LETTER pubs.acs.org/Langmuir
Effect of Surface Mobility on the Uniformity of a Thin Film under a Bubble G. Berteloot, P. Sharif-Kashani, and H. P. Kavehpour* Complex Fluids and Interface Physics Laboratory, Department of Mechanical and Aerospace Engineering, University of California at Los Angeles, Los Angeles, California 90095, United States
bS Supporting Information ABSTRACT: The shape of a soap bubble placed on a solid surface is familiar to everyone—a thin hemispherical dome that thickens near the solid surface. This structure is stabilized by the balance between the film’s elasticity, provided by surfactant molecules, and the pressure inside the bubble. However, there is also a soap film on the flat solid surface that has been mostly ignored in previous studies; its thickness is typically assumed to be constant or varying monotonically. In this letter, for the first time, we show that the thickness of this film is not always monotonic. Depending on the surfactant type, it can exhibit a significant dip, similar to marginal pinching. This finding has a significant influence in numerous applications in which solid/foam interactions are important, such as oil extraction or foam-based drug delivery.
’ INTRODUCTION Although the shape of a bubble inside a fluid is widely understood as a competition between surface tension and the Laplace pressure,1 the case of a soap bubble sitting on a solid surface surrounded by air is more complex. The structure of the thin liquid film between the air inside the bubble and the solid surface has never been studied experimentally. A bubble is considered to be the unit structure of foam; therefore, its structure has a drastic effect on the dynamics of foams and their interactions with solid boundaries. The solid surface/foam interactions play a significant role in many industrial and medical applications;24 however, they are not well understood. Few studies focusing on foam rheology investigated surface/foam interactions5,6 and established shear stress as a function of the shear rate behavior and viscous friction, depending on the surfactants used. The question of interaction between foam and the surface on which it sits is crucial because the stability of the foam and hence the efficiency of a related process depend on it.2 ’ METHODS We used a 50% water/50% glycerol (by volume) solution as our base liquid with added surfactants. We used a nonionic, hydrophobic surfactant with a hydrophiliclipophilic balance (HLB) of 12.3, Triton X-114, and an anionic hydrophilic (HLB of 40) surfactant, sodium dodecyl sulfate (SDS), manufactured by Sigma-Aldrich. The SDS solution has a viscosity of 0.01 Pa 3 s and a surface tension of 35 mN/m, and the Triton solution has a viscosity of 0.15 Pa 3 s and a surface tension of 30 mN/m. These surfactants were both present at 5 times the critical micelle concentration. Before those surfactants were added, the liquid solution was rendered fluorescent using rhodamine dye. An epifluorescence r 2011 American Chemical Society
inverted microscope (Nikon Eclipse TE2000-S) and a confocal microscope (Leica TCS) were used to investigate the structure of the thin film. The substrate used was a microscope glass slide, rinsed with acetone, ethanol, and distilled water, and then plasma cleaned. A syringe was dipped into the solution, and then air was squeezed out to create a bubble. This bubble was deposited on the glass substrate by creating a physical contact and then pulling the needle away from the film. Using a 10 objective, we located the outer contact line of the bubble. We then focused on the horizontal liquid film near the vertical dome inside the bubble, as shown in Figure 1. The intensity of the fluorescence observed in the image is proportional to the thickness of the film due to the BeerLambert law. This is a valid assumption because the liquid film thickness is less than a millimeter.7 The calibration of the relation between the thickness and fluorescence intensity was explained in detail by Hoang and Kavehpour.20
’ RESULTS AND DISCUSSIONS Intensity profiles for bubbles made with different surfactants are shown in Figure 2a,b. The profiles obtained from bubbles with SDS as the surfactant exhibit a smooth, monotonic transition between the vertical dome and the horizontal liquid film. However, bubbles with Triton X-114 as the surfactant have a region of minimal height consisting of a dip of a few tens of micrometers in thickness. To exclude optical artifacts, an experiment was performed and this dip was confirmed by observation with a confocal microscope, as shown in Figure 3. The presence of the dip depends on the surfactant used and is independent of Received: July 12, 2011 Revised: November 2, 2011 Published: November 07, 2011 14705
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Figure 1. Position of the observation field: the inner region of the liquid film lying on the surface, close to the hemispherical dome, is investigated.
Figure 2. (a) Triton bubble, observed with 10 objective and a fluorescence microscope, with a height profile and a surface plot. The profile shows the existence of a minimum in fluorescence intensity near the hemispherical dome. (b) SDS bubble, observed with 10 objective and a fluorescence microscope, height profile, and surface plot. The profile exhibits a monotonic decrease from the hemispherical dome to the central liquid film.
the time and radius of the bubble (although, as we show later, the thickness of the dip is time-dependent). This structure has never been reported for a bubble wetting a solid substrate. It should be noted that the existence of a “dimple” between a drop or submerged bubble and a solid substrate has been reported and
analyzed by many researchers over the last 70 years.18,19 The reported feature is due to applied force and the existence of a pressure variation on the thin film from lubrication analysis. However, what we observe is different because the normal force on the thin film is very small and cannot produce a squeeze film effect. 14706
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Langmuir In addition, we do not observe this feature when SDS surfactants are used. To understand the presence of a dip in the film, one can look at theoretical and experimental work done for other geometries
LETTER
involving soap films. For example, plateau borders (sometimes referred to as Gibbs rings8) in foams have been studied in detail.911 It is shown that a soap film may exhibit a feature called marginal pinching12 when pulled out of a bath by a frame, a feature that is claimed to be physically impossible by Barigou and Danielson.13 Aradian et al.14 proposed a theoretical model for this phenomenon. First, the full nondimensional height profile E(X, T) was decomposed, where X is the nondimensional spatial length and T the nondimensional time, into E(X, T) = H(T) S(X). In this case, X = x/r with r being the radius of the metal frame and T being t/trelax, where trelax is the typical relaxation time needed for a bump of height e0 (the thickness of the soap film far from the metal wire) and width r to be leveled off by capillary flow. The governing equation of the film is written as follows:14 ET þ ðE3 EXXX ÞX ¼ 0
Figure 3. Bubble stabilized using Triton observed with a confocal microscope. The existence of a minimum in thickness near the hemispherical dome is confirmed in this experiment.
ð1Þ
The time-independent part of the S(X) profile must satisfy the following equation14 S3 S000 ¼ α
ð2Þ
Figure 4. Evolution of the fluorescence profile of the liquid film with time. Each profile is separated by 5 s. (a) The case of a bubble stabilized by Triton. The dip is slightly shifted toward the hemispherical dome after a long time and shows a decrease in its thickness with time. (b) The case of a bubble stabilized by SDS. The profile is subject to a horizontal shift toward the hemispherical dome while keeping its shape. 14707
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where α is a constant dependent on the boundary conditions. (For a free film restrained by a frame, the curvature of the film near the metal frame is set by the radius of the frame.) If the interface is immobile, then the solution to this equation has a minimum value, which is called marginal pinching. Furthermore, it is proposed that the minimal height of the dip Emin(T) decreases with time, following the scaling law Emin ðTÞ µ T 1=2
ð3Þ
The case of a bubble on a solid surface differs from the previous case in two ways: • One of the surfaces of the film is not free, and the presence of the substrate imposes another type of boundary condition, a wall with a no-slip condition. • The curvature of the film at one end is not imposed by a metal frame but rather by a connection to the dome. The role of surface mobility is emphasized in the work of Howell and Stone.15 It is shown that a mobile interface condition leads to a profile without any evidence of marginal pinching. Numerical simulations by Howell and Stone confirm this prediction. The two cases observed with different surfactants emphasize the importance of surface mobility (i.e., the velocity of the liquid at the liquid/air interface) as discussed by Howell and Stone. An experimental observation by Koehler et al.11 showed that SDS foams exhibit a high surface velocity. Denkov et al.6 also characterize SDS as a low-surface-modulus surfactant. This is consistent with the mobile interface condition leading to a film without any marginal pinching. In another study, Karakashev and Ivanova16 showed that it is proper to assume an immobile interface for Triton-stabilized foams, which agrees with the presence of a dip in the model of Aradian et al. In accordance with the model E(X, T) = H(T) S(X), the profile of a bubble exhibiting a dip varies with time, as shown in Figure 4. The evolution of the fluorescence profile is plotted for bubbles stabilized with Triton and SDS in Figure 4a,b, respectively. For Triton, the profile is subject to a slight shift in the horizontal direction, and the dip thickness decreases, as predicted. The case of the SDS bubble is different: with time, the fluorescence profile is shifted toward the hemispherical dome, without any change in thickness. This evolution is different from the one predicted in the case of a plateau border,15 where the plateau region is growing because of the difference in geometry. The evolution of the minimum thickness of the dip is shown in the inset of Figure 5. This can be rescaled using the lifetime of the bubble and the minimum intensity observed during the experiment for the fluorescence intensity at the minimum (Figure 5). At short times, the evolution in intensity does not always match the model given by Aradian et al. At that stage, the radius of the bubble is not constant because the bubble is spreading on the substrate. This movement was not accounted for by the aforementioned theory. At longer times, once the bubble radius is constant, the experiments show good agreement with the model. Moreover, other analyses17 show that this power law model is not valid for short time periods. In Figure 6, we compare the experimental data of a bubble with the theory proposed in eq 2.The profiles of the inner air/liquid interface were nondimensionalized in the following way: • For each profile, the height was divided by the minimum height and shifted so that this minimum height is observed for X = 0.
Figure 5. Evolution of the minimal intensity I, rescaled by the minimal intensity Imin observed in the experiment as a function of time (rescaled by the lifetime tburst) with respect to the bubble for three kinds of experiments: bubbles made with Triton having a diameter of ∼1 cm (circles), bubbles made with Triton having a diameter of ∼2 mm (squares), and bubbles made with soap (SoftSoap antibacterial hand soap) of a diameter of ∼1 cm (triangles). The inset shows the data before rescaling.
Figure 6. Comparison between experimental profiles (circles) separated by 5 s and a numerical simulation of the equation given by Aradian et al. The various experimental profiles have been rescaled by their minimum value of S(X) and rescaled by a single length for X so that their typical width is approximately 1.
• The width of all profiles was rescaled by a typical width of the dip (40 μm in our experiment). Then the profiles were compared with an equation similar to the proposed model. The results presented in Figure 6 show good agreement between the experimental and analytical results for α = 0.001. The difference in the α constant is due to the existence of the solid substrate at the lower boundary, replacing an “immobile” surfactant-laden interface in the theory. We observed, for the first time, the profile of a single bubble on a solid substrate. We addressed, in this particular geometry, the matter of marginal pinching. Using various surfactants, we were able to observe the different scenarios described in literature and to show good agreement between the experiment and models given for an immobile interface and a mobile interface. 14708
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The presence of marginal pinching was overlooked in the few studies on foam wetting a solid surface and could lead to improvements in fields as important as oil extraction and drug delivery. Indeed, Denkov et al.6 already emphasized the role of surface mobility on viscous friction, showing that an immobile interface leads to additional friction in the liquid film. Moreover, the presence of such a decreased thickness near the hemispherical dome leads to greater dissipation as the induced pressure gradient is increased, thus affecting the efficiency of foam spreading on solid substrates such as reservoir rocks (for oil recovery) or organic tissue (for drug delivery).
’ ASSOCIATED CONTENT
bS
Supporting Information. Experimental setup for calibration of the measurement technique. Thin film measurements. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ ACKNOWLEDGMENT We thank Professors Howard Stone, Stephen Davis, Elie Rapha€el, Dr. Cecile Monteux, and Prof. Ali Mohraz for fruitful discussions. This work was supported by the National Science Foundation (grant CBET-0730251). ’ REFERENCES (1) de Gennes, P. G.; Brochart-Wyart, F.; Quere, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves; Springer: New York, 2004. (2) Sanchez, H.; Hazlett, R. SPE Resrv. Eng. 1992, 7. (3) Hay, D. J.; Sharma, H.; Irving, M. H. Br. Med. J. 1979, 1, 1751. (4) Moody, C.; Field, J. Environ. Sci. Technol. 2000, 34, 3864. (5) Denkov, N. D.; Subramanian, V.; Gurovich, D.; Lips, A. Colloids Surf., A 2005, 263, 129. (6) Denkov, N. D.; Tcholakova, S.; Golemanov, K.; Ananthpadmanabhan, K. P.; Lips, A. Soft Matter 2009, 5, 3389. (7) Rost, F. W. D. Quantitative Fluorescence Microscopy; Cambridge University Press: Cambridge, U.K., 1991. (8) Isenberg, C. The Science of Soap Films and Soap Bubbles;Tieto Ltd.: Clevedon, U.K., 1978. (9) Plateau, J. Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires; Gauthier-Villard: Paris, 1873. (10) Desai, D.; Kumar, R. Chem. Eng. Sci. 1982, 37, 1361. (11) Koehler, S. A.; Hilgenfeldt, S.; Stone, H. A. J. Colloid Interface Sci. 2004, 276, 420. (12) Mysels, K.; Shinoda, K.; Frankel, S. Soap Films, Studies of Their Thinning, and a Bibliography; Pergamon Press: New York, 1959. (13) Barigou, M.; Davidson, J. F. Chem. Eng. Sci. 1994, 49, 1807. (14) Aradian, A.; Raphael, E.; de Gennes, P. G. Europhys. Lett. 2001, 55, 834. (15) Howell, P. D.; Stone, H. A. Eur. J. Appl. Math. 2005, 16, 569. (16) Karakashev, S. I.; Ivanova, D. S. J. Colloid Interface Sci. 2010, 343, 584. (17) Brush, L. N.; Davis, S. H. J. Fluid Mech. 2005, 534, 227. (18) Derjaguin, B.; Kussakov, M. Acta Physicochim. URSS 1939, 10, 153. (19) Frankel, S. P.; Mysels, K. J. J. Phys. Chem. 1962, 66, 190. (20) Hoang, A.; Kavehpour, H. P. Phys. Rev. Lett. 2011, 106, 254501.
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