pubs.acs.org/Langmuir © 2011 American Chemical Society
Stretching Liquid Bridges with Bubbles: The Effect of Air Bubbles on Liquid Transfer Shawn Dodds,† Marcio S. Carvalho,‡ and Satish Kumar*,† †
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States, and ‡Department of Mechanical Engineering, Pontifı´cia Universidade Cat olica do Rio de Janeiro, Rio de Janeiro, RJ 22453-900, Brazil Received November 1, 2010. Revised Manuscript Received December 22, 2010 Liquid bridges containing bubbles are relevant to industrial printing and are also a topic of fundamental scientific interest. We use flow visualization to study the stretching of liquid bridges, both with and without bubbles, at low capillary numbers. We find that whereas the breakup of wetting fluids between two identical surfaces is symmetric about the bridge midpoint, contact line pinning breaks this symmetry at slow stretching speeds for nonwetting fluids. We exploit this observation to force air bubbles selectively toward the least hydrophilic plate confining the liquid bridge.
1. Introduction Stretching liquid bridges are found in numerous industrial1-3 and natural3-5 systems, and as such, they have been a focus of research for over a century.6 Of particular importance in many of these cases is the wettability of the solid surfaces, which can significantly alter the stretching and breakup dynamics of the bridge.7 However, the presence of a moving contact line complicates both the experimental and computational analysis of liquid bridges and so has received relatively little attention despite its fundamental importance.7-19 The dynamics of bubbles are also believed to be important in various applications, such as the formation of aerosols,20 the debonding of adhesives,21 and in industrial printing. In printing processes such as gravure or flexography, bubbles can become
Figure 1. Schematic of the apparatus used for the experiments in this letter.
*To whom correspondence should be addressed. E-mail: kumar030@ umn.edu. (1) Powell, C. A.; Savage, M. D.; Guthrie, J. T. Int. J. Numer. Methods Heat Fluid Flow 2002, 12, 338–355. (2) Yao, M.; McKinley, G. H. J. Non-Newtonian Fluid Mech. 1998, 74, 47–54. (3) Vogel, M. J.; Steen, P. H. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 3377–3381. (4) Reis, P. M.; Jung, S.; Aristoff, J. M.; Stocker, R. Science 2010, 330, 1231– 1234. (5) Prakash, M.; Quere, D.; Bush, J. W. M. Science 2008, 320, 931–934. (6) Eggers, J.; Villermaux, E. Rep. Prog. Phys. 2008, 71, 036601. (7) Dodds, S.; Carvalho, M.; Kumar, S. Phys. Fluids 2009, 21, 092103. (8) Chadov, A. V.; Yakhnin, E. D. Kolloidn. Zh. 1979, 41, 817–820. (9) Darhuber, A. A.; Troian, S. M.; Wagner, S. J. Appl. Phys. 2001, 90, 3602– 3609. (10) Gupta, C.; Mensing, G. A.; Shannon, M. A.; Kenis, P. J. A. Langmuir 2007, 23, 2906–2914. (11) Cai, S.; Bhushan, B. Mater. Sci. Eng., R 2008, 61, 78–106. (12) Balu, B.; Berry, A. D.; Hess, D. W.; Breedveld, V. Lab Chip 2009, 9, 3066– 3075. (13) Kusumaatmaja, H.; Lipowsky, R. Langmuir 2010, 26, 18734–18741. (14) De Souza, E. J.; Brinkmann, M.; Mohrdieck, M.; Crosby, A.; Arzt, E. Langmuir 2008, 24, 10161–10168. (15) Huang, W.-X.; Lee, S.-H.; Sung, H. J.; Lee, T.-M.; Kim, D.-S. Int. J. Heat Fluid Flow 2008, 29, 1436–1446. (16) Huang, W.-X.; Sung, H. J.; Lee, T.-M.; Kim, D.-S.; Kim, C.-J. J. Micromech. Microeng. 2009, 015025. (17) Qian, B.; Loureiro, M.; Gagnon, D. A.; Tripathi, A.; Breuer, K. S. Phys. Rev. Lett. 2009, 102, 164502. (18) Villanueva, W.; Sjodahl, J.; Stjernstrom, M.; Roeraade, J.; Amberg, G. Langmuir 2007, 23, 1171–1177. (19) Panditaratne, J. C. Ph.D. Thesis, Purdue University, 2003. (20) Bird, J. C.; de Ruiter, R.; Courbin, L.; Stone, H. A. Nature 2010, 465, 759–762. (21) Foteinopoulou, K.; Mavrantzas, V. G.; Tsamopoulos, J. J. Non-Newtonian Fluid Mech. 2004, 122, 177–200.
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trapped in the liquid bridge that connects the image and the substrate. These bubbles can reduce the amount of liquid transferred to the substrate, resulting in a defect known as spackle. This is a potentially catastrophic defect in the manufacture of printed electronics, where any gap in the final pattern could ruin the entire device. The goal of this letter is to understand the role of bubbles in the dynamics of stretching liquid bridges, where the authors are aware of only three studies, all computational, that have been published to date.21-23 These studies do not consider the role of surface wettability on either the liquid bridge or the bubble dynamics and thus are unable to evaluate the effect that the bubble may have on liquid transfer. We also examine how the stretching of nonwetting fluids differs from that observed with wetting fluids, which is of fundamental scientific importance.
2. Experimental Details The apparatus used in this letter is shown in Figure 1. A glass microscope slide was used for the bottom plate, and a steel post that is 3.25 mm in diameter was used for the top plate. Both plates could be covered with poly(ethylene terephthalate) (PET), (22) Foteinopoulou, K.; Mavrantzas, V. G.; Dimakopoulos, Y.; Tsamopoulos, J. Phys. Fluids 2006, 18, 042106. (23) Chatzidai, N.; Giannousakis, A.; Dimakopoulos, Y.; Tsamopoulos, J. J. Comput. Phys. 2009, 228, 1980–2011.
Published on Web 01/06/2011
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low-density polyethylene (LDPE), or poly(oxymethylene) (Delrin), allowing for the variation of the wettability of either plate (Table 1). A 1 μL drop of distilled water was placed onto the bottom plate, and for certain experiments, a 0.1 μL air bubble was inserted into the drop with a syringe (Hamilton company, model 7001KH). The upper plate was brought into contact with the water, and the drop was compressed. The upper plate was then pulled away from the bottom, stretching the bridge at a constant velocity. In experiments performed with bubbles, the bubble was initially in contact with both plates before stretching. The stretching was visualized using a high-speed camera with a frame rate of 60 to 3000 frames/ s, depending on the stretching speed. Results were quantified using ImageJ analysis software.24 Fluid volumes were calculated using Pappus’ theorem, which relates the volume of a solid of revolution to its cross-sectional area in the r-z plane. Because this analysis technique assumes an axisymmetric drop shape, we are unable to account for asymmetries in the drop shapes. However, the calculated drop volume, both before and after stretching, was generally within 10% and often within 5% of the expected volume of 1 μL, indicating that our analysis is reasonably accurate. The maximum stretching speed used in these experiments was 69.3 mm/s, and the characteristic length scale for the drop Table 1. Material Characteristics Used in This Letter, Where θa and θr are the Advancing and Receding Contact Angles, Respectively material LDPE PET Delrin
θa
θr
95.9 ( 2.9° 78.5 ( 1.8° 68.5 ( 3.4°
79.8 ( 3.6° 60.4 ( 2.5° 23.0 ( 4.1°
Figure 2. Fraction of fluid resting on the top plate after bridge breakup for pure water (O) and water with an air bubble (b). Both the top and bottom surfaces were covered with PET. The dashed line represents φ = 0.5.
was on the order of 0.5 mm. Therefore, the maximum capillary, Weber, and Bond numbers were on the order of 1 10-3, 0.01, and 0.1, respectively, indicating that surface tension dominates inertial and viscous forces. Whereas the Bond number suggests that gravitational effects may be important, we did not observe this to be the case, within our experimental error. Additionally, Slobozhanin and Perales25 found that, for the experimental conditions studied here, there was a negligible difference in the stability of a liquid bridge between Bond numbers of 0 and 0.1 (Supporting Information), further supporting our assumption that gravitational forces do not play a significant role in our experiments.
3. Results and Discussion We first studied the stretching of water between two PET surfaces. Figure 2 shows the volume fraction of fluid resting on the top plate after breakup, φ, for different stretching speeds. The volume of fluid on the top plate is found to be the same as on the bottom plate, giving φ ≈ 0.5 regardless of the stretching speed. Because the effects of inertia and gravity are small in our experiments, any hydrodynamic force that might move the fluid preferentially toward one surface or the other is small. In addition, because the two plates are covered with the same material, there is no wettability difference to drive fluid toward one plate or the other. Therefore, it is expected that the breakup should be nearly symmetric about the bridge midpoint. When an air bubble is introduced into the bridge prior to stretching, the volume of fluid on the top plate is still the same as on the bottom plate, where we use the term fluid to refer to the total volume of liquid and gas. This suggests that the presence of the bubble does not have an effect on the breakup of the liquid bridge. To understand this result, it is helpful to examine a time series of images taken during stretching, both with and without a bubble (Figure 3). Comparing the shape of the outer air/liquid interface at a given time, there is virtually no difference in the shape of the interface with or without a bubble. This indicates that the dynamics of the two interfaces are decoupled, so the outer interface evolves as if no bubble is present. An examination of the dynamics of the bubble in Figure 3, highlighted in red (images are included without modification in the Supporting Information), shows that the air bubble slips entirely off of the bottom surface and onto the top surface. Therefore, the volume of fluid on the top plate is the same as on the bottom, but the volume of liquid on the top plate is significantly smaller. This is highlighted in the final two panels in the bottom series of Figure 3, where the bubble pops, leaving behind only the liquid that was transferred to the top surface. It should be noted that, whereas the bubble slips onto the top surface in Figure 3, we observed it resting on the bottom surface with equal frequency. This indicates that the motion of the bubble is not buoyancy-driven.
Figure 3. Time series of images taken during the stretching of a bridge without a bubble (top) and with a bubble, highlighted in red (bottom). The bridges were stretched between two PET surfaces at a speed of 0.89 mm/s. Langmuir 2011, 27(5), 1556–1559
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Figure 4. Comparison of the bubble position for (a) slow stretching speeds (0.89 mm/s) and (b) fast stretching speeds (61 mm/s) for water stretched between two PET surfaces.
The effect of the stretching speed on bubble breakup is shown in Figure 4. As was noted in the previous paragraph and in Figure 3, at slow speeds the bubble slips entirely off of one surface and onto the other. However, at faster speeds, the bubble breaks up near its center, resulting in breakup that is more symmetric than at slower speeds. That we observe the symmetry of the bubble dynamics breaking as the speed is decreased is a surprising result because one would expect surface tension, which is the dominant force in this system, to maintain symmetry during stretching for two plates that are covered with the same material. One possible explanation of this behavior is that wetting fluids (water on PET) behave in a different manner during stretching than do nonwetting fluids (air on PET). Some evidence for this is provided in Figure 8 of Dodds et al.,7 reproduced with modifications in the Supporting Information, which shows the computed interface profile just before breakup for the stretching of a nonwetting liquid bridge between two identical plates. These computations indicate that although the breakup of the bridge remains symmetric about its midpoint, as one would expect because the plates are identical, the thinnest portion of the bridge is now located near the two plates, instead of at the center. This change in behavior can be rationalized by noting that because the fluid is nonwetting it will attempt to dewet the two plates as the bridge is stretched. If the stretching rate is slower than the dewetting rate, then the contact lines will move quickly enough to slip off of both plates and the bridge will break at the solid surfaces instead of near its center. Because the bridge is connected to the plates by thin fluid threads, the region with the highest capillary pressure is near the contact lines. If one of the two contact lines pins on the top surface (for example) and the other contact line continues to slip (as in the second panel at the bottom in Figure 3), then the highest pressure in the bridge will be at the bottom plate. This high pressure causes more fluid to be pumped away from the bottom plate, further thinning the connecting fluid thread and eventually driving all of the fluid off the plate. Because contact line pinning should be due primarily to surface roughness, which surface the bubble pins on will be random. This explains why, at slow speeds, the bubble rests on both surfaces with equal frequency. Additionally, as the stretching rate is increased, the contact lines will no longer have time to dewet one surface completely, forcing breakup closer to the center of the air column instead of at one of the two plates, as is observed in Figure 4b. If the behavior of the bubble is related purely to the wetting dynamics of the air on the PET surface, as we suggest, and has (24) Abramoff, M. D.; Magelhaes, P. J.; Ram, S. J. Biophoton. Int. 2004, 11, 36–42. (25) Slobozhanin, L. A.; Perales, J. M. Phys. Fluids A 1993, 5, 1305–1314.
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Figure 5. Fraction of fluid composing the largest drop after bridge breakup for stretching between two LDPE plates. The dashed line represents φ = 0.5.
Figure 6. Change in volume of the fluid drop resting on Delrin (O) or PET (0) after the bubble pops. The dashed line represents the initial bubble volume inserted into the drop, 0.1 μL.
nothing to do with any interaction between the bubble and the outer gas/liquid interface, then identical behavior should be observed for a single nonwetting fluid, which is a simpler system to study and understand. Figure 5 shows the liquid fraction of the largest drop versus the stretching velocity for water between two LDPE plates. This presents a system where the liquid is nonwetting, in contrast to Figure 2, where the liquid is wetting and the air is nonwetting. It should be noted that the largest drop was found on the top and bottom surfaces with equal frequency over all stretching speeds (Supporting Information). For slow stretching speeds, the liquid is found almost entirely on one surface or the other. As the stretching speed is increased, however, the size of the largest drop begins to decrease, approaching the expected result of φ = 0.5 for a fluid stretched between two identical plates. Therefore, water between two hydrophobic surfaces exhibits the same behavior as the more complex liquid bridge/bubble system from Figure 3, supporting our hypothesis that the bubble motion is governed by wetting and contact line pinning and not by any hydrodynamic interactions between the water and the bubble. If we now consider a liquid bridge system with two chemically different surfaces, PET and Delrin, then the air bubble should wet the PET preferentially,26 even though air is not a wetting fluid on (26) Because θair = π - θwater, θair > π/2.
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either surface. In addition, small differences in wettability have been shown to produce large differences in liquid transfer for nonwetting fluids,7 and we therefore expect that the entire bubble will slip onto the PET surface, leaving only water on the Delrin. Although it is difficult to measure the volume of the bubble accurately because of the resolution of the bubble interface, we find that the bubble does appear to have transferred entirely to the PET surface after breakup, regardless of the stretching speed (Supporting Information). In the PET/Delrin systems, the bubble would nearly always pop after stretching. We can therefore compare the volume of the drop, both before and after popping, to get an estimate of the size of the bubble on each surface (Figure 6). We find that there is a negligible change in volume for the drop on the Delrin surface, indicating that if any air remains it did not pop during visualization. We also find that the drop on the PET consistently decreases in volume by approximately 0.1 μL, which is the volume of the bubble originally inserted into the drop before stretching. This supports our hypothesis that the bubble has moved entirely to the PET surface, leaving only water on the Delrin surface. The time between breakup and the bubble popping was on the order of 1 s. In an industrial printing process, where the pattern may dry within milliseconds of being printed, it is possible that the bubble does not pop but is instead dried into the final product. This type of defect could go unnoticed in graphic arts applications because the bubble may not make the printed feature visibly different from a feature that had printed correctly. However, a bubble in a printed circuit could significantly alter the electrical properties of the device.
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This highlights the importance of understanding and controlling the dynamics of the bubble during printing, as we have attempted to do in this letter. The work presented in this letter has shown that the breakup behavior of a nonwetting fluid stretched between two plates is fundamentally different from that of a wetting fluid. When the two solid surfaces are made of the same material, we find that at slow stretching speeds a nonwetting fluid will slip entirely onto whichever surface its contact line first pins on. This behavior was found to be robust, occurring both when water alone was stretched between hydrophobic plates and when water with an air bubble was stretched between hydrophilic plates. We were then able to use a wettability difference between the two plates to drive the bubble selectively toward the most hydrophobic plate, allowing us to remove the bubble defect entirely from one of the plates. Acknowledgment. This work was supported by the Industrial Partnership for Research in Interfacial and Materials Engineering (IPrime) and the University of Minnesota graduate school through a doctoral dissertation fellowship to S.D. We thank Wieslaw Suszynski for his help in setting up the visualization experiments and Taylor Beck for his help in performing image analysis. Supporting Information Available: In-depth discussion of the role of gravity in our experiments. Unmodified experimental images. Computational result, modified from Dodds et al. ,7 supporting our discussion of the dynamics of stretching for nonwetting fluids. This material is available free of charge via the Internet at http://pubs.acs.org/.
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