Effect of a Rupturing Encapsulated Bubble in Inducing the Detachment

Nov 26, 2012 - Here, we examine how the rupture of an encapsulated bubble causes the detachment of a drop previously pinned on an incline. When the dr...
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Effect of a Rupturing Encapsulated Bubble in Inducing the Detachment of a Drop William Yeong Liang Ling,* Adrian Neild,* and Tuck Wah Ng Department of Mechanical & Aerospace Engineering, Monash University, Clayton Campus, VIC 3800, Australia S Supporting Information *

ABSTRACT: Droplet-based microfluidics is inherently based on the ability to control the motion of liquid drops. In most situations, drops are required to be controlled individually. Here, we examine how the rupture of an encapsulated bubble causes the detachment of a drop previously pinned on an incline. When the drop is located on a horizontal surface with a low liquid−solid adhesion energy (such as water on a superhydrophobic surface), the entire drop is propelled vertically off the surface without the input of an external energy source. From an energy balance, we determined that the majority of the stored surface energy is consumed by the formation of a large jet. When a surfactant is introduced into the system, the adhesion energy is then too large to overcome, resulting in a pinned oscillating drop. We also show that the process can be used to selectively cause drops to slide (at usually stable inclines) on a hydrophobic surface. The required sliding angle was decreased by almost 20° for a 48 μL water drop and a 10 μL bubble. This process enables the selective pinning and depinning of drops, a method that may prove useful for future droplet control techniques.

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modification.11,12 This mimics the water repellent qualities of natural surfaces such as the lotus leaf.13,14 In most cases, individual drops need to be moved separately, rather than all at once. It is therefore required that energy be delivered only to specific drops while leaving others stationary. A previous study has demonstrated that the introduction of a bubble into a drop on an incline pins it beyond an incline that would normally result in detachment and sliding (see Figure 1a and b).15 As the drops are held in place by an encapsulated bubble, the deliberate rupture of this bubble would enable individual drops to be released at will.

INTRODUCTION The ability to manipulate liquid has tremendous potential for applications in microfluidics. The development of microfluidic devices is motivated by advantages such as the minimization of chemical usage, automation, reduction in errors, a high throughput, and the portability of analysis equipment to the point of use. Such devices are now used in life science applications such as drug discovery1 and gene regulation studies in cells.2 Many of these are batch-wise or discrete volume processes, whereby discrete volumes of liquid are added to another, after which operations such as heating, cooling, separation, and detection can occur. Fluidic devices can be separated into two basic paradigms: continuous-flow and digital droplet-based microfluidics. A continuous-flow paradigm involves the constant circulation of liquid through complex fluidic networks. To mimic a batch process, plugs of reactants suspended within a carrier liquid are cycled to the various areas of a chip.3 Some research has also been conducted regarding the flow of water in carbon nanotubes.4,5 Continuous-flow microfluidics necessitates a closed-channel architecture that adds complexity and cost to the manufacturing process. The permanent channels also limit the ability to reconfigure flow processes. In contrast, digital microfluidics involves open structures with discrete droplets that can be controlled independently, a process that is finding increasing use in assay applications.6 A key aspect of digital microfluidics is the control of discrete liquid drops. Several methods that rely on external energy sources have been reported such as thermal Marangoni flow,7 electrowetting,8 dielectrophoresis,9 and surface vibration.10 The movement of a drop can also be aided with surface roughness © 2012 American Chemical Society

Figure 1. (a) A drop on an incline of α, which exhibits a divergence in the front and rear contact angles due to contact angle hysteresis. For detachment to occur, the component of FG in the direction of the incline must exceed the retention force FR. (b) A drop with an encapsulated bubble of comparable size, which affects the liquid−air interface of the drop and the rear contact angle.15 Received: August 21, 2012 Revised: November 21, 2012 Published: November 26, 2012 17656

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THEORETICAL CONSIDERATIONS Phase 1: Encapsulated Bubble within a Drop on a Horizontal Superhydrophobic Surface. When a bubble is introduced into a system, energy is also introduced in the form of increased surface energy. If a bubble of comparable volume is introduced into a drop, this is manifested as an increase in the liquid−air surface area. This increased surface area occurs in (i) the surface area of the new bubble and (ii) the increased liquid−air surface area of the drop caused by the presence of the bubble. The surface area of the bubble can be determined by approximating the bubble as a sphere. Conversely, the increased surface area of the drop’s external liquid−air interface can also be estimated. For simplification, we will assume that the profile of a drop with an encapsulated bubble is equal to the profile of a drop with volume V + Vbubble, where V is the liquid volume of the drop and Vbubble is the volume of the encapsulated bubble. Assuming the compressibility of air to be negligible, the total increase in the energy of the system can be expressed as:

This study examines the effect of the rupture of an encapsulated bubble on the encapsulating drop, with the volume of both measured in microliters. The underlying aim of the study is to determine how a rupturing bubble affects a drop and how it may be applied to droplet control in future microfluidic devices. To aid the discussion, this study can be separated into two phases: (1) the effect of bubble rupture within a drop on a horizontal superhydrophobic surface, and (2) the effect of bubble rupture within a drop on an arbitrary hydrophobic incline. For phase 1, because a superhydrophobic surface has an extremely high contact angle and abhors water (i.e., it has a low adhesion energy),13,16−19 most of the released energy will therefore be constrained within the drop. This allows us to directly observe the physical effect of the bubble rupture process on a drop prior to introducing other variables such as surface inclination into the system. In phase 2, a surface inclination will be introduced, and the process through which the rupture of an encapsulated bubble affects the sliding mechanics of a drop will be investigated. While the extremely low sliding angles of water drops on superhydrophobic surfaces may prove useful in future applications, there are currently several challenges faced regarding the introduction of bubbles on a superhydrophobic surface.20,21 For this reason, while a horizontal superhydrophobic surface is useful for the observation of the bubble rupture process in phase 1, phase 2 will use a hydrophobic surface to investigate the process when a surface inclination is introduced. The rupture of bubbles on the free surface of a pool of liquid is a widely studied topic,22−28 and the concept is also relatively easy to visualize. It is well understood that the rupture process results in the formation of a jet.22−27 Under certain conditions, this jet may separate into droplets.22,24,27 The collapse of the jet then produces capillary waves that radiate across the free surface. With a large volume of liquid, a jet is easily formed from the extensive liquid available. However, the effect of a limited liquid volume on the rupture process is currently unknown and is a common feature in all phases of this work. Note that for a liquid pool, the resulting capillary waves are able to radiate across the liquid−air interface until they encounter an obstacle. For a drop, the propagation length prior to this occurring is several orders of magnitude smaller. If we consider a spherical drop in air, we can see that the liquid−air interface is a closed loop. A wave that radiates out from any point on the sphere will eventually converge and interact at the antipodal point. There are various complex oscillation modes possible for a drop, some of which have previously been studied.29−35 A previous study also demonstrated that the coalescence of condensation drops on superhydrophobic surfaces results in out-of-plane motion.36,37 Various other studies have also been conducted regarding the bouncing dynamics of drops on superhydrophobic surfaces.16−18 In addition to oscillation modes and rebound dynamics, another study showed that the impact of a water droplet on a superhydrophobic surface at relatively high speeds can also result in the formation of a small air cavity, which produces a liquid jet upon its collapse.19 These prior studies in related areas suggest that the study of the rupture of an encapsulated bubble within a drop may provide us with interesting results, which may lead to possible future applications in microfluidics. In the work presented here, we are interested in systems that are initially static, with the rupture of a bubble causing a dynamic reaction in the system.

⎛ 3V ⎞2/3 Epotential = γ 4π ⎜ bubble ⎟ + γ(A(V + Vbubble) − A(V )) ⎝ 4π ⎠

(1)

where γ is the surface tension of the liquid, and A is the liquid− air surface area of a sessile drop at a given volume. A more comprehensive formulation of eq 1 is provided as Supporting Information. Now that we have an estimate of the potential energy of the system, we can consider what happens upon the release of that energy, that is, when the bubble ruptures. There are three major components that require energy: (i) translation of the liquid mass, (ii) overcoming the adhesion energy of the substrate, and (iii) drop deformation, which will result in the oscillation of the drop’s liquid−air interface as it attempts to return to an equilibrium. Over time, this oscillation is damped out due to viscous damping.38 First, we will consider the energy component associated with translating a drop. We will assume that the majority of translation occurs vertically. It should also be noted that this component corresponds only to the energy required to translate the center of mass and is different from the energy required to deform the drop (which will be addressed later). The translation can be considered from the point of view of the gravitational potential energy at the maximum height of the center of mass: U = mg Δh

(2)

where m is the mass of the liquid, g is gravitational acceleration, and Δh is the maximum change in height of the center of mass. Next, the energy required to overcome adhesion to the surface can be estimated using the Young−Dupré equation:39,40 W = γ(1 + cos θ )A wetted

(3)

where γ is the surface tension of the liquid, θ is the contact angle of the drop, and Awetted is the wetted liquid−solid interfacial area of the drop. The Young−Dupré equation typically uses the Young contact angle and calculates the energy difference when liquid−air and solid−air interfaces are formed from the liquid−solid interface of a drop. Therefore, the equation only applies when the entire drop detaches from the surface, and does not take into consideration dynamic situations or shape changes. While it is a reasonable approximation for superhydrophobic surfaces,40 it will under17657

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The eventual rupture of thin films is known to occur via drainage of liquid from the film 51 and spontaneous fluctuations,49,50 while the specific flow characteristic of this drainage is a function of the system properties.28

estimate the actual energy required for surfaces with a higher contact angle hysteresis.41 For such cases, it will be more suitable to use the receding contact angle as this is the angle that is expected just before the detachment of a drop from a substrate. Therefore, the experimental variables required to calculate the adhesion energy using eq 3 are θR, γ, and the maximum value of Awetted. Finally, the last major component of energy expenditure is the energy required to deform the drop (which is subsequently damped over time). The resulting oscillation pattern may be extremely complex, making it hard to quantify or even estimate analytically. However, knowing the other components of the energy balance will allow us to estimate the magnitude of this particular component. As mentioned previously, it is also worthy to note that with subsequent deformations and oscillations, it is possible for energy loss to occur via dissipation into the solid substrate as well as through viscous damping.38 Phase 2: Encapsulated Bubble within a Drop on an Inclined Hydrophobic Surface. The ideal equilibrium of a liquid drop on a horizontal surface is governed by a balance of the surface tensions at the triple-phase interface where the liquid, solid, and vapor phases meet. The balance, which is attributed to Young, is expressed as γLS + γLV cos θo = γSV, where θo is the equilibrium contact angle, and γLS, γLV, and γSV are the interfacial tensions between the liquid−solid, liquid− vapor, and solid−vapor interfaces, respectively. This balance does not consider the presence of contact angle hysteresis, whereby a range of contact angles are observed instead of only one equilibrium contact angle. It is widely accepted that contact angle hysteresis arises from factors such as surface roughness and chemical heterogeneity.42 The existence of contact angle hysteresis is readily apparent for drops placed on an inclined surface (Figure 1a). For a surface that is inclined at an angle α to the horizontal, the component of gravitational force acting to pull the drop down the incline can be represented as FG = ρVg sin α, where ρ is the density of the liquid, V is the volume, g is the gravitational acceleration, and α is the angle of the incline. The retention force (FR) of the drop that prevents it from sliding is related to the drop width (w), and the forward and rear contact angles (θforward and θrear, respectively).43,44 This can be approximated as FR ≈ wγLV(cos θrear − cos θforward). We can see from this that the retention force is caused by the existence of contact angle hysteresis. Therefore, systems with extremely low contact angle hysteresis (such as water on superhydrophobic surfaces) exhibit very little resistance to the motion of drops. Some other factors that may affect the retention force have also been explored. Examples of these are surface deformation due to the unsatisfied normal component of Young’s equation,45,46 the presence of microbubbles near the receding contact line,47 the presence of an encapsulated bubble at the receding contact line,15 and interference with the receding contact line by other means.48 As mentioned previously, this Article is concerned with the rupture of an encapsulated bubble of comparable size with the drop (Figure 1b; the relevant volumes are in the tens of microliters). An encapsulated bubble like this is able to deform the liquid−air interface of the drop, thereby affecting the receding angle and increasing the incline required for sliding to occur.15 Even if a deliberate attempt is not made to rupture the bubble mechanically, it is reasonable to expect it to rupture eventually due to the natural thinning of the liquid film separating the bubble from the external atmosphere.28,49−51

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METHODS

The superhydrophobic sample used for experiments was fabricated using an electroless galvanic deposition process.52,53 Details regarding the sample preparation process, a scanning electron microscope image of the resulting micro/nanostructures, and details regarding the experimental setup are available as Supporting Information. The liquids used on the superhydrophobic surface in phase 1 were Milli-Q water (θA = 167°; θR = 158°; γ = 0.072 N/m) and a 0.096 mM solution of the surfactant TX-100 in Milli-Q water (θA = 161°; θR = 41°; γ = 0.050 N/m, measured using the drop shape method;54 critical micelle concentration = 0.24 mM). While water exhibited a Cassie− Baxter state on the superhydrophobic surface, the inclusion of a surfactant resulted in a pinned Wenzel state55 (as can be seen by the dramatic reduction in the receding contact angle). Any timedependent adsorption effect of the surfactant during the rupture process was assumed to be negligible for the short time scales involved. This behavior has previously been alluded to in the literature16 and was observed here qualitatively, whereby carefully deposited drops of surfactant solution were pinned while falling drops bounced off the surface. As the rupture process occurs on even shorter time-scales, the assumption should be valid. For phase 2, the hydrophobic sample used for experiments was polytetrafluoroethylene (PTFE) printed on glass, and the liquid used was Milli-Q water (θA = 120°; θR = 34°). A fixed surface region on which a single drop was placed on each time was selected to minimize surface roughness and inhomogeneity factors. The surface spot was dried with compressed inert gas before each drop was placed. Dust and minute particle contaminants were removed from the surface spot by tape stripping (3M No. 810). This was observed to remove particles as small as 15 μm. The surface cleaning method was carefully ensured to leave no residue. Using sessile drop contact angle measurements, the surface properties were observed to be unchanged. For each phase of the study, the relevant sample was attached to a purpose built rotation stage that allowed the surface inclination to be recorded (or controlled to be horizontal in the case of phase 1). Images and videos were captured from the side to verify the surface inclination via image analysis and to perform additional measurements. Phase 1: Encapsulated Bubble within a Drop on a Horizontal Superhydrophobic Surface. An Eppendorf pipet with a tip diameter of 0.3 mm was used to deposit liquid drops of 10 μL on the surface. Following this, the same pipet was used to inject a 10 μL bubble into the drop. After injection, the pipet was removed vertically from the drop. The system was then allowed to proceed naturally, allowing sufficient time for the entire system to stabilize before rupture of the thin film was observed. Therefore, all subsequently observed behavior can be directly attributed to the rupture of the encapsulated bubble alone. The ensuing process was imaged at 1000 frames per second using a high speed camera (Fastec Imaging Troubleshooter). For each frame, the centroid of the drop was calculated by weighting each pixel corresponding to the drop equally. This is equivalent to assuming that each captured frame is an axisymmetric slice of the drop. This calculation was only performed for frames where no cavity is obscured by the outer region of the drop. An incalculable concave shape was only observed for a very short period of time after the rupture of the bubble. Phase 2: Encapsulated Bubble within a Drop on an Inclined Hydrophobic Surface. Drops of various volumes between 48 and 100 μL were dispensed using an Eppendorf 10−100 μL pipet in steps of 4 μL (i.e., 44 μL, 48 μL, etc.). The volume of the encapsulated bubble was chosen to be 10 μL, and bubble deposition was accomplished using an Eppendorf 0.5−10 μL pipet, which penetrated the droplet to leave it as close to the substrate as possible. The bubble volume was selected out of experimental considerations: larger 17658

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volumes deform the drop even on a horizontal incline and have a higher likelihood of rupturing early, while volumes that are too low may not produce effects that can be reliable observed. Similarly, the liquid volume range was also selected out of experimental considerations. While the liquid and air volume of 10 μL each used in phase 1 is useful in visualizing the effect of bubble rupture and informing us of the direction to take in phase 2, the same practical considerations mentioned previously (a high bubble volume and a low liquid volume will result in a more unstable system) necessitate the use of larger liquid volumes in the second phase of this study. It is also important to note that the time required for a bubble in phase 2 to rupture naturally is longer than that for the system in phase 1. In the first phase, the bubble is freely buoyant and “floats” at the apex of the encapsulating drop, while in this phase, the bubble is attached to the solid surface (minimizing the force pressing against the thin film between the bubble and the external atmosphere).15 This is not possible to accomplish on a superhydrophobic surface in the Cassie−Baxter state due to a previously identified bursting effect.20,21 The pipet tips were chosen to be as small as practicable to minimize disturbance to the droplet width and contact line. The experiment continued only when it was ascertained that the air bubble was attached stably to the PTFE substrate. The stage was then rotated to a selected incline below the critical sliding incline of a drop without a bubble. For a first attempt, this incline was 1° below the critical sliding incline of a standard drop (i.e., a drop without an encapsulated bubble). After rotation, the drop with a bubble was then allowed to rest at this incline until bubble rupture occurred naturally.28,49−51 This happened within time-frames that were short enough (tens of seconds at most) to ignore the effect of evaporation on the overall drop. Two situations were then possible: the drop could slide due to the rupture of the bubble, or it could remain stable and static at a new equilibrium. In the case of sliding induced by the rupture of the bubble, the present incline was then reduced by 1° and the process was repeated. Conversely, if the drop was stable, the incline was increased by 1° and the process was repeated. The lowest incline at which sliding due to bubble rupture was reliably observed (five or more occurrences) was then recorded. This provides a lower bound for the incline at which bubble rupture is able to induce the detachment of a drop. To observe the drop detachment process in better detail, a highspeed camera (Fastec Imaging Troubleshooter) was used to image the rupture process and the subsequent motion of drops at 1000 frames per second. Drops with a constant volume at inclines just above and below the lower bound (where bubble rupture caused drop detachment) were observed to compare and contrast the difference between a detaching drop and one that stabilized at a new equilibrium. Image analysis was then performed on the video frames to determine the front contact angle of the drops and the movement of the advancing triple-phase contact line over time.

Figure 2. (a)−(f) Selected frames depicting the process after bubble rupture for a water drop on a superhydrophobic surface. The scale bars represent 0.5 mm, and the red circles indicate the centroid location. (g) Vertical and (h) horizontal location of the centroid over time. The centroid location is defined as 0 at t = 3 ms when the liquid is no longer obscured by the presence of the bubble.

energy with pure water is extremely low, the triple-phase interface recedes when the capillary wave is reflected. The contact line of the drop eventually meets, resulting in the complete detachment of the drop from the surface. At this point, it lifts off completely from the surface while the liquid− air interface exhibits a complex oscillation pattern. The Bond number of the system (Bo = (ΔρgL2)/γ, where L is the contact radius) can be calculated to be in the order of 1 × 10−1, indicating that surface tension is dominant. Figure 2g shows the vertical centroid location of the drop over time. The first major peak that occurs between 3 and 46 ms can be seen to be a function of both a general rise and fall of the drop and a complex oscillation pattern (which produces its own peaks and troughs within the overarching peak). After the first impact with the surface, most of the complex oscillation is damped out, and the pattern of the vertical centroid location over time starts to resemble damped harmonic motion. The horizontal location of the centroid over time is shown in Figure 2h. It is apparent that the drop slowly drifts to one side, with only very small oscillations present. The drift is likely due to the bubble not rupturing at the exact apex of the drop, resulting in a slight asymmetry in the ensuing process. In contrast to pure water, Figure 3a−f shows a series of selected frames depicting the process after rupture for a 0.096 mM solution of TX-100. The first four images that cover the rupture process, resulting capillary wave, and jet formation are similar to those observed in Figure 2a−f. However, differences occur when the capillary wave encounters the solid surface. In

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RESULTS AND DISCUSSION Phase 1: Encapsulated Bubble within a Drop on a Horizontal Superhydrophobic Surface. Shortly following the introduction of the bubble, the apex of the drop-bubble configuration thins naturally,28,49−51 eventually resulting in the rupture and release of stored surface energy. The eventual rupture of a thin film occurs via the drainage of liquid from the film. The specific flow characteristic of this drainage is a function of the properties of the system and the presence of a surfactant.28 Figure 2a−f shows a series of selected frames depicting the process after bubble rupture for a representative drop of Milli-Q water. The released surface energy rapidly produces a capillary wave as surface tension attempts to minimize the surface area. While the capillary wave travels toward the base of the drop, a jet begins to form at the apex of the drop, eventually jetting out of the field of view. The capillary wave encounters the solid surface and reflects back. Because the surface is superhydrophobic and the adhesion 17659

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Having observed the physical behavior of the bubble rupture process, we can now make estimates regarding the energy balance of the system using the equations presented earlier. We can generate theoretical drop profiles by solving the Young− Laplace equation for the measured contact angles and their relevant surface tensions.54 Further details and the computed profiles are provided as Supporting Information. Having computed the sessile drop profiles, it is then simple enough to calculate the surface area for V and Vbubble both equal to 10 μL. Substituting the relevant values into eq 1, we can estimate the potential energy of a pure water drop and a drop of TX-100 solution to be 2.5 × 10−6 and 1.7 × 10−6 J, respectively. There is a difference of ∼30% in the stored energy even with identical bubble and liquid volumes because the surface tension of a 0.096 mM TX-100 solution (measured as 0.050 N/m using the drop shape method) is lower than that of pure water (0.072 N/ m). As for the energy output distribution, we will first consider the energy required to translate the drops vertically. By tracking the centroid over time, the maximum change in height of the water drop was found to be 1.4 mm, while that of a TX-100 drop was found to be 0.7 mm. This difference is due to the fact that the water drop was able to detach completely from the surface, while a TX-100 drop was pinned down on the surface. In light of this, we can also consider the energy required to completely separate a drop from the solid surface using eq 3. The adhesion energy of a water drop is ∼1% of the potential energy (3.4 × 10−8 J), while it is ∼30% for a drop of TX-100 solution (4.7 × 10−7 J). This is a substantial difference and is due to the extremely low contact angle hysteresis of water on a superhydrophobic surface, whereas the contact angle hysteresis is many times larger when a surfactant is introduced.55,56 However, it is worthy to note that there is sufficient potential energy available for a drop of TX-100 solution to separate from the surface. The reason that this does not happen is because the majority of the potential energy is consumed in deforming the drop, as can be seen in the surface flow visible as capillary waves. Furthermore, it must be noted that while the drop does not detach from the surface, Figure 3 shows that there is still motion of the contact line present. This depinning of the contact line will result in the consumption of energy even though complete detachment does not occur.57 If we consider a water drop, the energy converted into gravitational energy and that required to overcome the adhesion energy total to ∼6% of the total potential energy. This is an extremely small proportion of the total energy output, suggesting that ∼94% of the energy was consumed in the deformation of the drop and associated viscous damping. With this in mind, we should also consider how this significant energy component was expended. In Figures 2 and 3, we can observe the formation of a large jet after the rupture of the bubble. As previously mentioned, the formation of this jet has been widely studied in the context of bubble rupture on a free surface.22−27 The jet then breaks into droplets, the closest of which are clearly visible. As the top of the jet extends outside the field of view, it is not possible to see its maximum height. However, on occasions where the bubble rupture process is sufficiently symmetric, ejected droplets can be observed to return into the camera’s field of view (see the Supporting Information). The return velocity of the last six ejected droplets for one such case is shown in Figure 4a. As the measured velocities are an order of magnitude smaller than the terminal velocity for water droplets of similar size in stagnant air,58 the

Figure 3. (a)−(f) Selected frames depicting the process after bubble rupture for a drop of 0.096 mM TX-100 solution on a superhydrophobic surface. The scale bars represent 0.5 mm, and the red circles indicate the centroid location. (g) Vertical and (h) horizontal location of the centroid over time. The centroid location is 0 at t = 3 ms.

this case, the nature of the reflection is strongly affected by the higher contact angle hysteresis of the solution. The contact line retracts a little, but never completely detaches. While the early behavior after bubble rupture is similar to the behavior observed by Noblin et al. for a mobile contact line (Type II),32 the contact line is eventually pinned as energy is damped, and an oscillation is observed that is akin to a partial Type I mode (immobile contact line) as characterized by Noblin et al.32 It is also reasonable to expect that due to the short timescales involved, the surfactant (when present) may not have enough time to completely diffuse to a new contact line. Therefore, for such cases, it is possible that a newly expanded liquid−solid area may initially require less energy to detach than a pre-existing liquid−solid area. Figure 3g shows the vertical centroid location of the main drop of TX-100 solution over time. The maximum height of the centroid is lower than that of a pure water drop. This is a result of the pinned contact line preventing the drop from completely detaching from the surface. Furthermore, as the drop is rapidly pulled back to the surface by surface tension, the oscillation frequency of the centroid location is higher than that of a water drop. The erratic oscillation of the drop is also quickly damped due to the higher oscillation frequency. Figure 3h shows the horizontal location of the centroid over time. As was seen for the water drop, there is a shift to one side. However, as the contact line of the TX-100 solution never completely detaches, damped harmonic motion ensues in the horizontal direction as well as the vertical direction. 17660

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but would immediately rewet the surface instead of completely detaching. For any practical applications, however, such a case (where the drop never detaches from the surface) would be little different from a pinned drop. The observation that the amount of energy released by a rupturing encapsulated bubble is more than enough to cause contact line detachment (and even propel a water drop off a surface with a sufficiently low adhesion energy) is a promising sign for the use of rupturing bubbles in microfluidic drop control. However, the results shown in the first phase of this study suggest that the detachment of a drop due to the rupture of an encapsulated bubble may be more complex than simple detachment due to the lack of a pinning bubble. This allusion therefore directs our investigation in the next phase of this study. Phase 2: Encapsulated Bubble within a Drop on an Inclined Hydrophobic Surface. Figure 5a shows a region

Figure 4. (a) Return velocity of the last six ejected droplets, with droplet 6 being the last. The liquid used was pure water. (b) Normalized wetted area (against t = 0) as a function of time.

dominant force acting on them should be gravitational. The approximately linear nature of the velocity distribution suggests a regular spacing in the maximum height of their origin, consistent with the regular breakup of a jet due to Rayleigh instability. A slight deviation from a linear profile can be seen in the case of droplets 3 and 4 in Figure 4a. As the origin height increases (i.e., as the droplet no. increases), the cross-section of the jet is expected to decrease, resulting in a decreasing droplet size. The terminal velocity decreases with decreasing droplet size,58 suggesting that the relative air drag may be more significant for these droplets. However, the last droplets are expected to be dominated by gravity again as it has previously been shown that they are larger than the preceding jet droplets.23,24 The velocity of the very last droplet was 0.54 m/s, suggesting an origin height of around 18 mm and indicating the extent to which the liquid interface was deformed. In addition to the formation of the jet and ejected droplets, there also appears to be significant motion of the contact line shortly after bubble rupture (Figure 4b). We can determine that the approaching capillary wave first causes the contact line to recede slightly (Figures 2c and 3c) before advancing to a great extent (Figures 2d and 3d) and more than doubling the wetted area of the droplet. It is apparent that the energy used to overcome the adhesion energy and propel the main drop upward is merely a byproduct of the capillary wave directed into the surface (Figure 2c−e). The extremely low contact angle hysteresis and adhesion energy of water on a superhydrophobic surface allow the contact line to easily recede and eventually detach from the surface. However, when the adhesion energy is increased by the addition of a surfactant, there is insufficient energy remaining to force the contact line to completely retract (Figure 3). The majority of the potential energy (∼96% for the surfactant solution) is therefore consumed in the formation of the jet and the oscillation and damping of the drop. Having now observed the process through which a drop is propelled vertically, we can also consider what would occur at the maximum volume that can be propelled by a given bubble size. At this critical volume, the contact line of the drop would converge after the capillary wave reaches the base of the drop,

Figure 5. (a) A region graph that identifies the region within which the rupture of an encapsulated bubble results in the detachment of the drop (red; unstable) and where the drop eventually stabilizes in a new equilibrium (green; stable). The range above the red unstable region slides regardless of the presence of an encapsulated bubble. (b) The decrease in the required sliding angle as a function of drop volume for an encapsulated bubble of 10 μL (which ruptures). The error bars show two standard deviations for both graphs.

graph detailing inclines and volumes at which a drop will either stabilize or detach upon the rupture of an encapsulated bubble. Drops in the green region (stable) will stabilize in a new equilibrium upon the rupture of a bubble, whereas drops in the red region (unstable) will detach and continue sliding. For the purposes of this study, the upper limit in Figure 5a represents the sliding angle of a standard drop without an encapsulated bubble. However, it is important to note that the sliding angle’s upper limit in the unstable region can actually take on higher 17661

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eventually reaching the front contact line. This wave causes the front contact line to momentarily exceed the advancing contact angle, resulting in depinning and movement of the front contact line. However, the drop does not immediately detach when this occurs. Figure 7 shows a graph of the front contact angle and the displacement of the front contact line as a function of the time after bubble rupture. The data points have been connected with a smoothed curve for presentation purposes, and the dotted horizontal line indicates the advancing contact angle (120°). Careful consideration is required due to the complicated nature of this figure. Some key moments are labeled in Figure 7 for the discussion that follows. Immediately after bubble rupture, a capillary wave passes along the surface of the drop, taking a few milliseconds before reaching the front. When it reaches the front, an increase in the front contact angle is then observed (A). The wave requires approximately 1 ms longer to reach the front of the unstable drop (red; ▲) as compared to the stable drop (green; ■) due to the slightly higher incline of the unstable drop and the resulting increase in the length of the drop. After the initial contact of the capillary wave with the front contact line, the wave reflects off the substrate, resulting in a decrease in the front contact angle (B). Following this, a complex wave motion is then observed as the wave interacts with itself after multiple reflections (C). An oscillation in the front contact angle is seen, eventually building up to exceed the advancing contact angle multiple times at around 10−20 ms (D). This results in a relatively large displacement of the front contact line (relative to previous displacements) (F). Still, the unstable drop does not completely detach at 20 ms. The wave instead reflects again, causing a large decrease in the front contact angle and resulting in a brief moment of relative calm at the front contact line (which also happens for the stable drop). The major divergence between the stable and unstable situation occurs at around 23−33 ms when the drop begins to stabilize and the capillary wave heads for the front contact line once again. In the case of an unstable drop, the front contact

values due to the effect of an encapsulated bubble in inhibiting the sliding of a droplet.15 A plot is shown in Figure 5b of the maximum change in the sliding angle caused by rupturing bubbles, as a function of the liquid volume. This is essentially the difference between the upper and lower limits of the sliding angle in the unstable region from Figure 5a, and provides us with a measure of how much the sliding angle is reduced (due to the rupturing of a 10 μL bubble) as a function of the liquid volume. From Figure 5b, we can see that the maximum change in the sliding angle is observed at lower liquid volumes. This may be due to lower drop masses requiring less force to induce movement, and the fact that lower volumes have a shorter liquid−air propagation length, resulting in less damping and energy loss. Figure 6 shows frames from a high-speed video of the bubble rupture and subsequent events. The corresponding videos are

Figure 6. Selected high-speed frames depicting the rupture of an encapsulated bubble and the resulting capillary waves. The liquid volume is 64 μL, the bubble volume is 10 μL, and the incline is 48°. The black horizontal line indicates 2 mm. In this case, the drop eventually stabilized after the front contact line advanced a small distance (0.6 mm).

included as Supporting Information. A capillary wave can be seen passing along the liquid−air interface of the drop,

Figure 7. A graph showing the front contact angle and the displacement of the front contact line as a function of the time after the rupture of an encapsulated bubble. The liquid volume is 64 μL, the bubble volume is 10 μL, and the inclines are 48° (stable) and 49.7° (unstable). The dotted horizontal line indicates the measured advancing contact angle (120°). Momentary breaching of the advancing angle can be seen to cause the front contact line to advance and exhibit a stick−slip motion. 17662

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Langmuir angle slowly increases steadily, eventually exceeding the advancing contact angle (Gu). A displacement in the front contact line is then observed, and the contact angle oscillates at a range above the advancing contact angle while the front contact line continues slipping. This is a runaway process and results in the complete detachment of the drop (Hu). Conversely, the front contact angle of the stable drop also increases, but does not appear to breach the advancing contact angle (Gs). It then continues to oscillate at a range below the advancing contact angle. Because the advancing contact angle is not breached in this case, the location of the front contact line is then stable (Hs). Oscillations in the contact angle at the front contact line continue for some time (hundreds of milliseconds; not shown in Figure 7, but visible in videos available as Supporting Information) but damp out over time. It appears to damp out faster in the unstable case due to the motion of the front contact line. From the results, it is apparent that the rupture of a bubble within a drop is able to cause drop motion below the traditional critical sliding angle. For a constant air volume, the sliding mechanism is more effective at lower liquid volumes due to the lower mass of liquid that has to be compelled to move. An interesting observation in Figure 5b is that even at high liquid volumes of up to 100 μL, a drop can still be coerced to slide before its typical sliding angle. This is likely to be due to the shape change of the drop due to the rupturing bubble and the momentum imparted to the front contact line. Our high speed data show that rather than simple detachment occurring at the rear contact line upon bubble rupture, a capillary wave is in fact produced, which travels across the liquid−air interface of the drop. This wave eventually interacts with itself after multiple reflections and results in complex wave patterns. From Figure 7, it then appears that the front contact line displaces forward when the advancing contact angle is breached. One notable exception to this is the first advance that occurred at around 6 ms. In this case, the contact line appears to advance without the contact angle exceeding the advancing contact angle. However, we believe that this is due to the limitation in the time resolution of the high-speed video. It is possible that this advance occurred at a faster rate than could be captured by our equipment (1000 frames per second). Similarly, although the retreat of the contact line should only occur when the receding contact angle (measured to be 34°) is breached, it appears that our equipment was not sensitive enough to capture the exact event. It is likely that the retreat of the contact line occurs on very short time scales, after which the contact angle would then take on a larger value (due to the shift in the contact position). This stick−slip motion has been previously observed in areas such vibrated sessile drops32 and the receding contact line of evaporating drops.59 Despite the limitation in time resolution, we are able to draw the conclusion from our results that the sliding of a drop caused by from bubble rupture occurs not only due to a disruption to the rear contact line, but also from a series of complex waves, which cause the front contact line of the drop to periodically advance and recede. The final fate of the drop is then dependent on whether the new equilibrium shape of the drop causes the front contact angle to exceed the advancing angle. If so, the drop then continues sliding; if not, it settles comfortably at a new equilibrium.

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CONCLUSION

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ASSOCIATED CONTENT

Article

We have presented here an analysis of the effect of the rupture of a bubble encapsulated in a drop of similar size. When the system is comprised of water on a horizontal superhydrophobic surface, the reflected energy of the resulting capillary wave from the surface is sufficient to propel the entire drop off the surface. From an energy balance, we determined that only a small proportion of the potential energy stored as surface energy is converted to the energy required to overcome the adhesion to the surface and propel the main drop mass. Hence, when a surfactant (TX-100) is introduced, the adhesion to the surface is then too large to overcome, with the drop remaining pinned to the surface and experiencing a damped oscillation pattern. Similar to bubble rupture on the free surface of a liquid pool, a large jet is formed, which consumes a large proportion of the potential energy. For drops on a hydrophobic incline, the rupture of an encapsulated bubble was found to cause premature sliding. The rupture of a 10 μL bubble within a 48 μL drop was able to reduce the sliding angle by almost 20°. Even higher volumes such as 100 μL experienced a decrease in the sliding angle of around 7°. The process behind how the rupture of a bubble causes the detachment of a drop was found to be due to the complex motion of capillary waves. Upon the rupture of a bubble, a capillary wave spreads out along the liquid−air interface of the drop, eventually reaching the front contact line. When the drop volume is near the threshold between sliding and eventual stability, the first encounter of the capillary wave with the front contact line causes it to advance, but does not immediately cause the drop to slide. Instead, the capillary wave reflects off the solid surface, and after a complex interaction with waves reflected from the rear of the drop, the liquid within the drop eventually settles within the front and the drop is detached from the rear. If the incline of the surface is below the threshold, the drop eventually settles into a new equilibrium, with the front contact line advancing some distance due to the rupture of the bubble, but not enough to cause the sliding of the drop. The results presented here demonstrate that the rupture of an encapsulated bubble within a drop releases stored surface energy that can possibly be utilized for intriguing applications. If the liquid drop experiences a low adhesion to the surface (such as between water and a superhydrophobic surface), the rupturing bubble is able to propel the entire drop off the surface. It may be possible in the future to use this process as a means to transfer droplets vertically between different horizontal planes of a microfluidic device. The ability to selectively cause the sliding of a drop without the use of an external energy source may also prove useful for future droplet control techniques.

* Supporting Information S

Formulation of the energy balance, details regarding surface preparation and the experimental setup, images of the surface micro-/nanostructures, video frames and videos depicting bubble rupture and subsequent events on a horizontal superhydrophobic surface, and videos showing how the rupture of an encapsulated bubble causes either the eventual detachment or the restabilization of a drop on a hydrophobic incline. This material is available free of charge via the Internet at http://pubs.acs.org. 17663

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (W.Y.L.L.); adrian.neild@ monash.edu (A.N.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Portions of this work were made possible by funding support from the Australian Research Council Discovery grant DP0878454 and the Monash University Postgraduate Publication Award.

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