pubs.acs.org/Langmuir © 2010 American Chemical Society
Effect of an Encapsulated Bubble in Inhibiting Droplet Sliding William Yeong Liang Ling, Tuck Wah Ng,* and Adrian Neild Laboratory for Optics, Acoustics, and Mechanics, Department of Mechanical and Aerospace Engineering, Monash University, Clayton VIC3800 Australia Received April 28, 2010. Revised Manuscript Received September 17, 2010 The transport of liquid droplets on surfaces carrying reactants offers advantages in the creation of fluidic devices crucial for life science applications. In a majority of situations, a selection of these droplets on a surface, rather than all of them, will need to be moved at any one time. It is a formidable challenge to deliver the motive energy source only to specific droplets while leaving the others unmoved. Here, we describe an alternative novel solution of momentarily pinning specific droplets to the surface while allowing the rest to be moved. We demonstrate this concept via the injection of a sizable bubble that is attached to a PTFE surface within a droplet. This then affects the contact line of the droplet, pinning it despite the introduction of an incline that will normally result in sliding. The use of bubbles offers easy release of pinning at will by simple rupture using mechanical means.
Introduction The impetus to fashion integrated fluidic devices stems from the advantages gained by the minimization of chemical usage, automation, reduction in errors, high throughput, and portability of chemical analysis equipment to point of use. These devices are now harnessed in important life science applications such as drug discovery1 and gene regulation studies in cells.2 Many of these processes are inherently batch-wise or discrete volume processes, where a precisely known volume of liquid is added to another and the mixture undergoes a series of unit operations, such as heating, cooling, separation, and detection phases. Many fluidic devices are built on a continuous flow paradigm where the liquid continuously circulates through a complex fluidic network. To mimic the batch process, plugs of reactants are suspended within the carrier liquid, which are cycled to different areas of the chip.3 Limitations to designing the fluidics this way include possible contamination of isolated plugs from diffusion of reactants within the carrier fluid and accumulation of residual liquid on the channel walls. Precise volume apportionment is generally difficult in continuous-flow devices, and the necessity for closed-channel architecture adds complexity and cost to the manufacturing. The use of droplets in isolation logically overcomes these limitations and is, not surprisingly, finding increasing use in assay applications.4 The obvious challenge in designing a device for such a purpose lies in moving discrete liquid drops on a surface. Several reported methods rely on the supply of external energy sources to achieve this goal, such as thermal Marangoni flow,5 electrowetting,6 dielectrophoresis,7 and surface vibration.8 The effectiveness of droplet movement has been facilitated by approaches that capi*To whom correspondence should be addressed. E-mail: engngtw@ gmail.com.
(1) Dittrich, P. S.; Manz, A. Nat. Rev. Drug Discov. 2006, 5, 210. (2) Bennett, M. R.; Hasty J. Nat. Rev. Genetics 2009, 10, 628. (3) Kline, T. R.; Runyon, M. K.; Pothiawala, M.; Ismagilov, R. F. Anal. Chem. 2008, 80, 6190. (4) Tewhey, R.; et al. Nat. Biotechnol. 2009, 27, 1025. (5) Brzoska, J. B.; Brochard-Wyart, F.; Rondelez, F. Langmuir 1993, 9, 2220. (6) Ajdari, A. Phys. Rev. E 2000, 61, R45. (7) Velev, O. D.; Prevo, B. G.; Bhatt, K. H. Nature 2003, 426, 515. (8) Daniel, S.; Chaudhury, M. K.; de Gennes, P. -G. Langmuir 2005, 21, 4240. (9) Daniel, S.; Sircar, S.; Gliem, J.; Chaudhury, M. K. Langmuir 2004, 20, 4085.
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talize on surface energy gradients and texture modifications.9-14 In a large majority of cases, a selection of reactant-carrying droplets on the surface, rather than all, will need to be moved at any one time. It is a challenge then to deliver the motive energy source only to specific droplets while leaving the others unmoved. This is also a challenge faced in continuous and plug-based microfluidic devices wherein the recourse is to operate under a complex network of channels and valves. In the case of droplets on a surface, an alternative solution is to momentarily pin specific droplets onto the surface while allowing the rest to be moved. In this work, we show that this is possible via the somewhat counterintuitive usage of bubbles. We describe and demonstrate this method in the context of droplets residing on an incline.
Theory Liquid surfaces in equilibrium are governed by the wellestablished laws of Laplace and Young. Laplace’s law has the liquid surface behaving like a membrane, while Young’s condition15 dictates that γLS þ γLV cos θ ¼ γSV
ð1Þ
where θ is the equilibrium contact angle, and the interfacial tensions between the liquid-solid, liquid-vapor, and solidvapor interfaces are γLS, γLV, and γSV, respectively. The theoretical thermodynamic contact angle of a droplet is based on very clean environmental conditions. The ability of the contact line to be pinned within a range of contact angles (hysteresis) imbues ability for the droplet to, in some cases, assume hydrophilic to hydrophobic characteristics. Thus far, it is widely accepted that surface roughness, chemical contaminants, and solutes are the major culprits of contact angle hysteresis.16 The use of roughness to modify the wetting characteristics of surfaces is arguably the most widely researched aspect. This mimics the ability of natural (10) (11) (12) (13) (14) (15) (16)
Petrie, R. J.; Bailey, T.; Gorman, C. B.; Genzer, J. Langmuir 2004, 20, 8993. Yamada, R.; Hirokazu Tada, H. Langmuir 2005, 21, 4254. Fang, G.; Li, W.; Wang, X.; Qiao, G. Langmuir 2008, 24, 11651. Zhang, J.; Han, Y. Langmuir 2009, 25, 14195. Lv, C.; Yang, C.; Hao, P.; He, F.; Zheng, Q. Langmuir 2010, 26, 8704. Young, T. Philos. Trans. R. Soc. London Ser. A 1805, 95, 65. de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827.
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Figure 1. Droplet on a surface inclined at R to the horizontal, with advancing and receding angles due to hysteresis causing it to stay unless FG exceeds the retention force.
surfaces such as the lotus leaf17 and rose petal18 to assume superhydrophobic states via the presence of surface micro and nanostructures. The ability of droplets to assume contact angle hysteresis is evident when placed on an inclined surface on which “advancing” and “receding” contact angles are present at the drop front and rear, respectively. This is easily observed in the case of a droplet placed on a hydrophobic surface. On a surface inclined at angle R to the horizontal, the component of gravitational force acting on a droplet can be represented as FG ¼ FVg sin R
ð2Þ
where F is the density of the liquid, V is the volume, g is the gravitational acceleration, and R is the angle of the incline as shown in Figure 1. The retention force FR can be related to the drop width w, as well as the forward and rear contact angles θforward and θrear via the approximation FR wγLV ðcos θrear - cos θforward Þ
ð3Þ
Equation 3 indicates that the contact angle hysteresis of the droplet creates the force opposing motion. For droplet motion to occur, it is generally taken that the gravitational component FG must exceed the retention force FR. This occurs when the forward and rear contact angles exceed the maximal advancing and minimal receding contact angles θA and θR, respectively. It has been observed that the advancing contact angle is normally breached first, leaving the receding contact line to hold the drop from sliding.19,20 This causes an elongation of the droplet, from which the receding contact angle will eventually be breached to engender full sliding of the droplet down the incline. In terms of the critical incline RC at which this occurs, the force balance can then be represented as FVg sin RC ¼ wγLV ðcos θR - cos θA Þ
ð4Þ
A previous study has found that a needle tip immersed in a drop results in a delay in sliding due to a shape change.21 This surface deformation results in a component of the surface tension parallel to the incline acting to pin the drop. The force balance of a droplet usually consists only of the gravitational component FG and the retention force FR. However, the introduction of surface deformation results in additional force FD acting in opposition to FG. This force presents itself as a consequence of extended surface tension in the direction of the incline. This is a result of the hysteresis of the liquid-vapor surface deformation with respect to the incline. The force balance (vertical components) (17) Yu, Y.; Zhao, Z. -H.; Zheng, Q. Langmuir 2007, 23, 8212. (18) Feng, L.; Zhang, Y.; Xi, J.; Zhu, Y.; Wang, N.; Xia, F.; Jiang, L. Langmuir 2008, 24, 4114. (19) Tadmor, R.; Chaurasia, K.; Yadav, P. S.; Leh, A.; Bahadur, P.; Dang, L.; Hoffer, W. R. Langmuir 2008, 24, 9370. (20) Yang, C.; Hao, P.; Feng, H. E. Chin. Sci. Bull. 2009, 54, 727. (21) Pierce, E.; Carmona, F. J.; Amirfazli, A. Colloids Surf. A. 2008, 323, 73.
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Figure 2. (a) A free air bubble in a volume of fluid. (b) A free bubble in equilibrium on the surface of a fluid. (c) A free bubble within a droplet on an incline with the rear contact line being deformed. (d) A pinned air bubble in a volume of fluid. (e) A pinned air bubble with an interface impacting from above. Both the external and internal interfaces are deformed by the interaction.
is then FR þ FD ¼ FG
ð5Þ
Two possible situations exist when a bubble is introduced into droplet such that it deforms the liquid-air interface. We discuss first the case of a freely buoyant bubble. Consider for the moment a free air bubble in a volume of fluid as shown in Figure 2a. Assuming that the density of the fluid is far greater than the density of air, the buoyancy force acting on the bubble is approximately FB FVA g
ð6Þ
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where F is the density of the liquid, and VA is the volume of the bubble. When a freely floating bubble comes in equilibrium with the liquid-gas interface (Figure 2b), a distinct surface deformation occurs due to a balance between surface tension and the buoyancy of the bubble. For the sake of clarity, we will refer to the upper interface as the external interface, as opposed to the internal interface of the bubble. This situation has been well established for a horizontal interface.22,23 It is important to note that only the portion of air in the bubble that lies below the mean external interface results in a buoyancy force.24 This is a nonzero value as the bubble is not completely above the surface. If we now imagine a droplet with a free floating bubble as shown in Figure 2c, a deformation in the interface will be observed due to the droplet accommodating for the buoyancy provided by the bubble. At an incline, the bubble will tend to move to the rear of the droplet due to the direction of buoyancy. A surface deformation is then apparent at the rear contact line of the droplet. This surface deformation in the direction of the incline will give rise to an additional retention force acting on the drop. This should then reduce the retention force required to be supplied by the original contact line, resulting in a change in the rear contact angle. Since the bubble is constantly pushing upward due to buoyancy, it tends to minimize the film thickness between the external and internal interfaces over time. A way to reduce this effect is to minimize the force acting on the interfaces while maintaining a similar deformation. As an aside, a freely floating bubble tends to have a short lifetime. Hence, its dependability in maintaining the surface deformation necessary to cause the drop to be retained more strongly on the incline is rather poor. We now consider the second case where the air bubble is pinned to the solid substrate. Under a situation where the bubble is stationary and fully submerged within the liquid phase (Figure 2d), the retention force FRB of the bubble is equal to the buoyancy force. However, when the liquid level is lowered below the height of the bubble (Figure 2e), a surface deformation effect similar to that seen previously in Figure 2b will be observed. The analysis of forces in equilibrium, however, requires looking at the droplet to air interface and the bubble interface systems separately. We consider first the droplet to air interface system. From this point of view, the force balance is between the surface tension of the interface and an external force (from the internal system) or FD ¼ FX
ð7Þ
where FX is an external force to the system and FD is the component of the deformation force in the direction of FX. The situation where an undeformable interface presses down on a bubble has been addressed in the literature.25,26 Neglecting gravity and assuming weak forces, the deformation force in such a case was determined to follow a linear Hooke’s relation with the spring constant being a function of the surface tension. In the case of a deformable interface, the relationship is not necessarily linear, but the surface tension component of the deformation should still balance the force exerted on the interface. If we now consider the system comprising the bubble alone, the balance of forces is between the buoyancy force, the retention force, and an external force pushing on the bubble (transferred (22) Allan, R. S.; Charles, G. E.; Mason, S. G. J. Colloid Sci. 1961, 16, 150. (23) Princen, H. M. J. Colloid Sci. 1963, 18, 178. (24) Joseph, D. D.; Wang, J.; Bai, R.; Yang, B. H.; Hu, H. H. J. Fluid Mech. 2003, 496, 139. (25) Attard, P.; Miklavcic, S. J. Langmuir 2001, 17, 8217. (26) Pushkarova, R. A.; Horn, R. G. Langmuir 2008, 24, 8726.
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Figure 3. (a) A sizable bubble on the surface within the droplet and its associated forces has the contact angles exchanged. The sliding of the droplet down the incline brings the rear contact line in close proximity to the bubble and creates a film of liquid there. (b) The contact line has been deformed by the encapsulated bubble. The altered receding contact angle of the droplet as a consequence of this permits the droplet to stay pinned to the surface beyond the inclination usually needed to cause the droplet to slide.
Figure 4. (a) Image of a 76 μL droplet placed on an PTFE surface
inclined at 45° to the horizontal and (b) an image of a 76 μL droplet placed on an PTFE surface inclined at the same angle in which a sizable bubble is clearly affecting the receding contact line. There is an evident ability of the liquid film to conform to the shape of the bubble as a result of the mating at the rear of the droplet.
from the droplet-air interface). This can be expressed as FRB þ FX ¼ FB
ð8Þ
It is important to note that this buoyancy force results only from the portion of air submerged below the mean liquid level. The difference between this and the case of a freely buoyant bubble is that the retention force here acts to mediate the force balance, and thus minimizes the force pressing against the interface (between droplet and air). On the basis of the force balance, the action of DOI: 10.1021/la1028959
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Figure 5. The rear contact angles of droplets both with and without an encapsulated bubble. Measurements were conducted at the critical incline of droplets with no bubbles. At the same incline, droplets with a bubble are pinned to the surface and exhibit a higher receding contact angle.
Figure 6. A plot of the inclination angles needed to cause sliding against droplet volume on the PTFE surface with and without an air bubble injected. The line is a theoretical solution to eq 4. There is a clear ability of the droplet to resist sliding better with air bubble present.
the external force acting via pressing on the bubble will also serve to reduce the retention force of the bubble. This occurs via a change in the contact angle of the bubble. Clearly, it is the manner of disruption of the droplet-air interface that produces the additional retention force of the droplet on the incline. The degree of disruption is somewhat proportional to the bubble size, which in turn is proportional to the buoyant force. Hence, by adopting a fraction f where f ¼
FD FB
ð9Þ
we have a rough depiction in which the retention force follows the manner of (1 - f) of the buoyancy force. Let us return to the droplet from when we began this formulation (Figure 1). If a sizable air bubble is created within the liquid droplet such that it attaches to the surface at the center of the droplet, the nature of the advancing and receding angles for the bubble are the opposite to that of the droplet when the surface is inclined (see Figure 3a). In addition, the buoyancy force also acts in opposition to the direction of gravity. In other words, the bubble should not slide down the incline, provided it can remain stably attached to the surface. It should be noted that it is necessary for the bubble to be positioned such that it interacts 17698 DOI: 10.1021/la1028959
with the droplet-air interface. Otherwise, there will not be any inhibition effect on the droplet sliding down the incline. This differs from the case where the bubble is freely floating; wherein there will always be an interaction and thus a deformation of the droplet-air interface. In the case of a large bubble (on the order of the droplet size), we can make the assumption that the deformation caused by interaction with the bubble is dominated by buoyancy. As previously mentioned, solid objects are also able to cause a deformation in the interface.21 Therefore, although the situation with a bubble is dominated by buoyancy, there may be other means to produce a deformation in the droplet-air interface. The interaction between the interface of the pinned bubble and the droplet-air interface results in changes in the contact angles (see Figure 3a), which makes it necessary to modify the conventional consideration on how they dictate the sliding of droplets on an incline. In the case of a droplet without a bubble, the critical incline RC (as per eq 4) corresponds to the point where the critical advancing and receding angles θR and θA are exceeded. For a system with a bubble, a portion of the gravitational force is supported by the deformation force resolved in the direction of the incline. Hence, the retention force of the droplet reduces in order to maintain equilibrium of the system. This results in changes in the forward and rear contact angles such that θforward with bubble < θforward without bubble and θrear with bubble > Langmuir 2010, 26(22), 17695–17702
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θrear without bubble, as shown in Figure 3b. Essentially, a similar incline will not result in the same advancing and receding angles; in fact, the system should be able to support a critical inclination angle that is higher than the original RC. This proceeds until the droplet is able to support a case where θrear = θR and θforward =θA. This observation can be depicted more mathematically if we adopt f as indicator of the added retention force as result of bubble incorporation. From eqs 4 and 5, we have FR þ fFB ¼ FG wγLV ðcos θrear - cos θforward Þ þ f FVA g sin R ¼ FVg sin R ð10Þ By rearranging eq 10 and substituting for the critical contact angles, the new force balance is thus wγLV ðcos θR - cos θA Þ ¼ FðV - fVA Þg sin RC
ð11Þ
where all the terms are as previously defined. When the bubble is small enough or does not interfere with the droplet-air interface, VA = 0, that is, the droplet behaves as in the standard case. When an interaction is present, the onus on the retention force to hold back the gravitational force should be reduced, thus allowing a droplet to stay pinned to the surface despite the surface being inclined beyond the critical incline case without a bubble.
Methods The sample used in our experiments was polytetrafluoroethylene (PTFE) printed on glass. Using a Veeco Dektak 150 surface profiler, the surface peak-to-peak value and root mean squared roughness parameters were measured to be 39.538 and 8.147 μm, respectively. The liquid used was deionized Milli-Q water. To minimize surface roughness and inhomogeneity factors, we selected a fixed surface region on which a single droplet was placed each time. The surface spot was dried with compressed inert gas before each droplet was placed. Dust and minute particle contaminants were removed from the surface spot by tape stripping (3 M No. 810). This was observed to remove particles as small as 15 μm. The surface cleaning method was carefully ensured to leave no residue and using sessile drop contact angle measurements, the surface properties were observed to be unchanged. The PTFE sample was attached to a purpose built rotation stage which allowed the surface inclination to be recorded. Images and videos were also captured from the side to verify the surface inclination via image analysis and to perform additional measurements. Droplets of various volumes between 44 and 100 μL were dispensed using an Eppendorf 10-100 μL pipet in steps of 4 μL (i.e., 44 μL, 48 μL, etc.). After a droplet was deposited, the stage was rotated until sliding occurred. The inclination angle was then recorded, and this was later verified with higher accuracy using recorded video footages. Three injected air volumes were examined: no bubble, 10 μL, and 20 μL. For the no bubble case, the stage was simply rotated after deposition of a droplet. Bubble deposition was also accomplished with the Eppendorf 10-100 μL pipet penetrating the droplet in order to leave it as close to the substrate as possible. The pipet tips were chosen to be as small as practicable so as to minimize disturbance to the droplet width and contact line. After this, the stage was rotated until sliding was observed. This was only performed when it was ascertained that the air bubble was attached stably to the PTFE substrate. As with the no bubble case, the inclinations were later verified using recorded video. Several instances were observed where the air bubble did not remain stable and instead ruptured during rotation. These instances were recorded but disregarded from the final results. Analysis was only done on cases where a stable air bubble remained throughout the inclination and sliding process. Langmuir 2010, 26(22), 17695–17702
Figure 7. Sequence of images of a 76 μL drop injected with a sizable bubble taken at increments of 5 degrees inclination from the horizontal on the PTFE surface used. Continual breaching of the advancing contact line allows the droplet to finally detach in two from its rear that remains pinned down by the bubble present there.
Results and Discussion Figure 4a shows a 76 μL droplet on the PTFE surface that is inclined at 45° to the horizontal. In contrast, Figure 4b shows an image of a droplet of identical volume placed on the PTFE surface at an identical incline but with a sizable bubble that clearly interferes with the rear contact line. The images appear to suggest that the interface is being pushed upward by the encapsulated bubble, thus serving as an obstacle to prevent the droplet from sliding down the incline. The ability of the liquid film to stretch considerably to conform to the shape of the bubble is noteworthy. The liquid film between the bubble and the atmosphere is reminiscent of what one would observe from a bubble forming out of soap solution; even though in this case the liquid DOI: 10.1021/la1028959
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Figure 8. A comparison of the theoretical solutions for VA = 10 μL and 20 μL with experimental data.
was a nonsurfactant. It is also noticeable that the film does not appear to be of equal thickness over the rear section of the droplet; the thinnest section corresponding to the furthermost protrusion of the bubble from the rear as the surface was inclined. A plot of the rear contact angles is shown in Figure 5. These were measured at the average critical incline of droplets with no bubbles. For example, the contact angle of 76 μL droplets with VA=0 μL were measured at their respective critical inclines. Their average critical incline was then found to be 48.4°. The contact angles of 76 μL droplets with VA = 10 and 20 μL were then measured at 48.4°. The data set for VA = 0 μL is less scattered because they are in fact the defacto minimal receding angles for the droplets. On the other hand, the droplets with air bubbles within them were far from their critical incline. These recorded angles can be considered as transition angles. What is clear, nevertheless, is the general trend of the rear contact angle being larger with increasing air volume. This indicates that the presence of a bubble tends to result in an increased receding contact angle. Figure 6 shows plots of the inclination angles needed to cause sliding against the droplet volume on the PTFE surface with and without an air bubble injected. The error bars depict two standard 17700 DOI: 10.1021/la1028959
deviations and the line is a theoretical solution to eq 4, assuming an initial spherical cap profile with a static contact angle of 110°. There is a clear ability of the droplet to resist sliding better with an air bubble present. Figure 7a provides a sequence of images of a 76 μL droplet injected with a sizable bubble in increments of approximately 5° inclination from the horizontal on the PTFE surface used. Clearly, while the rear of the droplet is pinned, its forward contact line can still move if the contact angle there exceeds the maximum advancing contact angle. This movement will obviously elongate the droplet. What ensues is a continuation of the earlier discussion of Figure 4. The rear contact line appears to “travel” across the bubble to an extent that it eventually detaches from it and forms a new contact line on the surface. Before such an attachment can happen, however, the droplet will have lost all traction due to the strong gravitational component arising from heightened inclination. What is intriguing, nonetheless, is the possibility of the bubble being left behind in the process; resulting in a situation where excess liquid is shed to form a filmed dome. This raises the possibility of some complementary physics involved when bubbles are created by blowing air across the surface of surfactants. The detachment method of the droplet from the bubble is akin to the necking and pearling of a rivulet. In an applied situation, the Langmuir 2010, 26(22), 17695–17702
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bubble can be ruptured to allow the droplet to move when needed so as not to leave such an air filled artifact behind. We are now in a position to examine the theoretical premise provided by eq 11, in which it will be necessary to estimate a value for f as defined in eq 9. Using the rear contact angles measured and shown previously in Figure 4b, in addition to the forward contact angles which were also measured, it is possible to obtain an approximate number for f. This can be done by calculating the retention force of VA = 0 droplets and comparing it to VA = 10 and 20 μL droplets. From eq 10, the difference in force should then be the deformation force, allowing us to estimate f using experimental results. This was found to be approximately 0.37, meaning that on average, the deformation force had a magnitude of around 30-40% of the buoyancy force. This, however, is not indicative of the entire sliding process as will be discussed later. Figure 8 presents the theoretical solutions for VA = 10 and 20 μL, plotted in addition to the experimental data shown previously in Figure 6. Another viewpoint is shown in Figure 8b, depicting the theoretical solution in 3D as a function of V, VA, and RC instead. All the experimental data points are included as an overlaid stem plot. It can be seen from these two figures that the theoretical solution provides a reasonable estimate of the experimental behavior. With higher volumes of VA, RC can be seen to reach 90° at a lower V, indicating a higher tendency for pinning to occur. A deviation at higher angles can be seen between the theory and experimental data, possibly due to the assumptions made. We now address the interpretation of the value of f, which was approximated earlier by experiment. Although we assumed a constant f, the deformation force FD can only apply when the encapsulated bubble touches the external interface. For droplets with VA=10 μL, this does not occur until the droplet is somewhat inclined. In addition, FD is represented by the actual deformation of the external interface. From our observations, this is also a function of the incline as could be seen in Figure 7a. The deformation is much more apparent at higher inclines as the bubble is squeezed into the rear of the droplet. Furthermore, the actual effective buoyancy force FB changes with the incline. This is because the buoyancy force decreases with increasing deformation as less of the air is located below the mean fluid level. A complete analytical solution for FD would require a balance between the surface tension of the internal and external interfaces and must take into account how a larger VA would result in a larger deformation, as well as how a higher R allows the bubble to deform the external interface more, and also results in a greater component of the deformation force in the direction of the incline. This is clearly a nontrivial task to achieve. The situation with the pinned bubble is interesting because, although the overall system should not be affected by the internal buoyancy, the fact that the bubble is able to deform the interface offers a unique situation where internal buoyancy has a role to play. Admittedly, the results may be slightly affected by small differences in the droplet width due to the injected bubble. Nevertheless, it should not be significant enough to account for the distinct change in the rear contact angle caused by deformation of the interface. It must also be noted that the equation balance in eq 11 is offered as an approximate rather than a rigorous depiction. Changes in the rear contact angle are expected to be more significant than changes at the front, due primarily to the propensity of the bubble to affect the rear contact line. In addition to the hydrophobic PTFE surface, we also briefly examined a highly hydrophobic rose petal. The petal was attached to a glass slide with double-sided tape, heated at approximately Langmuir 2010, 26(22), 17695–17702
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Figure 9. (a) Image of a droplet placed on a highly hydrophobic rose petal surface (as-placed contact angle of approximately 147°). (b) Image of the same droplet within which a sizable bubble is now present. (c) Another case with a larger volume of air at an incline of 20° to the horizontal. These images demonstrate the ability of the encapsulated bubble to deform the interface tremendously. Nevertheless, these bubbles were unstable and were prone to rupturing, thereby hindering attempts to use them to delay sliding on highly hydrophobic surfaces.
80 °C for 1 h, and left to rest for a day to dry it out. Figure 9a shows a droplet on the rose petal surface with an equilibrium contact angle of approximately 147°. Attempts to introduce a bubble were hampered by a high propensity of bursting at the external interface. In addition, attempts to attach bubbles on the surface results in them dissipating across the substrate and escaping outside the contact area. The high tendency of bubbles to burst on superhydrophobic surfaces has been reported recently27 and is attributed to the air pockets entrapped on the nanostructures coalescing with the air bubbles, forming air bridges that allow it to expand and eventually collapse. Although difficult to obtain and unstable, we encountered occasions where a bubble could successfully be introduced into the droplet on the rose petal surface. A situation is shown in Figure 9b, wherein due to the absence of retention forces on the bubble, the entirety of the buoyancy force (of the air volume below the mean liquid level) was able to deform the external interface of the droplet. Even with the bubble not attached to the surface, it still had the ability to deform the interface as shown in Figure 9c at an incline of 20°. Unfortunately, this system was not stable enough for us to obtain sufficient quantitative data. This instability is likely due to the higher force exerted against the external interface, which had the effect of making it easier for the thin film to rupture. As a rule of thumb, it would appear that the encapsulated bubble must either be stable while pressing against the external (27) Wang, J.; Zheng, Y.; Nie, F. -Q.; Zhai, J.; Jiang, L. Langmuir 2009, 25, 14129.
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interface, or the bubble must be stably attached to the surface, thereby minimizing the thinning of the film separating the external and internal interfaces. We also make mention that the ability of a bubble to stably exist on a surface is dependent on thermal, chemical, and mechanical conditions. The mechanical conditions required have been well established in a previous study.28 However, since the external interface is continuously deformed, we can postulate that similar mechanics should also apply at the external interface in this situation, whereby the imbalance of the deformation force in the direction of the incline causes an additional retention force. (28) Kralchevsky, P Langmuir 1996, 12, 5951. (29) Ferraro, P.; Coppola, S.; Grilli, S.; Paturzo, M.; Vespini, V. Nat. Nanotechnol. 2010, 5, 429. (30) Ng, T. W.; Yu, Y.; Tan, H. Y.; Neild, A. Appl. Phys. Lett. 2008, 93, 174105. (31) Xu, L.; Neild, A.; Ng, T. W.; Shao, F. Appl. Phys. Lett. 2009, 94, 034104.
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In summary, we show a purely mechanical method using a bubble to inhibit the tendency of droplets to move over a surface, thereby imbuing greater control useful for applications such as biochemical analysis. This is achievable without changing the surfaces characteristics (important when the surface is functionalized for other purposes) or affecting the liquid properties (e.g., electrowetting) that may have consequences on the contents (e.g., biomolecules, organisms etc.). Once a droplet is delivered to a desired venue in timely fashion, methods, such as the recent novel use of lasers,29 can be applied to cause filling into capillaries for important biochemical functions such as microplating30 and the harvest of particle and cells.31 Acknowledgment. Portions of this work were made possible by funding support from the Australian Research Council Discovery grant DP0878454.
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