Article pubs.acs.org/Langmuir
Drop Impact Dynamics on Oil-Infused Nanostructured Surfaces Choongyeop Lee,*,† Hyunsik Kim,‡ and Youngsuk Nam*,‡ †
School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang 412-791, Korea Department of Mechanical Engineering, Kyung Hee University, Yongin 446-701, Korea
‡
ABSTRACT: We experimentally investigated the impact dynamics of a water drop on oilinfused nanostructured surfaces using high-speed microscopy and scalable metal oxide nano surfaces. The effects of physical properties of the oil and impact velocity on complex fluid dynamics during drop impact were investigated. We show that the oil viscosity does not have significant effects on the maximal spreading radius of the water drop, while it moderately affects the retraction dynamics. The oil viscosity also determines the stability of the infused lubricant oil during the drop impact; i.e., the low viscosity oil layer is easily displaced by the impacting drop, which is manifested by a residual mark on the impact region and earlier initiation of prompt splashing. Also, because of the liquid (water)−liquid (oil) interaction on oil-infused surfaces, various instabilities are developed at the rim during impact under certain conditions, resulting in the flower-like pattern during retraction or elongated filaments during spreading. We believe that our findings will contribute to the rational design of oil-infused surfaces under drop impact conditions by illuminating the complex fluid phenomena on oil-infused surfaces during drop impact.
1. INTRODUCTION Non-wettable superhydrophobic (SHPo) surfaces have attracted a lot of attention in recent years, as various useful functionalities, such as drag reduction,1,2 self-cleaning,3,4 antifouling,5 shedding condensates,6−8 and anti-icing,9 are demonstrated on such surfaces. Non-wettability of the SHPo surface is attributed to the combination of micro-/nanoscale roughness and surface hydrophobicity; i.e., the water does not intrude into micro-/nanoscale roughness because of the capillary pressure, whereas the interaction between the water and the solid is limited to the uppermost region of roughness.10 Many theoretical and experimental studies have been devoted to advance an understanding of unique fluid phenomena on SHPo surfaces by investigating the influence of geometric parameters of micro-/nanostructures on each relevant fluid phenomenon.1−16 However, despite many desirable properties of the SHPo surfaces, superhydrophobicity may break down (i.e., known as the Cassie−Wenzel wetting transition) under various conditions, such as drop impact,14 drop squeezing,15 and drop evaporation.16 Recently, it was shown that hydrophobic micro-/ nanostructured surfaces infused with low-surface-tension lubricant oil can avoid these shortcomings of SHPo surfaces while maintaining similar or better non-wetting characteristics.17,18 Non-wetting properties of oil-infused surfaces are attributed to the fact that micro-/nanoscale surface roughness holds the lubricant oil in place, while the atomically smooth liquid interface minimizes the contact line pinning of the water drop, resulting in a low contact angle hysteresis. Also, the fluidity of the lubricant oil renders the surface resistant to the external pressure and unwanted surface damages.17 With such unique properties, oil-infused nanostructured surfaces were shown to be promising in self-cleaning,17 anti-icing,19−22 water harvesting,23,24 and thermal management.25 © 2014 American Chemical Society
In designing oil-infused surfaces, it is important to understand how surface structures and physical properties of the lubricant oil affect their performance. Note that it was recently reported26,27 that distinctively different spreading dynamics of the water drop could be induced on polymer surfaces, when surfaces were sufficiently soft. Likewise, we can expect that the water dynamics on oil-infused surfaces would depart from that on hard solid surfaces because of a liquid nature of the surface. The previous study has reported that surface structures have the profound effect on the stability of the lubricant oil layer under a shear flow.28 It was also found that both the surface tension and viscosity of the lubricant oil directly affect the mobility of the water drop on oil-infused surfaces;29,30 i.e., the drop mobility is high only when the balance among interfacial tensions ensures the full coverage of the underlying nanostructures, with the lubricant oil preventing the direct contact between the water and solid structures,29 and the drop mobility under gravity is inversely proportional to the oil viscosity.29,30 Quite often, the water drop interacts with the surface via drop impact in natural or engineering systems, exemplified by raining, spray cooling, spray painting, and liquid fuel combustion.31 Under drop impact conditions, the interaction between the water drop and surface occurs over a very short time ranging from milliseconds to tens of milliseconds,32 and this dynamic nature of the interaction might lead to previously unseen phenomena on oil-infused surfaces, whose understanding would be crucial in establishing design rules for oil-infused surfaces under drop impact conditions. Unfortunately, to our knowledge, there is no Received: April 8, 2014 Revised: June 17, 2014 Published: June 29, 2014 8400
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Figure 1. Scanning electron microscope images of the CuO nanostructures with magnifications of (a) 10000× and (b) 50000×. 2.2. Drop Impact Test. The volume of the dispensed water drop was accurately controlled with picoliter resolution using the microsyringe pump connected to the microprocessor-based controller (SYSMICRO4). The dispensed drop radius R0 was measured to be about 1.1 mm. The drop impact dynamics on each test surface was observed with a high-speed charge-coupled device (CCD) camera (Phantom M110) connected to a macro lens (NIKKOR 60 mm F2.8D) from either 60° or 0° angle from the horizontal plane. The drop impact velocity and resulting Weber number We were varied by controlling the falling height of the drop dispense. Here, the We number is defined as We = ρwU02R0/γwa, where ρw, U0, R0, and γwa are the water density (≈1000 kg/m3), impact velocity, drop radius (≈1.1 mm), and water− air surface tension (≈72 mN/m), respectively. Impact velocity U0 was directly measured when the drop impact event was recorded from 0° angle from the horizontal plane. For drop impact events seen from 60° angle from the horizontal plane, the representative impact velocity for the given falling height was obtained from the captured images from 0° angle and was used throughout the study.
theoretical or experimental work that investigated the drop impact phenomena over oil-infused surfaces, which motivates the present work. In this study, we experimentally investigated how the physical properties of the lubricant oil and the impact conditions lead to different dynamic behaviors of the water drop during impact to better understand the complex interaction between the water drop and oil-infused surfaces under impact conditions. The results show that various fluid phenomena during drop impact, such as the stability of the oil layer, splashing, instabilities at the rim, and spreading and retraction dynamics, are influenced by the physical properties of the lubricant oil as well as the Weber number.
2. EXPERIMENTAL SECTION 2.1. Fabrication and Characterization of the Tested Surfaces. To create the SHPo surfaces, we nanostructured commercially available copper foils (99.8% purity, 0.8 mm thickness, and 2 × 2 cm size) with the chemical oxidation scheme reported in our previous publications.33−35 Then, the CuO nanostructured surface was functionalized with trichloro(1H,1H,2H,2H-perfluorooctyl)silane (TFTS, Sigma) through the vapor deposition process. A scanning electron microscopy (SEM) image of CuO nanostructures in Figure 1 shows that the created CuO film has unique blade-like morphologies with a height of h ≈ 1 μm, solid fraction of fs < 0.05, and roughness factor of r ≈ 10. The geometrical parameters were determined from the cross-sectional SEM images of CuO nanostructures and contact angle analysis reported in our previous study.35 To infuse oil, we dispensed oil droplets on the silanated CuO surfaces and blew dry nitrogen gas to spread the oil on the surface. Then, the surface was swept by a smooth Teflon blade to obtain uniform and thin ( 1,38 and the water drop velocity was inversely proportional to the oil viscosity when the water drop was driven by gravity.29 Also, when the pendant water drop was in contact with the oillubricated surfaces, the detachment time for the water drop from the needle was determined by the viscous time scale ηoR0/ γoa when Oh > 1. The difference between these studies and the present study might be attributed to the dynamic nature of the drop impact process. Right after spreading (lasting for 2−3 ms), the water drop does not have enough time to equilibrate with the lubricant oil, while the equilibrating process itself is influenced by the oil viscosity in a way that it is slowed with the increase of the oil viscosity. For example, as shown in Figure 4c, oil is drawn over the water drop by the capillary force equivalent to the spreading parameter S = γwa − (γwo + γoa), which is balanced by the viscous force inside the film given by ηo(Ve/e)l = (ηo/2e)(dl2/dt) ∼ (ηol2/eΔt), yielding l ∼ (SeΔt/ ηo)1/2. Here, l, Ve, and e are the length, velocity, and thickness of the oil layer over the water drop. With Δt ∼ 1 ms and S ∼ 10 mN/m, l is about 1 μm on SO-1000 and about 10 μm on SO-5 when we assume e ∼ 100 nm, which is far from the equilibrium state where the water drop is completely encapsulated by oil. This approximate calculation shows that the size of the oilaffected region near the contact line would decrease with the increases of the oil viscosity, which offsets the increases of the viscous dissipation at the contact line. 3.3. Influence of We Number on Drop Impact Dynamics. Figure 5 shows high-speed camera images captured from 60° angle on test surfaces in the order of increasing We
larger CAH on SO-5 might be attributed to the deformation of the oil layer by the water drop, which results in poorer lubricant performance of oils against the drop movement, even when the thermodynamic condition dictates the complete coverage of nanostructures by all of the lubricant oils used in the present study. On oil-infused surfaces, the static contact angle θs of a water drop is determined by the competition among interfacial tensions of the oil−air interface (γoa), water−air interface (γwa), and water−oil interface (γwo). The spreading parameter S of oil over water is given by S = γwa − (γwo + γoa). With γwa ≃ 72 mN/ m, S is calculated to be about 6 and 10 mN/m on KR (γwo ≃ 42 mN/m, and γoa ≃ 20 mN/m) and SO (γwo ≃ 49 mN/m, and γoa ≃ 17 mN/m), respectively, which suggests that an oil layer preferentially encapsulates over the water drop on both KR and SO. In this scenario, the CA of the water drop on oil-infused surfaces can be predicted by balancing the capillary forces along the horizontal direction at water−oil−air three phase contact lines, as shown in the schematic in Figure 2 under assumption that nanostructures are fully covered by the lubricant oil layer.36 By means of Neumann’s construction, the water CA θs is given by γoa − γwo = (γwo + γoa)cos θs, which yields ∼110° for SO and ∼120° for KR, which are close to the measured CA in this study. The CA measurement on oil-infused surfaces here indicates that oil-infused surfaces prepared using CuO nanostructures exhibit similar non-wetting characteristics as those previously reported.29 Also, good agreement between the predicted CA based on the schematic in Figure 2 and the measured CA implies that an oil layer would cloak around the water drop at equilibrium, as suggested in the previous study.29 3.2. Spreading and Retraction Dynamics at Low We. Figure 3 shows captured high-speed images of the impacting
Figure 3. Captured images of the water drop impact on test surfaces from 0° angle at low We = 45.
water drop on test surfaces seen from 0° angle at low We = 45. On oil-infused surfaces, the water drop is deformed to a pancake shape after impact, followed by a retraction from the surface, similar to what is observed on hydrophobic solid surfaces. In Figure 3, no noticeable difference is observed during spreading of the water drop among the surfaces, including the instance when the drop reaches the maximal deformation (i.e., ∼2.1 ms after impact), while a retraction rate appears to decrease as the oil viscosity increases (spreading dynamics begin to be differentiated on some surfaces as the We increases, which will be delineated in the next section). The retraction of the water drop after spreading is driven by the capillary force FC = (γwa + γoa)(cos θ(t) − cos θR), which is 8402
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Figure 4. (a) Temporal evolution of the water drop radius normalized by the initial drop radius on each test surface at We = 45. (b) Viscous force FD (open symbols) and retraction velocity Vret (filled symbols) at the contact line during retraction on KR (red squares) and SO (black circles) as a function of the Oh number. The inset shows the viscous dissipation rate during retraction (i.e., the product of viscous force FD and retraction velocity Vret). (c) Schematics of oil encapsulation dynamics over the water drop.
showed that the depletion of the oil layer proceeded rapidly under icing conditions, accompanied by deterioration of antiicing performance. In panels b and c of Figure 5, at sufficiently high We number, the rim starts to become destabilized on KR and SO-5 during the later stage of spreading and this instability continues to develop during the retraction stage, leading to the flower-like pattern formation. Meanwhile, on SO-100 and SO-1000, this type of instability is absent because the high oil viscosity suppresses the instability development. Although the pattern formation during spreading might be induced on solid surfaces with pre-defined physical patterns,39 it is not normally seen on randomly structured solid surfaces. It should be noted that the development of flower-like patterns was reported at the end of spreading on the thin liquid film by drop impact, and it was surmised that Rayleigh−Plateau instability was a responsible leading instability mechanism.40 Although the thickness of the liquid layer in ref 37 was distinctively larger than that of the present study and the tested liquid (i.e., water versus oil) was different for liquid film, the similar pattern formation at the end of spreading might imply that the same instability mechanism is involved as a result of the dynamic interaction between water and oil. An in-depth theoretical study will be required to determine which instability mechanism is responsible for the flower-like pattern formation observed in this study. Another interesting observation is the development of another type of instability at the rim at an even higher We number. This instability begins to develop during spreading of the water drop only on KR, as shown in Figure 8. As the We number increases, the rim becomes increasingly more unstable, resulting in the formation of several elongated filaments along the circumference, followed by their breaking up into smaller satellite droplets. Please note that, despite a relatively small difference in interfacial surface tensions and viscosity between KR and SO-5, this type of instability was never observed on SO-5 and then the observed instability mechanism might be
number. First, a clear residual mark is found at the impact location on KR and SO-5 at all tested We numbers, which gradually disappears over a few seconds as the oil reflows back to the impact location. On the other hand, there is no such mark seen on SO-100 and SO-1000, even at the high We number of 287, which implies that the oil layer is more easily displaced by the impacting drop when the oil viscosity is low. At the impact location, the dynamic pressure incurs the pressure gradient along the radial direction given by ρwU02/R0, which is balanced by the viscous force in the oil layer given by ηo∂2Uoil/∂y2 ∼ η0Uoil/t2, with Uoil and t being the characteristic velocity and thickness of the oil layer, respectively. Then, the lubricant oil is displaced by the impacting water drop with the velocity Uoil ∼ (ρt2U02)/(η0R0), which is inversely proportional to the oil viscosity. Second, as the We number increases, we observe that several small droplets begin to eject from the water drop right after impact on some surfaces, as shown in Figure 6. Figure 7 shows that this splashing begins to occur beyond We = 108 on KR and SO-5, while it was not observed on SO-100 and SO-1000 until the We number was beyond 250. Also, the number of ejected droplets on KR and SO-5 was significantly larger than that on SO-100 and SO-100 at the same We number. This so-called prompt splashing is known to be induced by surface roughness, in a way that higher roughness facilitates splashing.38 It means that the different prompt splashing on each test surface could be attributed to the exposure of underlying surface morphology, resulting from the displacement of the oil layer by the impacting drop, which is in line with the residual mark on the surfaces infused with low viscous oils. Easier displacement of low-viscosity oil under impact conditions should be considered in designing oil-infused surfaces for anti-icing applications, where the direct contact between the water drop and the solid surface as well as the partial drainage of the oil layer should be avoided. The importance of the stability of the oil layer under icing conditions was demonstrated in the recent study,21 which 8403
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Figure 5. Captured images of the water drop on test surfaces during drop impact from 60° angle from the horizontal plane at (a) We = 45, (b) We = 135, and (c) We = 287 (scaling bar = 1 mm).
those of silicone oils (918−970 kg/m3) are similar to the water density. Nevertheless, the breakup of liquid filaments is the typical feature of the Rayleigh−Plateau instability, which reflects the complexity of impact dynamics on oil-infused
attributed to the liquid density difference between oil and water, which is normally associated with the Rayleigh−Taylor instability. Note that the density of Kryptox oil (1860 kg/m3) is distinctively larger than the water density (1000 kg/m3), while 8404
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Figure 6. Prompt splashing incurred right after impact at We = 134. Prompt splashing is observed on SHPo and surfaces infused with low-viscosity oils (KR and SO-5).
We number directly influence the maximal spreading radius Rmax, as shown in Figure 9. Here, because of the irregular shape
Figure 7. Occurrence of prompt splashing on each test surface as a function of the We number. Figure 9. Maximal spreading ratio Rmax/R0 on test surfaces as a function of the Weber number.
surfaces and implies that the observed instability might be the ramifications of several instability mechanisms instead of a single mechanism. To better understand the hydrodynamic instability at stake, further theoretical studies would be needed, which is beyond the scope of the present study. Once elongated filaments are formed at the rim on KR, they eventually break up into many tiny satellite droplets, resulting in a significantly larger number of fragmented droplets on KR compared to SO-5. Interestingly, similarly elongated filaments at the rim were observed on the SHPo surfaces patterned with micropillars in the previous study.39 However, the leading instability mechanism appears to be different, because the formation of elongated filaments coincided with the crystallographic direction of micropillars in that study,39 while no such directionality is present on random nanostructures used in this study. 3.4. Maximal Spreading Radius at High We Number. The different spreading characteristics on test surfaces at high
of the rim at high We number, Rmax was calculated after subtracting the rim, as shown in the inset of Figure 9. Normally, on the non-wetting surface, the maximal spreading radius is determined by the balance between capillarity and effective acceleration created at the impact,41 following the scaling law Rmax/R0 ∼ We1/4. In Figure 9, although the overall trend follows this scaling, there is a clear difference in Rmax on each surface at high We numbers; i.e., the maximal spreading ratio is largest on SHPo, followed by SO and KR. Please note that there is no observable influence of oil viscosity on the maximal spreading ratio on SO surfaces. This finding can be explained by taking the viscous dissipation inside an oil layer into account. To the first approximation, the viscous dissipation inside the drop is expressed as ∫ ηw(∂U/∂y)2dV ∼ ηw[(U − Uoil)/h]2hRmax2, while that inside an oil layer is expressed as ηo(Uoil/t)2tRmax2, where ηw and ηo are the water viscosity and oil viscosity, respectively,
Figure 8. Development of instability at the rim during the spreading stage (scaling bar = 1 mm). 8405
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U and Uoil are the average drop spreading velocity and oil velocity, respectively, and h and t are the water drop thickness and oil layer thickness, respectively. The stress continuity at the water−oil interface is dictated as ηw(U − Uoil)/h ≃ ηoUoil/t. Then, the ratio of the viscous dissipation inside an oil layer to that inside the water drop is expressed as [(ηo(Uoil/t)2tRmax2)/ (ηw[(U − Uoil)/h]2hRmax2)] ≈ [Uoil/(U − Uoil)] ≈ (ηwt/η0h) ≪ 1, where the last inequality is always satisfied in the present study. This relation clearly shows that the viscous dissipation inside the oil layer during the spreading stage remains negligible compared to that inside the water drop, which explains why there is no oil viscosity effect on the maximal spreading radius. On the other hand, the effective slip length δ reaching up to tens of micrometers42 is induced on SHPo because of the composite interface of liquid−solid and liquid−air interfaces of the surface, which results in the sizable amount of frictional drag reduction during spreading. In the presence of slippage, the viscous dissipation inside the water drop would be reduced roughly by a factor of 1/(1 + δ/h), which indicates that the larger frictional drag is expected at the higher We number because of the decrease of the drop thickness h. Please note that the increase of the maximal spreading radius on SHPo because of the frictional drag reduction at the high We was also demonstrated with complex fluids in the recent study.43 Meanwhile, on KR, additional energy cost is diverted in creating new surfaces in the form of elongated filaments at the rim, which results in the noticeable decrease of the maximal spreading radius on KR.
Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, Information and Communications Technology (ICT), and Future Planning (2012R1A1A1014845).
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4. CONCLUSION In this study, we experimentally investigated the drop impact dynamics on oil-infused surfaces and demonstrated how physical properties of the infused oil and the Weber number affected various fluid phenomena observed during drop impact. Although the oil viscosity had the limited influence on the radius change of the water drop during spreading and retraction, it had a pronounced effect on the stability of the oil layer by the impacting drop, which was manifested by a residual mark on the impact location and prompt splashing. Also, because of the liquid (water)−liquid (oil) interaction on oil-infused surfaces, several instabilities were found to develop at high We numbers, revealing the flower-like pattern during retraction or elongated filaments at the rim, the latter of which particularly contributed to the decrease of the maximal spreading radius. Our findings demonstrate that, depending upon physical properties of the lubricant oil and impact conditions, various complex fluid phenomena occur on oilinfused surfaces during drop impact, which should be considered in the rational design of oil-infused surfaces for many applications, where drop impact phenomena frequently occur.
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REFERENCES
AUTHOR INFORMATION
Corresponding Authors
*Telephone: +82-2-300-0292. E-mail: [email protected]. *Telephone: +82-31-201-3652. E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by the 2014 Korea Aerospace University Faculty Research Grant and the Basic Science 8406
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Drop Impact Dynamics on Oil-Infused Nanostructured Surfaces Choongyeop Lee,*,† Hyunsik Kim,‡ and Youngsuk Nam*,‡ †
School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang 412-791, Korea Department of Mechanical Engineering, Kyung Hee University, Yongin 446-701, Korea
‡
ABSTRACT: We experimentally investigated the impact dynamics of a water drop on oilinfused nanostructured surfaces using high-speed microscopy and scalable metal oxide nano surfaces. The effects of physical properties of the oil and impact velocity on complex fluid dynamics during drop impact were investigated. We show that the oil viscosity does not have significant effects on the maximal spreading radius of the water drop, while it moderately affects the retraction dynamics. The oil viscosity also determines the stability of the infused lubricant oil during the drop impact; i.e., the low viscosity oil layer is easily displaced by the impacting drop, which is manifested by a residual mark on the impact region and earlier initiation of prompt splashing. Also, because of the liquid (water)−liquid (oil) interaction on oil-infused surfaces, various instabilities are developed at the rim during impact under certain conditions, resulting in the flower-like pattern during retraction or elongated filaments during spreading. We believe that our findings will contribute to the rational design of oil-infused surfaces under drop impact conditions by illuminating the complex fluid phenomena on oil-infused surfaces during drop impact.
1. INTRODUCTION Non-wettable superhydrophobic (SHPo) surfaces have attracted a lot of attention in recent years, as various useful functionalities, such as drag reduction,1,2 self-cleaning,3,4 antifouling,5 shedding condensates,6−8 and anti-icing,9 are demonstrated on such surfaces. Non-wettability of the SHPo surface is attributed to the combination of micro-/nanoscale roughness and surface hydrophobicity; i.e., the water does not intrude into micro-/nanoscale roughness because of the capillary pressure, whereas the interaction between the water and the solid is limited to the uppermost region of roughness.10 Many theoretical and experimental studies have been devoted to advance an understanding of unique fluid phenomena on SHPo surfaces by investigating the influence of geometric parameters of micro-/nanostructures on each relevant fluid phenomenon.1−16 However, despite many desirable properties of the SHPo surfaces, superhydrophobicity may break down (i.e., known as the Cassie−Wenzel wetting transition) under various conditions, such as drop impact,14 drop squeezing,15 and drop evaporation.16 Recently, it was shown that hydrophobic micro-/ nanostructured surfaces infused with low-surface-tension lubricant oil can avoid these shortcomings of SHPo surfaces while maintaining similar or better non-wetting characteristics.17,18 Non-wetting properties of oil-infused surfaces are attributed to the fact that micro-/nanoscale surface roughness holds the lubricant oil in place, while the atomically smooth liquid interface minimizes the contact line pinning of the water drop, resulting in a low contact angle hysteresis. Also, the fluidity of the lubricant oil renders the surface resistant to the external pressure and unwanted surface damages.17 With such unique properties, oil-infused nanostructured surfaces were shown to be promising in self-cleaning,17 anti-icing,19−22 water harvesting,23,24 and thermal management.25 © 2014 American Chemical Society
In designing oil-infused surfaces, it is important to understand how surface structures and physical properties of the lubricant oil affect their performance. Note that it was recently reported26,27 that distinctively different spreading dynamics of the water drop could be induced on polymer surfaces, when surfaces were sufficiently soft. Likewise, we can expect that the water dynamics on oil-infused surfaces would depart from that on hard solid surfaces because of a liquid nature of the surface. The previous study has reported that surface structures have the profound effect on the stability of the lubricant oil layer under a shear flow.28 It was also found that both the surface tension and viscosity of the lubricant oil directly affect the mobility of the water drop on oil-infused surfaces;29,30 i.e., the drop mobility is high only when the balance among interfacial tensions ensures the full coverage of the underlying nanostructures, with the lubricant oil preventing the direct contact between the water and solid structures,29 and the drop mobility under gravity is inversely proportional to the oil viscosity.29,30 Quite often, the water drop interacts with the surface via drop impact in natural or engineering systems, exemplified by raining, spray cooling, spray painting, and liquid fuel combustion.31 Under drop impact conditions, the interaction between the water drop and surface occurs over a very short time ranging from milliseconds to tens of milliseconds,32 and this dynamic nature of the interaction might lead to previously unseen phenomena on oil-infused surfaces, whose understanding would be crucial in establishing design rules for oil-infused surfaces under drop impact conditions. Unfortunately, to our knowledge, there is no Received: April 8, 2014 Revised: June 17, 2014 Published: June 29, 2014 8400
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Figure 1. Scanning electron microscope images of the CuO nanostructures with magnifications of (a) 10000× and (b) 50000×. 2.2. Drop Impact Test. The volume of the dispensed water drop was accurately controlled with picoliter resolution using the microsyringe pump connected to the microprocessor-based controller (SYSMICRO4). The dispensed drop radius R0 was measured to be about 1.1 mm. The drop impact dynamics on each test surface was observed with a high-speed charge-coupled device (CCD) camera (Phantom M110) connected to a macro lens (NIKKOR 60 mm F2.8D) from either 60° or 0° angle from the horizontal plane. The drop impact velocity and resulting Weber number We were varied by controlling the falling height of the drop dispense. Here, the We number is defined as We = ρwU02R0/γwa, where ρw, U0, R0, and γwa are the water density (≈1000 kg/m3), impact velocity, drop radius (≈1.1 mm), and water− air surface tension (≈72 mN/m), respectively. Impact velocity U0 was directly measured when the drop impact event was recorded from 0° angle from the horizontal plane. For drop impact events seen from 60° angle from the horizontal plane, the representative impact velocity for the given falling height was obtained from the captured images from 0° angle and was used throughout the study.
theoretical or experimental work that investigated the drop impact phenomena over oil-infused surfaces, which motivates the present work. In this study, we experimentally investigated how the physical properties of the lubricant oil and the impact conditions lead to different dynamic behaviors of the water drop during impact to better understand the complex interaction between the water drop and oil-infused surfaces under impact conditions. The results show that various fluid phenomena during drop impact, such as the stability of the oil layer, splashing, instabilities at the rim, and spreading and retraction dynamics, are influenced by the physical properties of the lubricant oil as well as the Weber number.
2. EXPERIMENTAL SECTION 2.1. Fabrication and Characterization of the Tested Surfaces. To create the SHPo surfaces, we nanostructured commercially available copper foils (99.8% purity, 0.8 mm thickness, and 2 × 2 cm size) with the chemical oxidation scheme reported in our previous publications.33−35 Then, the CuO nanostructured surface was functionalized with trichloro(1H,1H,2H,2H-perfluorooctyl)silane (TFTS, Sigma) through the vapor deposition process. A scanning electron microscopy (SEM) image of CuO nanostructures in Figure 1 shows that the created CuO film has unique blade-like morphologies with a height of h ≈ 1 μm, solid fraction of fs < 0.05, and roughness factor of r ≈ 10. The geometrical parameters were determined from the cross-sectional SEM images of CuO nanostructures and contact angle analysis reported in our previous study.35 To infuse oil, we dispensed oil droplets on the silanated CuO surfaces and blew dry nitrogen gas to spread the oil on the surface. Then, the surface was swept by a smooth Teflon blade to obtain uniform and thin ( 1,38 and the water drop velocity was inversely proportional to the oil viscosity when the water drop was driven by gravity.29 Also, when the pendant water drop was in contact with the oillubricated surfaces, the detachment time for the water drop from the needle was determined by the viscous time scale ηoR0/ γoa when Oh > 1. The difference between these studies and the present study might be attributed to the dynamic nature of the drop impact process. Right after spreading (lasting for 2−3 ms), the water drop does not have enough time to equilibrate with the lubricant oil, while the equilibrating process itself is influenced by the oil viscosity in a way that it is slowed with the increase of the oil viscosity. For example, as shown in Figure 4c, oil is drawn over the water drop by the capillary force equivalent to the spreading parameter S = γwa − (γwo + γoa), which is balanced by the viscous force inside the film given by ηo(Ve/e)l = (ηo/2e)(dl2/dt) ∼ (ηol2/eΔt), yielding l ∼ (SeΔt/ ηo)1/2. Here, l, Ve, and e are the length, velocity, and thickness of the oil layer over the water drop. With Δt ∼ 1 ms and S ∼ 10 mN/m, l is about 1 μm on SO-1000 and about 10 μm on SO-5 when we assume e ∼ 100 nm, which is far from the equilibrium state where the water drop is completely encapsulated by oil. This approximate calculation shows that the size of the oilaffected region near the contact line would decrease with the increases of the oil viscosity, which offsets the increases of the viscous dissipation at the contact line. 3.3. Influence of We Number on Drop Impact Dynamics. Figure 5 shows high-speed camera images captured from 60° angle on test surfaces in the order of increasing We
larger CAH on SO-5 might be attributed to the deformation of the oil layer by the water drop, which results in poorer lubricant performance of oils against the drop movement, even when the thermodynamic condition dictates the complete coverage of nanostructures by all of the lubricant oils used in the present study. On oil-infused surfaces, the static contact angle θs of a water drop is determined by the competition among interfacial tensions of the oil−air interface (γoa), water−air interface (γwa), and water−oil interface (γwo). The spreading parameter S of oil over water is given by S = γwa − (γwo + γoa). With γwa ≃ 72 mN/ m, S is calculated to be about 6 and 10 mN/m on KR (γwo ≃ 42 mN/m, and γoa ≃ 20 mN/m) and SO (γwo ≃ 49 mN/m, and γoa ≃ 17 mN/m), respectively, which suggests that an oil layer preferentially encapsulates over the water drop on both KR and SO. In this scenario, the CA of the water drop on oil-infused surfaces can be predicted by balancing the capillary forces along the horizontal direction at water−oil−air three phase contact lines, as shown in the schematic in Figure 2 under assumption that nanostructures are fully covered by the lubricant oil layer.36 By means of Neumann’s construction, the water CA θs is given by γoa − γwo = (γwo + γoa)cos θs, which yields ∼110° for SO and ∼120° for KR, which are close to the measured CA in this study. The CA measurement on oil-infused surfaces here indicates that oil-infused surfaces prepared using CuO nanostructures exhibit similar non-wetting characteristics as those previously reported.29 Also, good agreement between the predicted CA based on the schematic in Figure 2 and the measured CA implies that an oil layer would cloak around the water drop at equilibrium, as suggested in the previous study.29 3.2. Spreading and Retraction Dynamics at Low We. Figure 3 shows captured high-speed images of the impacting
Figure 3. Captured images of the water drop impact on test surfaces from 0° angle at low We = 45.
water drop on test surfaces seen from 0° angle at low We = 45. On oil-infused surfaces, the water drop is deformed to a pancake shape after impact, followed by a retraction from the surface, similar to what is observed on hydrophobic solid surfaces. In Figure 3, no noticeable difference is observed during spreading of the water drop among the surfaces, including the instance when the drop reaches the maximal deformation (i.e., ∼2.1 ms after impact), while a retraction rate appears to decrease as the oil viscosity increases (spreading dynamics begin to be differentiated on some surfaces as the We increases, which will be delineated in the next section). The retraction of the water drop after spreading is driven by the capillary force FC = (γwa + γoa)(cos θ(t) − cos θR), which is 8402
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Figure 4. (a) Temporal evolution of the water drop radius normalized by the initial drop radius on each test surface at We = 45. (b) Viscous force FD (open symbols) and retraction velocity Vret (filled symbols) at the contact line during retraction on KR (red squares) and SO (black circles) as a function of the Oh number. The inset shows the viscous dissipation rate during retraction (i.e., the product of viscous force FD and retraction velocity Vret). (c) Schematics of oil encapsulation dynamics over the water drop.
showed that the depletion of the oil layer proceeded rapidly under icing conditions, accompanied by deterioration of antiicing performance. In panels b and c of Figure 5, at sufficiently high We number, the rim starts to become destabilized on KR and SO-5 during the later stage of spreading and this instability continues to develop during the retraction stage, leading to the flower-like pattern formation. Meanwhile, on SO-100 and SO-1000, this type of instability is absent because the high oil viscosity suppresses the instability development. Although the pattern formation during spreading might be induced on solid surfaces with pre-defined physical patterns,39 it is not normally seen on randomly structured solid surfaces. It should be noted that the development of flower-like patterns was reported at the end of spreading on the thin liquid film by drop impact, and it was surmised that Rayleigh−Plateau instability was a responsible leading instability mechanism.40 Although the thickness of the liquid layer in ref 37 was distinctively larger than that of the present study and the tested liquid (i.e., water versus oil) was different for liquid film, the similar pattern formation at the end of spreading might imply that the same instability mechanism is involved as a result of the dynamic interaction between water and oil. An in-depth theoretical study will be required to determine which instability mechanism is responsible for the flower-like pattern formation observed in this study. Another interesting observation is the development of another type of instability at the rim at an even higher We number. This instability begins to develop during spreading of the water drop only on KR, as shown in Figure 8. As the We number increases, the rim becomes increasingly more unstable, resulting in the formation of several elongated filaments along the circumference, followed by their breaking up into smaller satellite droplets. Please note that, despite a relatively small difference in interfacial surface tensions and viscosity between KR and SO-5, this type of instability was never observed on SO-5 and then the observed instability mechanism might be
number. First, a clear residual mark is found at the impact location on KR and SO-5 at all tested We numbers, which gradually disappears over a few seconds as the oil reflows back to the impact location. On the other hand, there is no such mark seen on SO-100 and SO-1000, even at the high We number of 287, which implies that the oil layer is more easily displaced by the impacting drop when the oil viscosity is low. At the impact location, the dynamic pressure incurs the pressure gradient along the radial direction given by ρwU02/R0, which is balanced by the viscous force in the oil layer given by ηo∂2Uoil/∂y2 ∼ η0Uoil/t2, with Uoil and t being the characteristic velocity and thickness of the oil layer, respectively. Then, the lubricant oil is displaced by the impacting water drop with the velocity Uoil ∼ (ρt2U02)/(η0R0), which is inversely proportional to the oil viscosity. Second, as the We number increases, we observe that several small droplets begin to eject from the water drop right after impact on some surfaces, as shown in Figure 6. Figure 7 shows that this splashing begins to occur beyond We = 108 on KR and SO-5, while it was not observed on SO-100 and SO-1000 until the We number was beyond 250. Also, the number of ejected droplets on KR and SO-5 was significantly larger than that on SO-100 and SO-100 at the same We number. This so-called prompt splashing is known to be induced by surface roughness, in a way that higher roughness facilitates splashing.38 It means that the different prompt splashing on each test surface could be attributed to the exposure of underlying surface morphology, resulting from the displacement of the oil layer by the impacting drop, which is in line with the residual mark on the surfaces infused with low viscous oils. Easier displacement of low-viscosity oil under impact conditions should be considered in designing oil-infused surfaces for anti-icing applications, where the direct contact between the water drop and the solid surface as well as the partial drainage of the oil layer should be avoided. The importance of the stability of the oil layer under icing conditions was demonstrated in the recent study,21 which 8403
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Figure 5. Captured images of the water drop on test surfaces during drop impact from 60° angle from the horizontal plane at (a) We = 45, (b) We = 135, and (c) We = 287 (scaling bar = 1 mm).
those of silicone oils (918−970 kg/m3) are similar to the water density. Nevertheless, the breakup of liquid filaments is the typical feature of the Rayleigh−Plateau instability, which reflects the complexity of impact dynamics on oil-infused
attributed to the liquid density difference between oil and water, which is normally associated with the Rayleigh−Taylor instability. Note that the density of Kryptox oil (1860 kg/m3) is distinctively larger than the water density (1000 kg/m3), while 8404
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Figure 6. Prompt splashing incurred right after impact at We = 134. Prompt splashing is observed on SHPo and surfaces infused with low-viscosity oils (KR and SO-5).
We number directly influence the maximal spreading radius Rmax, as shown in Figure 9. Here, because of the irregular shape
Figure 7. Occurrence of prompt splashing on each test surface as a function of the We number. Figure 9. Maximal spreading ratio Rmax/R0 on test surfaces as a function of the Weber number.
surfaces and implies that the observed instability might be the ramifications of several instability mechanisms instead of a single mechanism. To better understand the hydrodynamic instability at stake, further theoretical studies would be needed, which is beyond the scope of the present study. Once elongated filaments are formed at the rim on KR, they eventually break up into many tiny satellite droplets, resulting in a significantly larger number of fragmented droplets on KR compared to SO-5. Interestingly, similarly elongated filaments at the rim were observed on the SHPo surfaces patterned with micropillars in the previous study.39 However, the leading instability mechanism appears to be different, because the formation of elongated filaments coincided with the crystallographic direction of micropillars in that study,39 while no such directionality is present on random nanostructures used in this study. 3.4. Maximal Spreading Radius at High We Number. The different spreading characteristics on test surfaces at high
of the rim at high We number, Rmax was calculated after subtracting the rim, as shown in the inset of Figure 9. Normally, on the non-wetting surface, the maximal spreading radius is determined by the balance between capillarity and effective acceleration created at the impact,41 following the scaling law Rmax/R0 ∼ We1/4. In Figure 9, although the overall trend follows this scaling, there is a clear difference in Rmax on each surface at high We numbers; i.e., the maximal spreading ratio is largest on SHPo, followed by SO and KR. Please note that there is no observable influence of oil viscosity on the maximal spreading ratio on SO surfaces. This finding can be explained by taking the viscous dissipation inside an oil layer into account. To the first approximation, the viscous dissipation inside the drop is expressed as ∫ ηw(∂U/∂y)2dV ∼ ηw[(U − Uoil)/h]2hRmax2, while that inside an oil layer is expressed as ηo(Uoil/t)2tRmax2, where ηw and ηo are the water viscosity and oil viscosity, respectively,
Figure 8. Development of instability at the rim during the spreading stage (scaling bar = 1 mm). 8405
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U and Uoil are the average drop spreading velocity and oil velocity, respectively, and h and t are the water drop thickness and oil layer thickness, respectively. The stress continuity at the water−oil interface is dictated as ηw(U − Uoil)/h ≃ ηoUoil/t. Then, the ratio of the viscous dissipation inside an oil layer to that inside the water drop is expressed as [(ηo(Uoil/t)2tRmax2)/ (ηw[(U − Uoil)/h]2hRmax2)] ≈ [Uoil/(U − Uoil)] ≈ (ηwt/η0h) ≪ 1, where the last inequality is always satisfied in the present study. This relation clearly shows that the viscous dissipation inside the oil layer during the spreading stage remains negligible compared to that inside the water drop, which explains why there is no oil viscosity effect on the maximal spreading radius. On the other hand, the effective slip length δ reaching up to tens of micrometers42 is induced on SHPo because of the composite interface of liquid−solid and liquid−air interfaces of the surface, which results in the sizable amount of frictional drag reduction during spreading. In the presence of slippage, the viscous dissipation inside the water drop would be reduced roughly by a factor of 1/(1 + δ/h), which indicates that the larger frictional drag is expected at the higher We number because of the decrease of the drop thickness h. Please note that the increase of the maximal spreading radius on SHPo because of the frictional drag reduction at the high We was also demonstrated with complex fluids in the recent study.43 Meanwhile, on KR, additional energy cost is diverted in creating new surfaces in the form of elongated filaments at the rim, which results in the noticeable decrease of the maximal spreading radius on KR.
Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, Information and Communications Technology (ICT), and Future Planning (2012R1A1A1014845).
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4. CONCLUSION In this study, we experimentally investigated the drop impact dynamics on oil-infused surfaces and demonstrated how physical properties of the infused oil and the Weber number affected various fluid phenomena observed during drop impact. Although the oil viscosity had the limited influence on the radius change of the water drop during spreading and retraction, it had a pronounced effect on the stability of the oil layer by the impacting drop, which was manifested by a residual mark on the impact location and prompt splashing. Also, because of the liquid (water)−liquid (oil) interaction on oil-infused surfaces, several instabilities were found to develop at high We numbers, revealing the flower-like pattern during retraction or elongated filaments at the rim, the latter of which particularly contributed to the decrease of the maximal spreading radius. Our findings demonstrate that, depending upon physical properties of the lubricant oil and impact conditions, various complex fluid phenomena occur on oilinfused surfaces during drop impact, which should be considered in the rational design of oil-infused surfaces for many applications, where drop impact phenomena frequently occur.
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REFERENCES
AUTHOR INFORMATION
Corresponding Authors
*Telephone: +82-2-300-0292. E-mail: [email protected]. *Telephone: +82-31-201-3652. E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by the 2014 Korea Aerospace University Faculty Research Grant and the Basic Science 8406
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