture. The symbols represent the experimental data. The dashed lines are the numerical results for an uncontaminated triethylene glycol film. The solid lines are the numerical results for a contaminant concentration of 0.105 μL/m2.
0.1 mN/m is extremely small [Figure 10b], such that the contaminant would be practically undetectable by means of tensiometry. Figure 10a compares the dependence of the film rupture time on ReD for the cases with and without initial surfactant concentration for D = 208 μm. If a small amount of surfactant is present, the film is stabilized for ReD Retrans = 55 there is no discernible difference between the two curves as indicated by the vertical arrow in Figure 10a. During the dip formation, surfactant is transported outward from the center due to the flow induced by the air-jet [Figure 10c]. The value of Retrans depends on the equation of state and increases with initial surfactant concentration Γ0, because the surface tension gradients become higher. For larger DS, the difference between simulations with and without contamination decreases in the regime ReD < Retrans, because diffusive surface transport diminishes surface tension gradients. Figure 11a,b shows the height profile of the dip h(r,t) at different times in the absence or presence of surfactant. In Figure 11c,d the same simulation data h(r,t) is converted to an interference pattern I(r,t) in the same fashion as Figure 8e. Figure 11 shows that the dip width Ddip at the rupture time in the case with a trace amount of surfactant [Figure 11b,d] is significantly lower than in the absence of surfactant, although the film thickness in the center
Figure 10. (a) Rupture time as a function of ReD. The circles represent the experimental data. The green dotted line are the numerical simulations without surfactant contamination and the blue solid line for an initial contaminant surface concentration Γ0 = 0.105 μL/m2. The other parameters in the simulations are D = 208 μm, h0 = 4.9 μm, (m,n,h*) = (10,4,10 nm), and θ = 29°. (b) The equation of state used in our numerical simulations. The circle indicates the initial surface concentration Γ0. (c) Surfactant surface concentration profiles for different times and D = 208 μm and ReD = 50.
approaches comparable values. Moreover, the off-center rupture is reproduced when surfactant is present [Figure 11a,c]. The solid lines in Figure 9 represent the simulation results for Ddip in the presence of surfactant, which accurately reproduce the measured trend for ReD < 200. F. Implications for Technological Applications. In technological applications4,7 it is desirable that a liquid film can be ruptured in only one point, which leads to the growth of a single dry-spot without any residual droplets left behind on the substrate. On the basis of the results presented in Figure 7, 9982
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is part of the research programme “Contact Line Control during Wetting and Dewetting” (CLC) of the “Stichting voor Fundamenteel Onderzoek der Materie (FOM)”, which is financially supported by the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)”. The CLC programme is cofinanced by ASML and Océ.
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(1) Holly, F. J. Formation and rupture of the tear film. Exp. Eye Res. 1973, 15, 515−525. (2) Grotberg, J. B. Pulmonary Flow and Transport Phenomena. Annu. Rev. Fluid Mech. 1994, 26, 529−571. (3) Ruschak, K. J. Coating Flows. Annu. Rev. Fluid Mech. 1985, 17, 65−89. (4) Bower, C. L.; Simister, E. A.; Bonnist, E.; Paul, K.; Pightling, N.; Blake, T. D. Continuous coating of discrete areas of a flexible web. AIChE J. 2007, 53, 1644−1657. (5) Dowson, D.; Higginson, G. R. Elasto-hydrodynamic lubrication; Pergamon Press: Oxford, U.K., 1977. (6) Switkes, M.; Rothschild, M. Immersion litography at 157 nm. J. Vac. Sci. Technol. B 2001, 19, 2353−2356. (7) French, R. H.; Tran, H. V. Immersion Lithography: Photomask and Wafer-Level Materials. Annu. Rev. Mater. Sci. 2009, 39, 93−126. (8) Mulkens, J.; Streefkerk, B.; Jasper, H.; de Klerk, J.; de Jong, F.; Levasier, L.; Leenders, M. Defects, overlay, and focus performance improvements with five generations of immersion exposure systems. Opt. Microlithogr. XX Proc. SPIE. 2007, 652005. (9) Collins, R. D.; Lubanska, H. The depression of liquid surfaces by gas jets. Br. J. Appl. Phys. 1954, 5, 22. (10) Banks, R. B.; Chandrasekhara, D. V. Experimental investigation of the penetration of a high- velocity gas jet through a liquid surface. J. Fluid Mech. 1963, 15, 13−34. (11) Olmstead, W. E.; Raynor, S. Depression of an infinite liquid surface by an incompressible gas jet. J. Fluid Mech. 1964, 19, 561−576. (12) Fagela-Alabastro, E. B.; Hellums, J. D. Laminar Gas Jet Impinging on an Infinite Liquid Surface. Numerical Finite Difference Solution Involving Boundary and Free Streamline Determinations. Ind. Eng. Chem. Fund. 1967, 6, 580−587. (13) Vanden-Broeck, J.-M. Deformation of a liquid surface by an impinging gas jet. SIAM. J. Appl. Math. 1981, 41, 306−309. (14) He, A.; Belmonte, A. Deformation of a liquid surface due to an impinging gas jet: A conformal mapping approach. Phys. Fluids 2010, 22, 042103. (15) Muñoz Esparza, D.; Buchlin, J.-M.; Myrillas, K.; Berger, R. Numerical investigation of imping- ing gas jets onto deformable liquid layers. Appl. Math. Model. 2011, 36, 2687−2700. (16) Tuck, E. O. Continuous coating with gravity and jet stripping. Phys. Fluids 1983, 26, 2352−2358. (17) Ellen, C. H.; Tu, C. V. Jet stripping of molten metallic coatings. Phys. Fluids 1985, 28, 1202−1203. (18) Lacanette, D.; Gosset, A.; Vincent, S.; Buchlin, J.-M.; Arquis, E. Macroscopic analysis of gas-jet wiping: Numerical simulation and experimental approach. Phys. Fluids 2006, 18, 042103. (19) Derjaguin, B. V.; Karessev, V. V. Viscosity studies of Liquid Boundary Layers buy the Blow-Off Method. Prog. Surf. Sci. 1992, 40, 301−308. (20) Scarpulla, M. A.; Mate, C. M.; Carter, M. D. Air shear driven flow of thin perfluoropolyether polymer films. J. Chem. Phys. 2003, 118, 3368−3375.
Figure 11. Simulated height profiles for D = 208 μm and ReD = 49.5 (a and c) without and (b and d) with surfactant contamination.
multiple rupture sites were observed for Reynolds numbers ReD ≳ 100. According to Figure 5, this corresponds to a rupture time in the order of 10 s. For the effective removal of liquid from a substrate it is important that this rupture time is significantly shorter than the typical time scales of evaporation and intrinsic instabilities. For instance the time scale of the spinodal instability on a flat and chemically homogeneous surface is given by32 T = 24
⎤−2 ηγ ⎡ dΠ ( ) h ⎢ ⎥⎦ 0 h03 ⎣ dh
REFERENCES
(10)
which for 3EG films of h0 = 1 μm, using the disjoining pressure isotherm Π(h) found in this study, T3EG ≈ 6 days.
V. SUMMARY We performed experiments and numerical simulations of the destabilization of thin liquid films on partially wetting substrates by means of impinging air-jets. We determined the forces exerted on the liquid by numerical simulations, which we validated by measurements of the jet pressure distribution as a function of Reynolds number. We measured the time from jet initiation until film rupture as a function of jet diameter and Reynolds number. Using an empirical model for the disjoining pressure isotherm, we obtained quantitative agreement in the film rupture time between experiments and simulations based on the lubrication approximation. The numerical model overestimated the width of the depression in the liquid film and predicted the rupture to occur close to the stagnation point for small Reynolds number. In our experiments, we observed off-center film rupture and smaller dip width for low ReD. By accounting for the presence of a minute surfactant contamination, the model properly reproduced off-center film rupture and dip widths in quantitative agreement with experimental observations. 9983
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Article
(21) Derjaguin, B. V.; Churaev, N. V. On the question of determining the concept of disjoining pressure and its role in the equilibrium and flow of thin film. J. Colloid Interface Sci. 1978, 66, 389−398. (22) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: Burlington, 2011. (23) Parsegian, V. A. Van der Waals Forces; Cambridge University Press: New York, 2006. (24) Tsao, Y. H.; Yang, S. X.; Evans, D. F.; Wennerström, H. Interactions between hydrophobic surfaces. Dependence on temperature and alkyl chain length. Langmuir 1991, 7, 3154−3159. (25) Yoon, R.-H.; Flinn, D. H.; Rabinovich, Y. I. Hydrophobic Interactions between Dissimilar Surfaces. J. Colloid Interface Sci. 1997, 185, 363−370. (26) Meyer, E. E.; Lin, Q.; Israelachvili, J. N. Effects of Dissolved Gas on the Hydrophobic Attraction between Surfactant-Coated Surfaces. Langmuir 2005, 21, 256−259. (27) Eriksson, J. C.; Henriksson, U. Bridging-Cluster Model for Hydrophobic Attraction. Langmuir 2007, 23, 10026−10033. (28) Karakashev, S. I.; Nguyen, A. V. Do Liquid Films Rupture due to the So-Called Hydrophobic Force or Migration of Dissolved Gases? Langmuir 2009, 25, 3363−3368. (29) Yaminsky, V. V.; Ohnishi, S.; Vogler, E. A.; Horn, R. G. Stability of Aqueous Films between Bubbles. Part 1. The Effect of Speed on Bubble Coalescence in Purified Water and Simple Electrolyte Solutions. Langmuir 2010, 26, 8061−8074. (30) Mishchuk, N. A. The model of hydrophobic attraction in the framework of classical DLVO forces. Adv. Colloid Interface Sci. 2011, 168, 149−166. (31) Faghihnejad, A.; Zeng, H. Hydrophobic Interactions between polymer surfaces: using polystyrene as a model system. Soft Matter 2012, 8, 2746−2759. (32) Vrij, A. Possible Mechanism for the Spontaneous Rupture of Thin, Free Liquid Films. Discuss. Faraday Soc. 1966, 42, 23−33. (33) Scheludko, A. Thin Liquid Films. Adv. Colloid Interface Sci. 1967, 1, 391−464. (34) Blake, T. D. Investigation of equilibrium wetting films of nalkanes on α-alumina. J. Chem. Soc., Faraday Trans. 1 1975, 71, 192− 208. (35) Sharma, A.; Ruckenstein, E. Finite-amplitude instability of thin free and wetting films: predic-tion of lifetimes. Langmuir 1986, 2, 480−494. (36) Butt, H.-J.; Jaschke, M.; Ducker, W. Measuring surface forces in aqueous electrolyte solution with the atomic force microscope. Bioelectrochem. Bioenerg. 1995, 38, 191−201. (37) Mahnke, J.; Stearnes, J.; Hayes, R. A.; Fornasiero, D.; Ralston, J. The influence of dissolved gas on the interactions between surfaces of different hydrophobicity in aqueous media. Part I. Measurement of interaction forces. Phys. Chem. Chem. Phys. 1999, 1, 2793−2798. (38) Xu, Z.; Ducker, W.; Israelachvili, J. Forces between Crystalline Alumina (Sapphire) Surfaces in Aqueous Sodium Dodecyl Sulfate Surfactant Solutions. Langmuir 1996, 12, 2263−2270. (39) Bergeron, V.; Radke, C. J. Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films. Langmuir 1992, 8, 3020−3026. (40) Read, A. D.; Kitchener, J. A. Wetting Films on Silica. J. Colloid Interface Sci. 1969, 30, 391−398. (41) Blake, T. D.; Kitchener, J. A. Stability of aqueous films on hydrophobic methylated silica. J. Chem. Soc., Faraday Trans. 1 1972, 68, 1435−1442. (42) Aronson, M. P.; Petko, M. F.; Princen, H. M. On the Stability of Aqueous Films Between Oil and Silica. J. Colloid Interface Sci. 1978, 65, 296−306. (43) Schulze, H. J.; Stöckelhuber, K.; Wenger, A. The Influence of Acting Forces on the Rupture Mechanism of Wetting Films Nucleation or Capillary Waves. Colloids Surf. A 2001, 192, 61−72. (44) Vazquez, R.; Nogueira, R.; Busquets, S.; Mata, J. L.; Saramago, B. Wetting films of polar and nonpolar liquids. J. Colloid Interface Sci. 2005, 284, 652−657.
(45) Vazquez, R.; Nogueira, R.; Orfão, M.; Mata, J. L.; Saramago, B. Stability of triglyceride liquid films on hydrophilic and hydrophobic glasses. J. Colloid Interface Sci. 2006, 299, 274−282. (46) Fischer, L. R.; Hewitt, D.; Mitchell, E. E.; Ralston, J.; Wolfe, J. The drainage of an aqueous film between a solid plane and an air bubble. Adv. Colloid Interface Sci. 1992, 39, 397−416. (47) Chen, J.-D.; Slattery, J. C. Effects of London-van der Waals forces on the thinning of a dimpled liquid film as a small drop or bubble approaches a horizontal solid plane. AIChE J. 1982, 28, 955− 963. (48) Ward, A. D.; Ottewil, R. H.; Hazlett, R. An investigation into the stability of aqueous films separating hydrocarbon drops from quartz surfaces. J. Pet. Sci. Eng. 1999, 24, 213−220. (49) Horn, R. G.; Asadullah, M.; Connor, J. N. Thin Film Drainage: Hydrodynamic and Disjoining Pressures Determined from Experimental Measurements of the Shape of a Fluid Drop Ap-proaching a Solid Wall. Langmuir 2006, 22, 2610−2619. (50) Manor, O.; Vakarelski, I. U.; Tang, X.; O’Shea, S. J.; Stevens, G. W.; Grieser, F.; Dagas-tine, R. R.; Chan, D. Y. C. Hydrodynamic Boundary Conditions and Dynamic Forces between Bubbles and Surfaces. Phys. Rev. Lett. 2008, 101, 024501. (51) Manor, O.; Vakarelski, I. U.; Stevens, G. W.; Grieser, F.; Dagastine, R. R.; Chan, D. Y. C. Dynamic Forces between Bubbles and Surfaces and Hydrodynamic Boundary Conditions. Langmuir 2008, 24, 11533−11543. (52) Kim, H. I.; Mate, C. M.; Hannibal, K. A.; Perry, S. S. How Disjoining Pressure Drives the Dewetting of a Polymer Film on a Silicon Surface. Phys. Rev. Lett. 1999, 82, 3496−3499. (53) Williams, M. B.; Davis, S. H. Nonlinear theory of film rupture. J. Colloid Interface Sci. 1982, 90, 220−228. (54) Brochard-Wyart, F.; Daillant, J. Drying of solids wetted by thin liquid films. Can. J. Phys. 1990, 68, 1084−1088. (55) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Dynamics of dewetting. Phys. Rev. Lett. 1991, 66, 715−718. (56) Reiter, G. Dewetting of thin polymer films. Phys. Rev. Lett. 1992, 68, 75−78. (57) Jacobs, K.; Herminghaus, S.; Mecke, K. R. Thin Liquid Polymer Films Rupture via Defects. Langmuir 1998, 14, 965−969. (58) Ghatak, A.; Khanna, R.; Sharma, A. Dynamics and Morphology of Holes in Dewetting of Thin Films. J. Colloid Interface Sci. 1999, 212, 483−494. (59) Thiele, U.; Velarde, M. G.; Neuffer, K.; Pomeau, Y. Film rupture in the diffuse interface model coupled to hydrodynamics. Phys. Rev. E 2001, 64, 031602. (60) Dhiman, R.; Chandra, S. Rupture of radially spreading liquid films. Phys. Fluids 2008, 20, 092104. (61) Mulji, N.; Chandra, S. Rupture and dewetting of water films on solid surfaces. J. Colloid Interface Sci. 2010, 352, 194−201. (62) Sykes, C.; Andrieu, C.; Détappe, V.; Deniau, S. Critical radius of holes in liquid coating. J. Phys. III France 1994, 4, 775−782. (63) Karapanagiotis, I.; Gerberich, W. W.; Evans, D. F. Early Dewetting Stages of Thin Polymer Films Initiated by Nanoindentation. Langmuir 2001, 17, 2375−2379. (64) Taylor, G. I.; Michael, D. H. On making holes in a sheet of fluid. J. Fluid Mech. 1973, 58, 625−639. (65) Oron, A.; Davis, S. H.; Bankoff, S. G. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 1997, 69, 931−980. (66) Schwartz, L. W.; Eley, R. R. Simulation of Droplet Motion on Low-Energy and Heterogeneous Surfaces. J. Colloid Interface Sci. 1998, 202, 173−188. (67) Aronson, M. P.; Princen, H. M. Destabilization of Aqueous Films On Silica by Nonionic Sur-factant. J. Colloid Interface Sci. 1975, 52, 345−355. (68) Aronson, M. P.; Princen, H. M. Aqueous films on silica in the presence of cationic surfactants. Colloid Polym. Sci. 1978, 256, 140− 149. (69) Gaver, D. P.; Grotberg, J. B. Droplet spreading on a thin viscous film. J. Fluid Mech. 1992, 235, 399−414. 9984
dx.doi.org/10.1021/la301353f | Langmuir 2012, 28, 9977−9985
Langmuir
Article
(70) Somasundaran, P.; Simpson, S.; Ivanov, I.; Jain, R. K.; Sarkar, D. Thinning and Rupture of Aqueous Surfactant Films on Silica. Langmuir 1999, 15, 7658−7661. (71) Lin, C.-K.; Hwang, C.-C.; Uen, W.-Y. A Nonlinear Rupture Theory of Thin Liquid Films with Soluble Surfactant. J. Colloid Interface Sci. 2000, 231, 379−393. (72) Warner, M. R. E.; Craster, R. V.; Matar, O. K. Dewetting of ultrathin surfactant-covered films. Phys. Fluids 2002, 14, 4040−4054. (73) Afsar-Siddiqui, A. B.; Luckham, P. F.; Matar, O. K. Dewetting Behavior of Aqueous Cationic Surfactant Solutions on Liquid Films. Langmuir 2004, 20, 7575−7582. (74) Tsekov, R.; Letocart, P.; Evstatieva, E.; Schulze, H. J. Effect of Ionic Surfactants on the Dimple Relaxation in Wetting Films. Langmuir 2002, 18, 5799−5803. (75) Goodall, D. G.; Gee, M. L.; Stevens, G. W. Effect of Surfactant on the Drainage of an Aqueous Film between an Oil Droplet Approaching a Hydrophobic Solid Surface. Langmuir 2001, 17, 3784− 3787. (76) Manev, E.; Nguyen, A. Critical thickness of microscopic thin liquid films. Adv. Colloid Interface Sci. 2005, 114−115, 133−146. (77) Delacotte, J.; Montel, L.; Restagno, F.; Scheid, B.; Dollet, B.; Stone, H. A.; Langevin, D.; Rio, E. Plate Coating: Influence of Concentrated Surfactants on the Film Thickness. Langmuir 2012, 28, 3821−3830. (78) Bhurke, A. S.; Askeland, P. A.; Drzal, L. T. Surface Modification of Polycarbonate by Ultraviolet Radiation and Ozone. J. Adhes. 2007, 83, 43−66. (79) Abràmoff, M.; Magalhães, P.; Ram, S. Image Processing with ImageJ. Biophotonics Int. 2004, 11, 36−42. (80) Reinold, A.; Rücker, A. On the Relation between the Thickness and the Surface Tension of Liquid Films. Philos. Trans. R. Soc. London 1886, 177, 627−684. (81) Corl, E.; Wimpfheimer, H. Thickness measurement of silicon dioxide layers by ultraviolet-visible interference method. Solid State Electron. 1964, 7, 755−761. (82) Fogt, N.; King-Smith, P. E.; Tuell, G. Interferometric measurement of tear film thickness by use of spectral oscillations. J. Opt. Soc. Am. A 1998, 15, 268−275. (83) Lemmon, E. W. Handbook of Chemistry and Physics, 9th ed.; CRC Press: Boca Raton, FL, 2011. (84) Chen, R.-Y. Flow in the Entrance Region at Low Reynolds Numbers. J. Fluids Eng. 1973, 95, 153−158. (85) Blevins, R. D. Applied Fluid Dynamics Handbook; Van Nostrand Reinhold Company: New York, 1984. (86) Sinz, D. K. N.; Hanyak, M.; Darhuber, A. A. Immiscible surfactant droplets on thin liquid films: Spreading dynamics, subphase expulsion and oscillatory instabilities. J. Colloid Interface Sci. 2011, 364, 519−529.
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dx.doi.org/10.1021/la301353f | Langmuir 2012, 28, 9977−9985
