pubs.acs.org/Langmuir © 2009 American Chemical Society
Underwater Sustainability of the “Cassie” State of Wetting Musuvathi S. Bobji,* S. Vijay Kumar, Ashish Asthana, and Raghuraman N. Govardhan Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India Received May 1, 2009. Revised Manuscript Received August 26, 2009 A rough hydrophobic surface when immersed in water can result in a “Cassie” state of wetting in which the water is in contact with both the solid surface and the entrapped air. The sustainability of the entrapped air on such surfaces is important for underwater applications such as reduction of flow resistance in microchannels and drag reduction of submerged bodies such as hydrofoils. We utilize an optical technique based on total internal reflection of light at the water-air interface to quantify the spatial distribution of trapped air on such a surface and its variation with immersion time. With this technique, we evaluate the sustainability of the Cassie state on hydrophobic surfaces with four different kinds of textures. The textures studied are regular arrays of pillars, ridges, and holes that were created in silicon by a wet etching technique, and also a texture of random craters that was obtained through electrodischarge machining of aluminum. These surfaces were rendered hydrophobic with a self-assembled layer of fluorooctyl trichlorosilane. Depending on the texture, the size and shape of the trapped air pockets were found to vary. However, irrespective of the texture, both the size and the number of air pockets were found to decrease with time gradually and eventually disappear, suggesting that the sustainability of the “Cassie” state is finite for all the microstructures studied. This is possibly due to diffusion of air from the trapped air pockets into the water. The time scale for disappearance of air pockets was found to depend on the kind of microstructure and the hydrostatic pressure at the water-air interface. For the surface with a regular array of pillars, the air pockets were found to be in the form of a thin layer perched on top of the pillars with a large lateral extent compared to the spacing between pillars. For other surfaces studied, the air pockets are smaller and are of the same order as the characteristic length scale of the texture. Measurements for the surface with holes indicate that the time for air-pocket disappearance reduces as the hydrostatic pressure is increased.
Introduction Superhydrophobic surfaces have been realized by controlling surface energy and surface roughness.1-6 Superhydrophobic properties such as contact angles greater than 150° and high drop mobility result from the Cassie state of wetting.7 In the Cassie state, a water drop is in contact with only a fraction of the solid surface (φs) at the summits of the rough surface, resulting in a composite interface.2 Over the remaining fraction (1 - φs) of the interface, the water is in contact with the entrapped air. The contact angle depends on the fraction φs and is given by the Cassie-Baxter relation.2,7,8 The air fraction (1 - φs) plays an important role in determining the superhydrophobic properties of rough hydrophobic surfaces. Keeping this in mind, the roughness/ texture of the surface can be suitably designed for specific applications. Apart from self-cleaning applications that have been widely discussed in the literature,2,3,5,7 the Cassie state of wetting could also be useful in underwater applications.9 The air trapped on the surface, in these cases, offers very low resistance to water flow compared to the solid surface, and this can give rise to substantial *Corresponding author. E-mail:
[email protected] (1) Shibuichi, S.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512. (2) Bico, J.; Marzolin, C.; Quere, D. Europhys. Lett. 1999, 47(2), 220. (3) Herminghaus, S. Europhys. Lett. 2000, 52(2), 165. (4) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (5) Callies, M.; Quere, D. Soft Matter 2005, 1, 55. (6) Cao, L.; Hsin-Hu, H.; Gao, D. Langmuir 2007, 23, 4310. (7) Dorrer, C.; Ruhe, J. Soft Matter 2009, 5, 51. (8) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (9) Marmur, A. Langmuir 2006, 22, 1400. (10) Choi, C.-H.; Ulmanella, U.; Kim, J.; Ho, C.-M.; Kim, C.-J. Phys. Fluids 2006, 18, 087105. (11) Voronov, R. S.; Papavassiliou, D. V.; Lee, L. L. Ind. Eng. Chem. Res. 2008, 47, 2455.
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reduction in the overall drag force on the surface.10,11 A parameter often used in the literature10-13 to quantify the extent to which this reduction happens is the slip length. The slip length is defined as the ratio of the velocity of the water layer in contact with the surface (slip velocity) to the velocity gradient at the surface. The larger the slip length, the lesser the resistance offered by the surface to the flow and hence a lower drag force on the surface. Typically, the slip length is of the order of a few nanometers12 for atomically smooth hydrophobic surfaces. On textured surfaces in the Cassie state of wetting, slip lengths up to a few tens of micrometers have been reported.13-15 It is becoming clear that the reason for this large slip length is the air present on the composite surface, which offers less resistance compared to the completely wetted “Wenzel state”.16 This large slip is referred to as apparent slip,11,12 in contrast to the inherent slip resulting from molecular level hydrophobic interactions. Huge reductions in flow resistance can result when the slip lengths are comparable to the characteristic length scale of the flow, such as the size of the channel for pipe flow. Prior studies17,18 have shown that lotus leaves immersed in water for a few minutes, or when subjected to higher hydrostatic pressure, lose their superhydrophobicity. The reason for this is that the surface has transitioned from the “Cassie” state to the “Wenzel” state. Such a transition from the metastable Cassie state has also been observed during evaporation of a drop on a (12) Choi, C.; Westin, K. J. A.; Breuer, K. S. Phys. Fluids 2003, 15, 2897. (13) Ou, J.; Perot, B.; Rothstein, J. P. Phys. Fluids 2004, 16, 4635. (14) Truesdell, R.; Mammoli, A.; Vorobieff, P.; van Swol, F.; Brinker, C. J. Phys. Rev. Lett. 2006, 97, 044504. (15) Lee, C.; Choi, C.-H.; Kim, C.-J. Phys. Rev. Lett. 2008, 101, 064501. (16) Govardhan, R. N.; Srinivas, G. S.; Asthana, A.; Bobji, M. S. Phys. Fluids 2009, 21, 052001. (17) Cheng, Y.-T.; Rodak, D. E. Appl. Phys. Lett. 2005, 86, 144101. (18) Zhang, J.; Sheng, X.; Jiang, L. Langmuir 2009, 25, 1371.
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superhydrophobic surface resulting in impalement of the “fakir” drops.19 Rathgen et al.20 observed that a superhydrophobic surface transitions to the Wenzel state when the water-air interface is subjected to a dynamic pressure beyond a certain threshold. The loss of air trapped on the surface would result in an increased resistance to the flow. Recent experiments have shown that the apparent slip measured on a superhydrophobic surface decreases gradually with immersion time.16 Thus, it is important for underwater applications not only to trap air on the surfaces initially but also to retain the “Cassie” state by sustaining the trapped air on the surface for longer periods of time. Sustaining the Cassie state is also important for some insects and spiders that remain underwater for prolonged periods.21 The wax coated hairs of these arthropods help to form an air bubble around their body called plastron. The constant gas exchange between the plastron and the surrounding water help these arthropods to breathe underwater. A biomimetic plastron that can sustain the Cassie state indefinitely would have many applications, such as, for example, in fuel cells and diving chambers.22 The sustainability of the Cassie state will primarily depend on the size and the shape of the water-air interface, which can be controlled by the texture of the hydrophobic surface. In this paper, we study experimentally the water-air interface on a series of hydrophobic surfaces with different types of surface texture when the surfaces are immersed in water. A technique based on total internal reflection (TIR) of light has been utilized to visualize the spatial distribution of the trapped air. We find that the shape of the air pockets depends critically on the texture. The numbers as well as the size of these pockets are found to decrease with time irrespective of the texture.
Experimental Section Visualization Setup. A schematic of the experimental setup used is shown in Figure 1. A fiber optic halogen lamp (Olympus LG-PS2) was used for cold light illumination. A parallel beam of light is incident on the hydrophobic surface at an angle of 53° that is greater than the critical angle given by θcric = sin-1 (1/μ) required for total internal reflection at a water-air interface. The beam would then undergo total internal reflection at a water-air interface, if present, and result in a bright spot as compared to the normal reflection at the water-solid interface. This effect has been used to detect the presence of air on immersed superhydrophobic surfaces previously.16,23,24 The reflected light from the water-air interface is brought to focus on a CCD camera with the help of a long working distance microscope. The Olympus (model no. SZX12) continuous zoom microscope is focused on the surface, enabling the spatial distribution of air on the surface to be recorded. The camera is programmed to take images at a regular interval of 30 s. The TIR experiments were carried out with deionized water at 20 °C after leaving the water in the lab environment for a minimum of 2 days, such that the water is saturated with air. Bubbling the air through the water overnight did not give any appreciable change in the results obtained. In between two trials, the hydrophobic surfaces were dried and flushed with dry nitrogen for 30 min. This restored the air retention capacity of the surfaces. (19) Reyssat, M.; Yeomans, J. M.; Quere, D. Europhys. Lett. 2008, 81, 26006. (20) Rathgen, H.; Sugiyama, K.; Ohl, C.-D.; Lohse, D.; Mugele, F. Phys. Rev. Lett. 2007, 99, 214501. (21) Flynn, M. R.; Bush, J. W. M. J. Fluid Mech. 2008, 608, 275. (22) Shirtcliffe, N. J.; McHale, G.; Newton, M. I.; Perry, C. C.; Pyatt, F. B. Appl. Phys. Lett. 2006, 89, 104106. (23) Sakai, M.; Yanagisawa, T.; Nakajima, A.; Kameshima, Y.; Okada, K. Langmuir 2009, 25, 13. (24) Larmour, I. A.; Bell, S. E. J.; Saunders, G. C. Agnew. Chem. Int. Ed. 2007, 46, 1.
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Figure 1. Schematic of the setup used for visualization. The textured hydrophobic surface is arranged such that the parallel beam of light undergoes total internal reflection at the water-air interface.
Textured Surfaces. Four different kinds of surface textures were generated with typical feature sizes as given in Table 1. A regular array of pillars was chosen to mimic the lotus leaf.25 In an effort to compartmentalize the trapped air pockets, such that any instability in one location would not result in complete loss of the Cassie state, arrays of ridges and holes were also generated. It was hoped that the ridges, mimicking duck feathers,26 would confine the air along one lateral direction while the holes would confine the air in both lateral directions. The surface with the array of holes can be thought of as a complementary or negative surface to the one with the pillars. The fourth texture chosen was composed of randomly distributed craters generated by an electrodischarge machining process.16,27 This texture was mainly chosen for its ease of manufacture over a large surface area that makes it attractive for some engineering applications. The first three textures, with a regular array of features, were generated by a photoetching process in silicon.27 A 110 silicon wafer was chosen such that it produced a texture with vertical walls. The root-mean-square roughness of this polished wafer as measured by using an atomic force microscope was about 0.5 nm. A positive photoresist was spin coated and exposed to UV light for 2.5 s through a photomask. Then the photoresist was developed and the oxide layer was removed with HF to expose the silicon at the desired locations. The anisotropic etching was carried out with a 40% by weight KOH solution at 75 °C. The photomask was oriented with the crystallographic directions of the wafer such that hexagonal holes and pillars were obtained. Figure 2a-c shows the optical micrograph of the surfaces generated on silicon. The dark regions in these images correspond to the polished silicon surface that was masked during the etching process. The surfaces that have been etched appear bright in these figures and are below the dark regions. The dimensions of the texture produced were measured with a noncontact 3-D optical profilometer (Veeco), and the 3-D images and the relevant parameters are given in Table 1. From these data, it was found that the surfaces with ridges and with holes satisfied the thermodynamic criterion developed by Marmur9 for stable underwater superhydrophobicity. The surface with random craters was generated in aluminum by locally evaporating the surface using tiny sparks generated by an electrodischarge machining (EDM) process. This process generates roughness that spans many length scales,16 and the measured root-mean-square roughness of this surface was 4.2 μm. The correlation length that characterizes the lateral roughness, rather than the distribution of heights, was 33 μm. Figure 2d shows an (25) Neinhuis, C.; Barthlott, W. Ann. Bot. 1997, 79, 667. (26) Liu, Y.; Chen, X.; Xin, J. H. Bioinspiration Biomimetics 2008, 3, 046007. (27) Asthana, A. M.Sc. (Engg.) Thesis, Indian Institute of Science, Bangalore, 2007.
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electron microscope picture of the surface showing craterlike texture of different sizes and shapes. A line profile of the surface, obtained from a contact profilometer, over a length of 1 mm is shown in Table 1. Hydrophobic Coating. To render the surfaces hydrophobic, a self-assembled layer of 1H,1H,2H,2H-perfluorooctyl trichlorosilane (FOTS) was formed from solution.28 The silicon samples of typical size 1 cm 1 cm were first cleaned in methanol and then hydrolyzed by soaking in water. The aluminum surfaces were ultrasonicated in a 50:50 deionized water/acetone mixture for 1 h and then cleaned in methanol solution. The surfaces were then dried in an oven at 60 °C for 1 h, and the samples were stored in a vacuum desiccator. FOTS with a purity of >98% was obtained from Aldrich Inc. and used as such. A mixture of 1 mM FOTS was prepared in isooctane solvent. The cleaned and hydrolyzed samples were immediately dipped into freshly prepared solution for 1 h. This duration was optimized for full surface coverage.28 The samples were then taken out, rinsed, and washed with isooctane to remove excess solution. The FOTS layer was always formed on the surfaces just before the start of the TIR experiments. Static contact angles on various surfaces with freshly formed FOTS were measured using a Rame-Hart 100 goniometer with deionized ultrapure Millipore water. The contact angle on the polished silicon surface with out any texture was found to be in the range of 115-120°. The diamond polished aluminum surface with a FOTS layer also had a water contact angle in the same range. The contact angles measured on each of the four textured hydrophobic surfaces are given in Table 1, and an image of a 5 μL drop of water resting on these surfaces is shown in the insets of (28) Devaprakasam, D.; Sampath, S.; Biswas, S. K. Langmuir 2004, 20, 1329– 1334.
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Figure 2. Among the surfaces studied, the surface with pillars had the largest contact angle and the water drops rolled off easily from it. The surface with holes had the smallest contact angle and had relatively large contact angle hysteresis. The contact angles obtained from the Cassie-Baxter relation, for a Young’s contact angle of 115°, are also tabulated in Table 1 for comparison.
Results The surfaces with a freshly formed FOTS layer were kept in an empty tank, and the water level was slowly raised such that the center of the area observed in the microscope was 6 cm below the final water level. This gave a hydrostatic pressure of about 600 Pa. The TIR experiments on different surfaces were repeated at least six times, and some experiments were also carried out at different magnifications. A typical image obtained showed many bright spots with each spot corresponding to the location where TIR occurs at the water-air interface of the trapped air pocket. The relative angles between the light source, surface, and microscope were adjusted (Figure 1) such that the TIR reflection will occur on a water-air interface that is parallel to the surface. As shown in the inset of Figure 1, ideally there will be only one spot per air bubble. Figures 3-6 show time sequences of images obtained from the TIR visualization setup for the four different surfaces studied. Time lapse videos obtained from such images taken at an interval of 30 s are available as Supporting Information. Surface with Pillars. The surface with pillars when immersed in water had many silvery patches that could be seen with the naked eye. When observed through the microscope in the TIR setup, it was clear that those patches were air pockets sitting on top of the pillars. Figure 3 shows the air pockets sitting on the Langmuir 2009, 25(20), 12120–12126
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Figure 2. Optical micrographs showing the various textures generated: (a) pillars, (b) ridges, and (c) holes generated by a photoetching process. (d) SEM micrograph showing the random cratered surface generated by EDM process. Insets in each case show a 5 μL drop resting on these hydrophobic surfaces.
Figure 3. TIR images of the hydrophobic silicon surfaces with micropillars at different immersion times. The contiguous region of air is enclosed within the dotted lines.
surface at different immersion times. The area enclosed in a dotted line corresponds to one contiguous area of air. With time, the large areas of air gradually became smaller and sometimes broke up into smaller areas, until they completely disappeared. Throughout this process, the water-air interface remained very close to the surface and could only barely be resolved when the immersed surface was looked at from the side through the microscope. If the water-air interface were spherical, then there would have been only one bright spot per bubble, as suggested, for example, in Figure 1. However, as may be seen in Figure 3, there is more than one bright spot for each contiguous area. As the area shrinks, this number increases as a bright spot is formed above each individual pillar location. These observations seem to indicate that the air pocket exists continuously above the pillars. This is in line with observations on plastrons that surround the whole body of some underwater insects.21 In our case, the water-air interface seems to be undulated and these undulations follow the structure of the texture present below. Probably TIR from these undulations is responsible for the shiny surfaces observed by other workers as well. Langmuir 2009, 25(20), 12120–12126
Surface with Ridges. On the surfaces with ridges, in contrast with the pillars, the water-air interfaces (Figure 4) seem to be confined within the ridges, barely projecting out of the surface. We do not observe any continuous film of air on the surface. The fractional area of the surface covered with air in this case appears very small. The number of bright spots corresponding to air pockets is found to decrease with time, and after about 50 min all the air pockets seem to have disappeared. The initial distribution of air pockets over the whole surface of area 1 cm 1 cm was found to be more or less uniform. For this surface with ridges, there is an interesting behavior that can be clearly observed from the video. With time, it appears that some of the tiny air pockets migrate along the groove formed between two ridges. The direction of this migration is found to be independent of gravity. We believe that this may be due to small variations in the groove dimension resulting from tiny misalignments between the mask and the crystallographic orientation of the single crystal silicon. As the air pockets become smaller with time, they will move toward the location where the groove dimensions are smaller. DOI: 10.1021/la902679c
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Figure 4. Visualization of air pockets at different immersion times on a hydrophobic surface with an array of ridges. The air is trapped in between the ridges in the form of tiny bubbles. Total internal reflection results in a bright spot for every bubble.
Figure 5. Visualization of air pockets at different immersion times on a hydrophobic surface with an array of holes. The holes with air appear as bright spots due to total internal reflection. The gradual reduction in the spots indicates that the water-air interface has disappeared or moved into the hole.
Figure 6. Time sequence of the TIR visualization of air pockets on a hydrophobic surface with random craters. Each bright spot corresponds to an air pocket trapped on a crevice of the surface.
Surface with Holes. Figure 5 shows the behavior of TIR spots on the surface with holes. As is the case with the ridges, we do not observe a continuous air film over the surface. Initially, there is a bright spot corresponding to almost every hole, indicating the presence of trapped air within the hole. The number of bright spots gradually decreases with time and eventually completely disappears after about 40 min. Although the time taken for an individual bright spot to disappear varies from a few minutes to nearly 1 h, there is a well-defined mean time for a bright spot to disappear. The intensity of the bright spot at some locations is found to increase with time instead of decreasing monotonically as in most of the cases. This could be due to the changes occurring in the shape of the water-air interface. For example, initially the shape of the water-air interface would be concave as indicated in the inset of Figure 1. As the amount of air in each hole decreases, the interface may become convex toward the water with the boundary getting pinned along the rim of the holes. The interface would probably recede into the hole once the pinning effects are overcome. The hole would appear dark either when the interface recedes deep into the hole or when the interface has completely disappeared, depending on the diameter to depth ratio of the hole. Surface with Random Craters. Figure 6 shows the TIR images of the surface with random craters taken at different 12124 DOI: 10.1021/la902679c
immersion times. On immersion into the water, the surface has a lot of tiny air pockets of varying size. Typically, the size of the larger air pockets is about 50 μm, while the size of the smaller pockets approaches the resolution of our setup that is about a few micrometers. The air pockets are uniformly and densely distributed over a large surface area of 7.5 1 cm. With immersion time, the air pockets gradually become smaller and eventually disappear. Occasionally, it has been found that two neighboring air pockets join to form a single bigger one. Except in such cases, all the pockets remain in the same location. This is in contrast to the behavior of air pockets trapped in between ridges where many pockets migrate slowly.
Discussion Depending on the texture, air can be trapped on the surfaces in two distinct ways. In the case of the surface with pillars, the air trapped is continuous over a length scale that is large compared to the pitch of the texture. A thin film of air seems to exist on top of the pillars, presenting a continuous water-air interface over a large surface area. In contrast, the other surfaces do not allow the air to be trapped as a continuous layer but confine the air to small volumes. In the surface with ridges, the air is found in small pockets in the grooves and the size of the pockets is of the order of the groove dimension. For the surface with holes, the air gets Langmuir 2009, 25(20), 12120–12126
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completely confined within the holes and the volume of the air trapped is determined by the volume of the hole. The surface with random craters behaves in a similar manner to the surface with holes. This is due to the fact that craters can be thought of as shallow holes with a range of sizes. A spherical air bubble suspended in stationary water would shrink by diffusion, and the rate of diffusion would be determined primarily by the concentration gradient across the interface.29,30 Even if the water is fully saturated, the air would diffuse out of the bubble due to surface tension effects. Epstein and Plesset,29 for example, have shown that a spherical bubble of radius 100 μm would take about 59 min for complete dissolution through diffusion in a saturated solution. For air bubbles or air pockets trapped on hydrophobic surfaces, the diffusion time would additionally depend on pinning effects. Further, in the current experiments, the presence of diffusing air bubbles nearby could affect the local concentration gradient and hence the time taken for dissolution. The mechanical stability of an water-air interface on a textured hydrophobic surface has been recently analyzed by Flynn and Bush21 in the context of the plastron of submerged insects. The dynamic stability of the water-air interface on a surface with holes has been studied experimentally by Rathgen et al.20 They found that the holes will get filled with water when the interface is subjected to dynamic pressures greater than a certain threshold value. In the current experiments, the time for dissolution of individual air pockets will depend on the volume of air in the pocket. The air pockets on the surface with pillars are the largest and hence take a longer time to disappear. As the air diffuses out, the water-air interface moves closer to the surface. From our observations, it is clear that the transition to completely wetting Wenzel state happens from the edges and moves inward. The continuous air film is not observed on surfaces with other textures. Many attempts were made to generate such continuous films on the surface with ridges, by changing the orientations with respect to gravity during submergence, as well as the rate of filling, but without success. Due to the well-defined nature of the air trapped and the absence of migration of air pockets, the surface with holes was chosen for further analysis to understand the mechanism for the disappearance of bright spots and hence of the trapped air pockets. In this case, the number of holes filled with air and appearing bright can be easily counted in each image by image analysis. Using intensity thresholds and filtering, the background of the image was eliminated and the bright spots were counted by identifying contiguous areas of brightness. The variation of the number of air pockets present on the surface can then be obtained as a function of immersion time from the sequence of images. Figure 7 shows the time variation of the number of bright spots (N) over an area of about 4 6 mm2 normalized by the initial number (N0 = 522) of bright spots. It can be seen that the rate at which the spots disappear is slow at the start and increases to a maximum value at about 15-20 min and then decreases back to a slower rate. Although only one trial is shown in Figure 3, similar behavior was observed in other trials as well, as long as the surface was flushed with dry nitrogen for 15 min prior to the start of the experiment. The disappearance of a bright spot would mean either that all the air in the hole has disappeared or that the water-air interface has moved deep into the hole, thus preventing the reflected light from reaching the microscope. (29) Epstein, P. S.; Plesset, M. S. J. Chem. Phys. 1950, 18(11), 1505. (30) Ljunggren, S.; Eriksson, J. C. Colloids Surf., A 1997, 129-130; 151.
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Figure 7. Time variation of the number of holes at which the total internal reflection condition is satisfied and hence appears as bright spots. The total number of holes that were bright at the start (N0) was 522. The straight line is the best fit curve of the form given by eq 1. Solid circles (b) marked (a)-(d) indicate the time at which different images in Figure 5 were taken.
If all the holes were identical in all respects, then one would expect all the bright spots to disappear at the same time. However, variations in the hole size, geometry, and roughness is likely to cause a scatter in the time taken for the disappearance of bright spots, as observed in the present experiments. If we make the simple assumption that the time taken for the disappearance of a bright spot follows a normal distribution, with a mean time (tμ) and standard deviation (tσ), then it is clear that the number of spots that have disappeared at time t would be given by an integral of the normal distribution between t = 0 and time t. It is thus possible to show that the normalized number of bright spots (N/N0) that would be seen at time t would be given by t -t 1 - erf pffiffi2tμ N σ ¼ N0 1 - erf p-tffiffi μ 2t
ð1Þ
σ
where erf(x) function given by √ R is the error erf(x) = (2/ π) x0 exp(-w2) dw. The parameters tμ and tσ were obtained from a least-squares fit of eq 1 to the data in Figure 7 and were found to be 17.1 and 7.7 min, respectively. The resulting functional form for (N/N0) was found to represent the data well, as shown by the solid line in Figure 7. The mean times tμ for the various surfaces studied are tabulated in Table 1. Effect of Depth. One factor that could affect the sustainability of trapped air is the hydrostatic pressure. As the depth increases, the pressure in the water will increase and hence the interface could become more unstable. We have systematically studied the effect of the hydrostatic pressure on the time taken for disappearance of bright spots by carrying out experiments at different immersion depths on the surface with holes. Figure 8 shows the variation of the mean time (tμ) for disappearance of the TIR condition and the standard deviation (tσ) at different immersion depths. The mean time is found to monotonically decrease with pressure. A similar trend has also been observed for the surface with random craters.16 One of the main applications of trapping air on a submerged hydrophobic surface is the reduction in the resistance offered by the surface to flow (drag). This is typically quantified by the slip length parameter. Huge slip lengths, in excess of 20 μm, indicating large drag reduction have been observed on textured hydrophobic surfaces.13-15 When water flows over a surface, the layer of water DOI: 10.1021/la902679c
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may be advantageous for the sustainability of the underwater Cassie state at higher pressures. It is possible that air pockets smaller than a micrometer (nanobubbles) can remain forever on suitably textured surfaces.33 However, these small air pockets may not give rise to large drag reduction.34 Further TIR studies are needed to understand the sustainability and stability of air pockets under flow conditions. Also, the dependence of the scale of the air pockets on macroscopic drag reduction needs to be studied.
Conclusions
Figure 8. Variation of the mean (tμ) and the standard deviation (tσ) of the time taken for the disappearance of bright spots as a function of immersion depth on the surface with holes.
that is in contact with the solid surface is stationary (no-slip boundary condition). If an air layer is trapped between the water and the solid surface, then there can be an enormous reduction in the resistance of the surface to the flow, as the viscosity of air is very low compared to that of water. Up to 20% drag reduction in a flow experiment with a hydrofoil having a hydrophobicirregular surface texture has been found by Gogte et al.31 Drag reductions of 5-15% have been very recently observed by measuring the terminal velocity of spheres that carry plastrons by McHale et al.32 The possibility of sustaining a large air layer on surfaces with pillars leads us to believe that, for drag reduction applications, surfaces with pillarlike textures could be ideal. However, since the air layer trapped is finite in lateral spreading and is projecting out of the surface, it is likely to be less stable when exposed to the flow. From this point of view, it may be better to trap the air within the texture, avoiding any outward projection of the air pockets in to the flow. Surfaces with holes and craters are perhaps better for drag reduction over extended periods for this point of view. Direct shear force experiments by Govardhan et al.16 with a random cratered surface have shown up to 30% reduction in the shear force when the surface is in the Cassie state compared to the completely wetted condition. They have also shown that the shear force increases gradually from the initial low values, reaching the value for the fully wetted condition in about 150 min. For the surface with holes or with random craters, the time taken for the disappearance of the Cassie state could possibly be increased by increasing the depth of the holes/craters, as this would increase the air contained within the hole. On the other hand, the pressure at which the surface needs to be utilized would decide the lateral size of these textures. A small microstructure (31) Gogte, S.; Vorobieff, P.; Truesdell, R.; Mammoli, A.; van Swol, F; Shah, P.; Brinker, C. J. Phys. Fluids 2005, 17, 051701. (32) McHale, G.; Shirtcliffe, N. J.; Evans, C. R.; Newton, M. I. Appl. Phys. Lett. 2009, 94, 064104.
12126 DOI: 10.1021/la902679c
A quantitative technique for measuring underwater sustainability of the Cassie state of wetting has been developed. Using this technique, the sustainability of the Cassie state has been studied on four different textured hydrophobic surfaces. In each case, it has been found that air pockets are initially trapped on the surface and appear as bright spots due to total internal reflection of light at the water-air interface. With time, the air pockets have been found to diffuse into water and eventually the surfaces become completely wetted. The geometry of the air pockets trapped on the surfaces depends on the type of texture. For the surface with a regular array of pillars, a thin layer of air extending over a large number of pitch lengths is perched on top of the pillars. For other textures, the air is trapped in small pockets, whose dimensions are of the order of the length scale of the texture. For the surface with ridges, the air drop is about the size of the gap between two ridges. In the case of the surface with holes, the air gets trapped within the holes. The air pockets on the surface with random craters have a comparatively wide range of sizes due to the large range of length scales associated with the random texture. In the case of the surface with a regular array of holes, the time for the disappearance can be easily quantified. This time is found have a statistical distribution possibly due to small geometrical variations between holes. Assuming this to be a normal distribution, a simple functional form for the total number of spots present at any point of time has been obtained based on error functions. This functional form is found to fit the measured experimental data well. As the hydrostatic pressure is increased, the mean time for disappearance is found to continuously decrease. This suggests that the size of holes could be an important parameter in designing the texture of hydrophobic surfaces to sustain the Cassie state for larger times for underwater/submerged applications. However, the present work suggests that, for all the surfaces studied, the Cassie state is sustained only for a finite time. Supporting Information Available: Time lapse videos visualizing air pockets on hydrophobic surfaces with four different textures. Time sequence of images from these videos are shown in Figures 3-6 of the paper. This material is available free of charge via the Internet at http://pubs.acs.org. (33) Liebermann, L. J. Appl. Phys. 1957, 28, 205. (34) Lauga, E.; Stone, H. A. J. Fluid Mech. 2003, 489, 55.
Langmuir 2009, 25(20), 12120–12126
