Increased Stability and Size of a Bubble on a Superhydrophobic

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Increased Stability and Size of a Bubble on a Superhydrophobic Surface William Yeong Liang Ling, Gabriel Lu, and Tuck Wah Ng* Laboratory for Optics, Acoustics, and Mechanics, Department of Mechanical & Aerospace Engineering, Monash University, Clayton VIC3800, Australia ABSTRACT: Computational and theoretical models of millimeter-sized bubbles placed on upright hydrophobic and superhydrophobic surfaces are compared with experimental data here. Although the experimental data for a hydrophobic surface corroborated the computational and theoretical data, the case of a superhydrophobic surface showed the bubbles to be able to contain significantly larger volumes than predicted. This is attributed to the greater ability of the bubble contact line to advance compared with its tendency to detach from the surface because of buoyancy. We surmise that a static model therefore describes only an unstable equilibrium for these bubbles, which unless heavily isolated from external influences are more likely to assume a larger stable size.

’ INTRODUCTION From the perspective of the Young-Laplace relation, there are similarities in the manner with which the gravitational and buoyant forces act respectively to dictate the shapes formed for a sessile drop in air and an air bubble attached to an inverted surface in water. The same applies for a suspended drop on an inverted surface and an air bubble in water (Figure 1). Interesting situations arise when dealing with surfaces at the extreme range of contact angles. A drop placed on a superhydrophilic surface, for instance, will spread out into a thin film in which the dynamics have been extensively studied.1-3 For inverted superhydrophobic surfaces, a recent study has reported the tendency of an air bubble to collapse as buoyancy brings it to the surface.4 This behavior is attributed to the violation of stability conditions of the wetting film—the thin layer of liquid that separates the solid surface from the air bubble—when interacting with air pockets entrained within the nanostructured surface. Using the equation for capillaries with a height-dependent cross section, we can approximate the Laplace pressure at the three-phase contact line using4,5 Pg - Po ¼ FgH -

2γ cosðφ þ RÞ R þ h tan R

ð1Þ

where Pg and Po are pressures of the captive air pockets and of the atmosphere, respectively, F is the density of water, g is the gravitational acceleration, H is the depth below the water line, γ is the liquid-gas interface surface tension, φ is the equilibrium contact angle, and R, R, and h are the geometries depicted in Figure 2. From the relation, the captive air pocket pressure will exceed the atmospheric pressure in the bubble, causing the air pockets to coalesce, thus leading to gas bridges that form and r 2011 American Chemical Society

spread, eventually resulting in the collapse of the air bubble. This positive pressure differential is increased when the length scale of R is decreased. Such a spontaneous air-bursting behavior has positive implications for the cleaning of superhydrophobic surfaces. An important question to emerge from this is whether the coalescence forces resulting from the air pockets merging with the bubble are able to sustain the spreading and thus eventual bursting or whether the process is crucially dependent on the buoyant force pushing the bubble toward the inverted surface. We believe that some insight into this may be attained by having the surface placed upright such that buoyancy is directed away from it. For upright surfaces in general, solving the YoungLaplace equation via a geometric approach will produce solutions for the bubble shape under the conditions of various contact angles to allow the determination of their detachment criterion.6,7 We have found that in reality there are additional subtleties in this process for superhydrophobic surfaces.

’ METHODS Sample Preparation. Superhydrophobic surfaces were created using an electroless galvanic deposition process.8-10 This process allowed the rough tuning of wettability depending on the variables in the preparation process. In this experiment, two distinct surfaces were prepared using similar processes but with different variables. Polished copper surfaces were first cleaned with absolute ethanol and allowed to dry. They were then immersed in a solution of aqueous AgNO3. The concentration of the solution for sample 1 was 12.38 mM, and the Received: December 16, 2010 Revised: February 1, 2011 Published: March 01, 2011 3233

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Figure 1. Similarity between (a) a suspended drop on an inverted surface with a contact angle of θ° and (b) an upright bubble in liquid with a contact angle of 180-θ°.

Figure 3. Images of the two surfaces obtained using a scanning electron microscope (FEI Quanta 3D FEG, accelerating voltage = 10 kV, working distance = 9.6 mm). (a, c) Sample 1 (hydrophobic). (b, d) Sample 2 (superhydrophobic). The surface roughness exists at various scale levels and presents as a dendritic fractal pattern.

Figure 2. Schematic of the wetting film between an air bubble and air pockets trapped on a superhydrophobic surface. immersion time was 2 min. For sample 2, the concentration was 24.75 mM and the immersion time was 1 min. After this, the respective surfaces were cleaned with absolute ethanol and dried with compressed inert gas. They were subsequently immersed in a 1 mM solution of surface modifier CF3(CF2)7CH2CH2SH in absolute ethanol. The samples were then thoroughly rinsed with a great deal of distilled water, followed by rinsing with absolute ethanol. They were then allowed to air dry. The sessile drop contact angles were measured to be 132° (standard deviation σ = 3.5°) and 158° (σ = 0.80°) on samples 1 and 2, respectively. Sample 1 was hydrophobic, and sample 2 was found to be superhydrophobic with a low contact angle hysteresis, allowing droplets to roll off the surface easily. Images of the samples obtained using a scanning electron microscope (FEI Quanta 3D FEG) are shown in Figure 3. Figure 3a,c shows the surface of sample 1 (hydrophobic), and Figure 3b,d shows sample 2 (superhydrophobic). It can be seen that the deposition process results in the growth of dendritic fractal structures that increase the roughness of the surfaces, thereby affecting their wettability. Although the hydrophobic sample does exhibit roughness, the growth is far more prominent on the superhydrophobic sample. Computational. Surface Evolver software was used to compute the predicted profile and size of inverted droplets.11,12 It does this using an energy-minimization method that evolves a surface down the energy gradient. The assumption made in the computation was that an inverted static water drop on a surface should be identical to an immersed bubble on another surface with an opposing contact angle (as described in Figure 1). For example, the static profile of a hanging pendant drop on a surface with a contact angle of 10° was assumed to be identical to the profile of an immersed bubble on a surface with a contact angle of 170°. This assumption was verified by comparing results with previously developed models.6,7 For consistency, all contact angles mentioned here are measured through the liquid medium as depicted in Figure 1. Experimental. The samples were immersed one at a time in a container filled with distilled water. The water depth to the surface of the

sample was 1.4 ( 0.1 cm. Two digital cameras (Canon SX1 IS 10.0 MP and Nikon D60 10.2 MP) were set up in front of and above the container to capture both the side and top profiles. A pipet was used to attach a 20 μL air bubble carefully onto the surface of the sample. The bubble volume was increased in steps of 20 μL, and images were taken after each increase in volume. The volume of air was slowly increased until detachment of the bubble occurred. The images were later studied to measure the diameter of the bubbles (as seen from above) for comparison with the computational and theoretical models. This process was repeated five times for each surface. Furthermore, 10 bubbles were sequentially recorded on sample 2 (superhydrophobic) with a volume of 275 μL. From previous results, this was found to be within the approximate volume range at which the bubbles exhibited their maximum diameter on the sample.

’ RESULTS AND ANALYSIS Figure 4 shows qualitative comparisons between the side profiles of immersed bubbles as determined experimentally with that computed using Surface Evolver. Figure 4a,b shows a 140 μL bubble with an equilibrium bubble contact angle of 120° (sample 1), and Figure 4c,d show a 220 μL bubble with a contact angle of 170° (sample 2). It can be seen that Surface Evolver produces a close estimate of the bubble profile. Figure 5 shows a plot of the maximum diameter of an immersed bubble as a function of the equilibrium contact angle. The computational results correlate well with the theoretical model developed by Lee et al.6,7 The vertical line in the Figure corresponds to a contact angle of 170°, whereas the horizontal line marks the average diameter of a 275 μL bubble. The significance of these values will be further elaborated on later. Figure 6a provides a plot of the average bubble diameter as a function of bubble volume for sample 1. The data terminates at the point of bubble detachment from the surface, and the error bars show two standard deviations derived from the data. It can be seen from this that the computational results also compare well quantitatively with experimental results for a hydrophobic 3234

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Figure 4. Side profiles of bubbles with a volume of 140 μL and a contact angle of 120° (a) as observed in reality and (b) as computed. Side profiles of bubbles with a volume of 220 μL with a contact angle of 170° (c) as observed in reality and (d) as computed.

Figure 6. Comparison between experimental and computational results of the change in diameter of bubbles as a function of volume for (a) sample 1 (hydrophobic) and (b) sample 2 (superhydrophobic). The error bars show two standard deviations above and below the mean.

Figure 5. Comparison of the relationship between the maximum diameter and contact angle as computed using Surface Evolver and theoretical solutions by Lee et al.6 The solid horizontal line shows the average diameter of 275 μL bubbles on sample 2 (superhydrophobic), and the dashed horizontal lines show three standard deviations above and below the mean. The dashed vertical line indicates the average bubble contact angle (170° with σ = 1.4°) of the measured bubbles.

surface with an equilibrium bubble contact angle of 124°. However, there is a strong departure if we study a similar plot for sample 2 in Figure 6b (with the error bars also depicting two standard deviations). The contact angle of the bubble was experimentally measured to be 170° (σ = 1.4°). The solid line in the Figure shows the computed results for a contact angle of 170°. In this case, it can be seen that the computational results grossly underestimate the stability and size of the immersed bubble. In fact, the solution for the extreme limit of a contact angle of 180° is also shown in Figure 6b using a dashed line. It is obvious from this that the experimental result pertaining to bubble size has exceeded the limit imposed by the theory. Hence, it addresses any suspicion that this may have been caused by

limitations in the accuracy of the contact angle measurement method. Let us refer back to Figure 5, where the solid horizontal line depicts the average diameter of a 275 μL bubble on superhydrophobic sample 2. This volume is in the approximate region in which the maximum diameter occurs. For the sake of conveniently providing a description, it will be referred to as the maximum diameter. The dotted horizontal lines show three standard deviations above and below the average maximum diameter. The dotted vertical line shows the average bubble contact angle of sample 2. Again, it can be seen from this that the maximum diameter observed in the experiment was far in excess of that predicted by both the computational model and previous theoretical models.

’ DISCUSSION The computational results have been verified against a theoretical model and were found to correspond well with the experimental results for a hydrophobic surface. In the case of a superhydrophobic surface, however, we found that the immersed bubbles consistently demonstrated a higher stability (ability to sustain larger diameters and volumes) than that predicted by previous models. As was seen in Figure 5, the maximum diameter was beyond three standard deviations above the maximum diameter 3235

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Langmuir predicted for a theoretical contact angle of 180°. With this, we can eliminate the possibility of the results being caused by uncertainties in the contact angle measurement. The process was repeated with several other superhydrophobic samples prepared in a similar fashion, with the same result observed each time. This led us to believe that there is some other factor operating to increase the stability of immersed bubbles on superhydrophobic surfaces. A possible explanation under a static model would be the volume in the smaller immersed bubbles being drawn into the larger bubble via the known convective Ostwald ripening effect.13 This happens when a larger bubble spontaneously absorbs smaller bubbles on the surface because of the difference in their Laplace pressure. However, the volume of air trapped on the surface (on the order of nanoliters) is negligible in comparison to the volume of the bubble used here (on the order of microliters). A starting point to account for this seemingly divergent behavior is to take into account that the computational results and theoretical models assume a static situation in their formulation, whereas such a state of equilibrium in reality is unstable in the context of a superhydrophobic surface because of its propensity to form air bridges at the three-phase contact line. These air bridges manifest in the contact line being able to support only low levels of hysteresis for the contact angle, where minor external forces can easily cause the critical receding angle of water to be breached. These forces can arise from factors such as vibration from the environment, the expansion of the bubble interface due to the increase in volume, and changes in the force balance from pipet interactions. Hence, although the advance in the outward direction is aided by the presence of trapped air on the superhydrophobic surface, the retreat of the contact line is not similarly aided; owing to the nonwetting characteristics of superhydrophobic materials, the interfacial area within the deposited bubble is devoid of “trapped water”. This results in a situation whereby once the contact line has advanced it becomes more difficult to rewet the air-filled area to pull the contact line in the reverse direction. Overall, one finds a directional ratcheting of the contact line outward with the extended contact line and the constantly restored original contact angle balancing any air volume increase. Another essential consideration in the case of an upright surface is that contact line advancement is fraught with the possibility that the bubble might detach from the surface altogether because of the action of buoyancy. At some stage, the ability of the bubble to detach overwhelms the ability of the contact line to advance, thereby imposing a seemingly static limit to bubble growth. This can be seen in Figure 6a,b, where expansion is rapid at low volumes when the buoyancy force of the bubble is small in comparison to the retention force. As the volume increases, the expansion slows, eventually resulting in the buoyancy force exceeding the retention force, thereby causing the detachment of the bubble from the surface. On a side note, the tendency of a micrometer-sized bubble to spread out over a superhydrophobic surface also limits its ability to be used as a means to pin droplets on an incline via a recently reported pinning method that disrupts the back contact line.14 This mechanism appears not to be operational when the bubble is introduced on an upright hydrophobic surface. The ability of spontaneous microbubbles to form on hydrophobic surfaces such as poly(tetrafluoroethylene) (PTFE)15,16 is proven, and despite initial reservations, the presence of nanobubbles has been confirmed using atomic force microscopy (AFM).17,18

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Because of the small length scales of these bubbles, their pressures will be higher than for the bubble that is introduced and should thus result in coalescence from mechanical perturbations. Nevertheless, movement of the contact line on a hydrophobic surface requires more energy than on a superhydrophobic surface. This is largely due to the lesser ability of a hydrophobic surface to trap air as compared to that of a superhydrophobic surface. This manifests itself as a larger contact angle hysteresis. Because of the higher hysteresis on hydrophobic surfaces, the receding angle of water can usually be less than 90°. Because this angle must be breached for the bubble to expand, the nature of the bubble shape when this happens results in a greater likelihood of bubble necking occurring at volumes close to the maximum sustainable volume. This ultimately results in the detachment of the bubble from the surface as opposed to contact line advancement.7,13 Consequently, one finds a much closer adherence to the theoretical and computational simulation results. Although the data here cannot conclusively establish whether the coalescence forces resulting from the air pockets merging with the bubble are able to sustain the spreading and result in eventual bursting or whether the process is crucially dependent on the buoyant force pushing the bubble toward the inverted superhydrophobic surface, it hints at the latter being operational. Our proposed elucidation of the imposed bubble behavior on an upright superhydrophobic surface has an avenue to allow the bubble size to correspond to that dictated by the computational and theoretical models. This will require the bubble to be introduced extremely gently with no external vibration and no interference at the interface or the contact line. As one would expect, this will be extremely difficult to accomplish in practice.

’ CONCLUSIONS We presented here computational and experimental results of the profile and diameter of bubbles on upright hydrophobic and superhydrophobic surfaces. The computational results were found to correspond well with previous theoretical solutions. Although the experimental results for the hydrophobic surface corresponded well with computational results, the measured diameters for the superhydrophobic surface were found to be in excess of computational and theoretical solutions. This indicates that current solutions underestimate the stability of bubbles on superhydrophobic surfaces. We attribute this to the greater ease that a contact line has in advancing compared to retreating under the action of minor external forces on a superhydrophobic surface. From this understanding, we can infer that a bubble may adhere to the predictions of the computational and theoretical models only if it is produced gently with no interference at the interface and while being heavily isolated from external influences. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Portions of this work were made possible by funding support from Australian Research Council Discovery grant DP0878454 and the Monash ESG scheme. Preliminary discussions with Dr. Adrian Neild are appreciated. We also thank Dr. Jing Fu for his help in obtaining the SEM images. 3236

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