Article pubs.acs.org/Langmuir
Rapid Bouncing of High-Speed Drops on Hydrophobic Surfaces with Microcavities Rui Zhang, Pengfei Hao, and Feng He* Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China ABSTRACT: Artificial hydrophobic surfaces that can induce rapid drop detachment have many significant engineering applications from self-cleaning to anti-icing. In the present study, we found that hydrophobic surfaces with microcavities can rapidly induce a centerassisted recoil of high-speed impacting drops and subsequently result in an approximately 40% reduction in contact time compared with conventional superhydrophobic surfaces. More intriguingly, the contact time on these surfaces has a rapid descent of over 50% at high-speed impacts compared with that at low-speed impacts, which is due to the rapid bouncing induced by the faster retraction of the liquid lamella triggered by the instability of air bubbles beneath the center of the colliding drops. We believe that these findings will provide a valuable strategy for designing self-cleaning and anti-icing surfaces by minimizing the contact time of high-speed drops.
1. INTRODUCTION Droplet impact has essential applications in engineering and everyday life, including self-cleaning and anti-icing and in inkjet printing, surface coating, spray-cooling, pesticide spraying, and forensic science.1−10 Extensive investigations have been made on the dynamics of the collision between drops and hydrophobic structured surfaces since decades ago, owing to the rapid development in the fabrication techniques.11−14 The physics underlying droplet impact is characterized by the delicate interplay of not only liquid inertia, viscosity, and surface tension15,16 but also the surface wettability and roughness,17−21 together with the ambient pressure.20−23 Drops impacting on superhydrophobic surfaces are found to bounce off rapidly owing to the low friction and adhesion. Normally the drop bounces on superhydrophobic surfaces with circular symmetric shapes, in which the contact time is found to be a function of the drop mass but independent of the impact speed.24,25 This is a time bounded below by the oscillating period of a freely vibrating drop, that is, the Rayleigh time.26,27 Therefore, there has been substantial efforts to decrease the contact time of an impacting drop. The so-called pancake rebound has been caught sight of when the impacting droplet spreads along the textured surface but subsequently rebounds at the maximum extension in a pancake shape before it retracts,28−30 resulting in an approximately 80% reduction in the contact time. Many studies have shown that cleverly constructing patterned superhydrophobic surfaces with ridges 1 order of magnitude smaller can help reduce the contact time.31−33 These surfaces, which are motivated by some leaves and butterfly wings, can introduce asymmetric bouncing and break the droplet into smaller pieces. Moreover, drops impacting on asymmetric surfaces with convex or concave macrotextures comparable to the drop size were found to © 2016 American Chemical Society
display asymmetric bouncing with a 40% reduction in contact time compared to that on an equivalent smooth surface.34 Apart from equipping varied surface structures, the rapid drop bouncing could also be promoted by the maintenance of the air layer between the drop and the surface either by using a soft and smooth interface with small energy dissipation or by controlling the phase change process.35−42 All of these experiments were performed using droplets with a small velocity of less than 2 m/s. However, vehicles, aircrafts, and buildings usually face raindrops with a much faster speed. The water repellency of high-speed drops should therefore be further investigated on natural and artificial nonwetting surfaces. In consideration of high-speed impacts, hydrophobic surfaces with closed microcavities were previously found to have a better water repellency than their micropillared counterparts.43 In this work, considering drops with a high velocity (3.9 m/s < U < 6.4 m/s), we show that the employment of microcavities on hydrophobic surfaces can effectively result in a nearly 40% reduction in contact time compared with traditional superhydrophobic surfaces. Interestingly, the contact time of colliding drops on these surfaces not only depends on the drop mass but also depends on the drop speed. The contact time on hydrophobic surfaces with microcavities undergoes a striking decrease of over 50% at high-speed impacts.
2. EXPERIMENTAL SECTION 2.1. Material Preparation and Wetting Property Measurement. Here, we report experiments in which water drops are released Received: July 17, 2016 Revised: August 16, 2016 Published: September 6, 2016 9967
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Langmuir with varied velocities on hydrophobic surfaces with microcavities and superhydrophobic silicon surfaces were used as a control group. The microtextured substrates were fabricated using standard photolithography technology and etching of inductively coupled plasma (ICP) as shown in Figure 1a. The etched silicon wafers with
Figure 2. Schematic diagram of experimental equipment. at the collision moment. The experiments were repeated at least three times for each condition. After each experiment, the substrate was dried using an air blower to remove the residual water drops.
Figure 1. Scanning electronic micrograph (SEM) of the prepared surfaces. (a) Microcavity surfaces: the wall thickness, spacing, and depth of the cavities are 3, 20, and 40 μm, respectively. (b) Superhydrophobic silicon surfaces coated with nanoparticles.
3. RESULTS 3.1. Drop Dynamics. Investigation of the dynamics of the drops with varied velocities impacting on hydrophobic surfaces with microcavities is shown in Figure 3. As shown in Figure 3a, low-speed (U0 = 1.4 m/s) drops collide with the surface with little deformation, spreading to the maximum extension, and retracting and bouncing in an approximately isotropic pathway. At a medium impact velocity (U0 = 3.5 m/s) indicated by Figure 3b, air bubbles begin to appear at the collision position. Low-speed drops undergo a longer collision with the surface, with a contact time of over 13 ms. As the velocity increases, instabilities arise at the rim of the liquid lamella and fingers develop during the impact process. At the high impact speed (U0 = 5.6 m/s) shown in Figure 3c, the air bubbles at the central region became larger. Instability develops rapidly, and the liquid lamella recedes, with the rim breaking up into smaller pieces. A hole appears at the central air bubble region at 2.6 ms and grows during the retraction of the liquid film, resulting in the rapid bouncing of smaller drops off the substrates. The contact time is defined here as the time period from the first contact to the moment when the last drop of the smaller droplet bounces off the surface. It was estimated by investigating the high-speed snapshots captured from the side-view (see the first row in Figure 3c) and seeking the frame when all the smaller drops have just completely bounced off. The high-speed drops rapidly bounce off the surface at 6.4 ms with a reduction of approximately 50% in the contact time. A typical and classical method to express the drop-impact dynamics is to plot the evolution of the nondimensional spreading diameter over time. Because of the approximate axisymmetric property of the impact dynamics, we plot the azimuthal-averaged nondimensional spreading diameter of drops colliding with varied surfaces prepared (see Figure 4). Previous studies found that the contact time of a bouncing drop on superhydrophobic surfaces with a circular symmetric shape was a function of the inertial-capillary timescale τ ≡ ρR3/σ .24,46 Therefore, we demonstrate the contact time in our experiments relative to τ, as plotted in Figures 4 and 5a. The drops with a velocity of 1.4 and 3.5 m/s impacting on the hydrophobic microcavity surfaces undergo a similar dynamic pathway (see red squares and green circles in Figure 4): They first spread to 2.4 or 4.0 times of its initial diameter and then retract at an approximately constant velocity, slowing down later because of the deformation of the drop (in
microcavities were first cleaned thoroughly with piranha solution (volume ratio: H2SO4/H2O2 = 3:1) stewing in a water bath at 90 °C for 30 min. Then, the materials were carefully cleaned with deionized water three times, before being dried using an air blower. The textured silicon wafers immersed in the octadecyl trif luoro silane (OTS)/ hexadecane solution (volume ratio: OTS/hexadecane = 1:250) were placed in a desiccator chamber for 20 min. After being immersed in trichloromethane for 15 min, the residual OTS solution on the silicon surfaces was washed away. To further wipe off the excess trichloromethane residue, the materials were placed in ethanol for another 30 min. Finally, the materials were dried and preserved properly. The contrasted smooth silicon wafers were first cleaned with absolute ethyl alcohol. After the substrates were carefully dried in a desiccator, the wafers were immersed in a hydrophobic nanoparticle solution (wt 85%−90% isopropyl alcohol, wt 0.1%−3% silica, and wt 10%−15% liquified petroleum gas) (made in Japan)44,45 for 5 min before being placed in a desiccator chamber (150 °C) for 2 min. Then, they were immersed in the nanoparticle solution for another 5 min. This procedure was repeated three or more times until the hydrophobicity of the substrates was effectively improved. The microscopic morphology of the superhydrophobic surfaces is shown in Figure 1b. The static and the dynamic contact angles on the substrates were measured from water drops (with a needle) of 5 μL using a standard contact angle goniometer. The apparent contact angle and the contact angle hysteresis of hydrophobic surfaces with microcavities are 131.2° ± 5.6° and 12.6° ± 4.4°, respectively. The apparent contact angle and the contact angle hysteresis of superhydrophobic smooth silicon surfaces are 156.4° ± 2.6° and 3.9° ± 1.4°, respectively. These values were averaged from three measurements. 2.2. Experimental Procedure. Deionized water droplets of millimetric size (D0 = 2.2−2.9 mm) at room temperature (25 ± 1 °C) were generated from fine capillary tubes of various diameters which were equipped with a syringe pump, at varied heights to vary the impact speed (from 1 to 6.5 m/s) before falling onto the sample substrates, as shown in Figure 2. The impact velocity ranges from 1 to 6.5 m/s, corresponding to 3000 < Re < 14 500 and 50 < We < 1250. Here, Re = ρD0U0/μ is the Reynolds number and We = ρD0U02/σ is the Weber number, where D0 is the drop diameter, ρ is the liquid density, U0 is the impact velocity, μ is the liquid viscosity, and σ is the liquid−gas surface tension. The dynamic process of drop impact was recorded using a high-speed camera (FASTCAM Mini UX100, Photron) at a frame rate of 8000 fps with a shutter speed of 1/40 000 s. The drop size and position were measured during each experiment to assure the drop size and to calculate the impact velocity 9968
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Figure 3. Impact dynamics between hydrophobic surfaces with microcavities and drops with varied velocities. (a)−(c) Selected high-speed side-view snapshots and 45° top-view images of a drop (D0 = 2.2 mm) impacting on hydrophobic microcavity surfaces at U0 = 1.4, 3.5, and 5.6 m/s, respectively. The scale bar is 2 mm.
The investigation of the collisions between drops with a speed of 5.6 m/s and hydrophobic surfaces with microcavities reveals a quite different recoiling mechanism (see blue triangles in Figure 4). The drop spreads at a faster speed to its maximum wetted area, over a much shorter dimensionless time of tS = 0.36. Then, the outer rim recoils at a nearly constant rate (see blue solid triangles in Figure 4), faster compared to that with smaller velocities. After a time interval of tR1 = 0.14 from retracting, a hole forms and grows at a speed greater than that of the receding outer edge, as indicated by the blue open triangles in Figure 4. The newly formed inward rim recoils outward and meets the outer periphery of the retracting lamella after a time interval of tR2 = 0.9. At this moment, all smaller droplets bounce off the surface, at a nondimensional time scale of t2 ≈ 1.4τ. The reduction in the contact time compared with that of low-speed impacts on the same microcavity surfaces is approximately Δt = t1 − t2 ≈ 1.8τ. 3.2. Contact Time. Results from previous experiments indicate that the minimum contact time for low-speed drop impacts can be approximated by the formula tc/τ = π / 2 ≈ 2.2 . 24,27−31 Therefore, we compare the contact time of impact drops on hydrophobic surfaces with microcavities with tc (see Figure 5a). Experimental results of the contact time between drops of varied sizes (D0 = 2.2 and 2.9 mm) and microcavities with different spacings (20 and 40 μm) are plotted as a function of the impact velocity in Figure
Figure 4. Effect of the center-assisted recoil on drop-bouncing dynamics. (a) Evolution of the dimensionless contact line position with varied velocities on hydrophobic surfaces with microcavities. Red squares, green circles, and blue triangles indicate the impact velocity of 1.4, 3.5, and 5.6 m/s, respectively. The solid and open triangle markers indicate the contact line positions due to traditional recoil from the periphery and the center-assisted recoil from inward, respectively (see insets). The different time scales (tS, tR1, tR2, and Δt) are relevant to our explanation. The contact time has an effective reduction of Δt at high-speed impacts.
pyramidal shape), which no longer resembles a liquid lamella.28 The drops with low and medium speeds recede and bounce off the surface intact at approximately t1 ≈ 3.2τ. 9969
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off intact. The bouncing dynamic process lasts longer (approximately 2.6τ in accordance with the data in refs 24 and 27) at a low-speed impact of less than 4.5 m/s, whereas the contact time becomes fluctuating slightly below the critical time scale tc, when increasing the speed over 4.5 m/s. On hydrophobic surfaces with microcavities, the contact time of identical experiments is much longer than that on superhydrophobic surfaces at a low speed (U < 4 m/s). When the velocity exceeds some specific value of Uc, the contact time gradually decreases and attains a new approximate critical value of tc/τ ≈ 1.35, which results in a contact time reduction of approximately 40%. This is caused by the hole formation and the center-assisted recoil as shown in Figure 3c, which results in the fragmentation of the main drop into smaller pieces. Because of the shrinking of the drop size (R), the contact time
(t ≈ ρR3/σ ) is shortened accordingly. 3.3. Effect of the Cavity Spacing and Depth. The drop collision experiments were performed on hydrophobic surfaces with microcavities of varied spacing and depths. The substrates designed in this work include four kinds of depths: 5, 10, 27, and 40 μm. The cavities have a series of spacing ranging from 6 to 70 μm. The liquid film rupture and the center-assisted recoil at high-speed impact do not occur on every substrate. The center-assisted recoil is found only on substrates with a depth of 27 and 40 μm. The experimental results of the drop impact at a velocity of 5.6 m/s is plotted in Figure 6a. The rupture of the liquid film occurs on substrates with both large depth and large spacing. Besides, the depth also confines the increment of the spacing, which indicates that the ratio between the spacing and the depth could not be too large. The smallest impact velocity when holes begin to form is named the critical impact velocity in this study. Experiments showed that the critical impact velocity is not greatly influenced by the spacing of the cavity at the same depth, as shown in Figure 6b. Because all the substrates reported in Figure 6b have the same solid fraction (defined as the relative area of the top of the microstructure to the apparent surface area), the volume of gas stored in the cavities of the same depth is similar. Therefore, the air bubbles that arise at the collision position would share a similar volume, which results in a perturbation similar to the liquid lamella. Thus, the critical impact velocities on microcavities with the same depth and varied spacing are roughly the same.
Figure 5. Effect of the center-assisted recoil on the contact time. (a) Dimensionless contact time of colliding drops of different sizes on varied substrates as a function of the impacting velocity. Red squares, green circles, and blue triangles indicate drops (D0 = 2.2 or 2.9 mm) impacting on microcavities with a spacing of 20 or 40 μm, respectively; black diamonds refer to drops (D0 = 2.2 mm) impacting on superhydrophobic silicon surfaces. (b) Selected high-speed side-view and 45° top-view images of a drop (D0 = 2.2 mm) impacting on superhydrophobic silicon surfaces at U0 = 5.6 m/s. The scale bar is 2 mm.
5a. To account for the rapid-bouncing effect at high speeds, we also compare the data with those on superhydrophobic smooth silicon surfaces (see black diamonds in Figure 5a). The superhydrophobic silicon wafers were uniformly coated with the nanoparticles (with a contact angle of 156.4° ± 2.6° and a contact angle hysteresis of 3.9° ± 1.4°). The microscopic topography of the surface is presented in Figure 5b. The dynamics of a drop (D0 = 2.2 mm and U0 = 5.6 m/s) impacting on superhydrophobic silicon surfaces is demonstrated with selected snapshots in Figure 5b. On superhydrophobic silicon surfaces, the main drop spreads to the maximum diameter rapidly, then retracts promptly in an approximately axisymmetric pathway and eventually bounces
Figure 6. Effect of cavity spacing and depth on the hole formation inside of the liquid lamella. (a) Outcomes of drop impacts on hydrophobic surfaces with various spacing and depths. The black squares and red circles indicate the experiments with the unbroken drop and the liquid film rupture, respectively. The green and yellow colors show the partition between stable and unstable of the liquid lamella. (b) Evolution of the critical impact velocity of drops with the cavity spacing at a depth of 40 μm. Experimental results demonstrate a similar value of critical impact speed for various spacings. 9970
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Figure 7. Schematic drawings illustrating the center-assisted recoil on microcavity surfaces. (a) Side-view diagrams demonstrating the entrapment of air bubbles and the formation of a hole. (b) Top-view diagrams illustrating the center-assisted recoil and rapid bouncing. (c) 45° Top-view snapshots of a drop-impact experiment (D0 = 2.2 mm, U0 = 5.6 m/s) on microcavity surfaces.
4. DISCUSSIONS 4.1. Center-Assisted Recoil. To interpret the dynamic mechanisms of the center-assisted recoil on hydrophobic surfaces with microcavities, a group of schematic diagrams are drawn, demonstrating the collision process between the drop and the surfaces as shown in Figure 7a,b. We attribute this center-assisted recoil to the air bubbles entrapped at the center between the liquid lamella and the microcavities. Microcavities can preserve the gas inside at the collision moment. Figure 7a shows the cross-sectional diagrams of the drop impacting on the microcavity surfaces. The drop drives some air into the microcavities during the collision and leads to the pressure increment. Then, the gas−liquid interfaces inside the cavities undergo a damping vibration process,43 before stopping above the top of the structure. The air entrapped by the impact bubble together with the oscillation of the air stored in the cavities results in the air bubble region. The volume of the air bubble grows with the impact velocity, according to our investigation. A small air bubble can induce only a little destabilization to the liquid film. When the size of the air bubble is comparable with the dynamic thickness of the liquid lamella, the perturbation magnifies, resulting in the appearance and growth of a hole. Figure 7b shows the top-view drawings of drop collisions illustrating this intriguing process, including colliding, spreading, recoiling, and bouncing. The selected 45° top-view snapshots corresponding to each picture in Figure 7a,b are shown in Figure 7c, respectively. A hole arises at the central air bubble region at 2.6 ms and grows during the receding process. The outer rim of the retracting liquid film continues to recoil inward, whereas the inner rim of the lamella recoils outward. When these two edges meet each other, the lamella converges into smaller drops, which rapidly bounce off the surface at 6.4 ms. Only when the hole forms, the contact time of high-speed drops could be reduced. Not much difference is found in the contact time of high-speed impacting drops, as shown in Figure 5a, which seems to have a lower limit, whereas the initial size of the holes formed increases with increase in the impact velocity just as the central air bubble.
Therefore, the size of the initial holes does not greatly influence the contact time of high-speed drops. Because the rate of movement of the liquid film is changing radially when the liquid at the perimeter begins to recede, the central liquid is still advancing. Therefore, holes always form during the retracting process because the thickness of the film is still decreasing during the initial stage of recoiling. The formation of holes greatly modifies the retracting dynamics of the liquid lamella. The retracting velocity of the liquid rim at the periphery (see blue solid triangles in Figure 4) is smaller (about 0.77 m/s) than that of the central rim (see blue open triangles in Figure 4; approximately 1.50 m/s) because of the existence of central air bubbles that attenuate the liquid lamella. Because the retracting speed of the film Vr ≈ 2σ /ρh increases with decreasing thickness h, the velocity of the interface inside of the lamella is greater than that of the rim. 4.2. Stability Analysis of the Liquid Film with Initial Holes. Hole formation can be observed in high-speed jet flows and drop impacts on rough surfaces. Holes are supposed to be induced by air bubbles entrapped at the liquid−solid interface or surface protuberances at high impact speed, and the size of the hole increases with the surface roughness.47 On rough superhydrophobic surfaces with Ra = 1.25 μm, the hole formation was found to be minimal even at Re = 11 600 (D0 = 580 μm and U0 = 20 m/s) and first appeared at Re = 17 400 (D0 = 580 μm and U0 = 30 m/s).47 However, on textured surfaces with microcavities in our experiments, the critical hole formation Re was effectively decreased to Re ≈ 9000 (U0 ≈ 4 m/s for a drop with D0 = 2.2 mm) because of the air bubble entrapment at the center by the microcavities. This is because high-speed drops impacting on rough surfaces would inevitably entrap air bubbles beneath themselves, and these air bubbles would become unstable factors that disturb the liquid lamella during the collision process. Larger air bubbles would lead to larger initial holes, which would grow more easily, and result in the rupture of the liquid lamella. Hydrophobic surfaces with microcavities could preserve the gas inside of the cavities at the collision position and result in the central air bubble region, 9971
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Langmuir owing to the effect of the “gas spring”.43 The size of the air bubbles on surfaces with microcavities is effectively enlarged compared with that on superhydrophobic surfaces with a micron-scale roughness. Therefore, the hole-formation conditions (such as critical Re and U0) can be decreased on the microcavity hydrophobic surfaces when compared with rough superhydrophobic surfaces. When a hole forms, it can either grow, which results in the rupture of the liquid film, or die out. Sharma et al. (1989) promoted a stability analysis method to predict the dewetting process of solid surfaces by the hole formation in liquid lamella.48 They came to a conclusion that the minimum critical film thickness hc was an implicit function of the hole radius r1 and the contact angle θ.48,49 The nondimensional form could be written as
Figure 8. Exponential curve fitting of the relation between the maximum spreading factor and the Reynolds number. Red stars indicate the experimental data, and the blue line indicates the fitted curve.
⎛ h* 1 ⎞ ⎛ h* ⎞ 1 (1 − cos θ )2 ⎡ ⎢cosh⎜2 c ⎟ 2⎜ c ⎟ =1+ 2 * ⎢⎣ sin θ ⎝ r1* sin θ ⎠ ⎝ r1 ⎠ sin θ ⎛ h * 1 ⎞⎤ ⎟⎥ − sinh⎜2 c ⎝ r1* sin θ ⎠⎥⎦
obtained the relationship between critical Reynolds number Rec and the dimensionless radius r1* of the hole (see the solid line in Figure 9a). We can infer that the liquid lamella would be vulnerable to larger holes at a small impact Re. Above the theoretical critical line of Rec, the liquid film is unstable and the film rupture occurs, whereas below the critical line, the hole does not grow with the liquid lamella remaining intact. Hole formation always occurs at the center of the liquid film on our substrates. Air bubbles at the central region are the original manifestations of small holes. Then some of these small holes grow, which results in the rupture at the center of the liquid film, whereas others retain their initial shape until overlapped by the receding liquid rim. Therefore, the radius of the air bubble in the center indicates the initial radius of the hole. Each experimental result is plotted in Figure 9a, with red stars indicating the rupture and blue crosses indicating the recovery of the recoiling liquid film. As Figure 9a reveals, the experimental results of rupture and recovery are just located on the two sides of the theoretical line of Rec, which is well interpreted by our model. To consider the effect of the receding contact angle θr on hole formation, the critical Reynolds number Rec is plotted as a function of the receding contact angle θr for varied values of nondimensional hole radius r*1 = 0.05, 0.1, and 0.15 (see Figure 9b). It can be summarized that substrates with low and high receding contact angles are more stable than those with a medium receding contact angle, with a higher critical Reynolds number Rec. The experimental data in which the initial holes grow are scattered, with red circles and blue crosses indicating the experiments with 0.05 < r1* < 0.1 and 0.1 < r1* < 0.15, respectively. Inspection of Figure 9b reveals that the experimental data with film rupture are all located in the unstable region in the diagram of Rec ≈ θr and the smallest unstable Reynolds number Rec appears at the receding contact angle of θr ≈ 125°, which just resembles that of the substrates with microcavities in our experiments. Therefore, the initial small holes on our substrates are more likely to induce the liquid film rupture and the center-assisted recoil as a result. We could use these diagrams to predict the critical conditions when holes forming at the liquid−solid interface grow in similar liquid−solid collision experiments.
(1)
where h*c = hc/D0 and r*1 = r1/D0. When a hole of radius r1 formed, films with thickness below hc would be unstable and were likely to rupture. Applying this stability criterion to dropimpact dynamics, estimating the liquid film thickness using a thin disc approximation h = 2D0/3β2, expressing β as a function of Re, and substituting θ with the receding contact angle θr,49 we obtain the critical Reynolds number Rec at which the holes at the liquid−solid interface would grow and the liquid film would rupture ⎛ 4 (1 − cos θr)2 ⎡ 4 1 1 ⎞ ⎢cosh⎜ 2 ⎟ 1 = + 2 * 2 ⎢⎣ 3β ·r1 sin θr sin θr ⎝ 3β ·r1* sin θr ⎠ ⎛ 4 1 ⎞⎤ ⎟⎥ − sinh⎜ 2 ⎝ 3β ·r1* sin θr ⎠⎥⎦
(2)
Here β = Dmax/D0 is the maximum spreading factor, indicating the ratio between the maximum spreading diameter and the initial diameter of a drop. A great deal of explorations have been made on the relationship between the maximum spreading factor β and the impact parameters. Various exponential formulas have been developed based on the balance among inertia, viscosity, and capillary forces. Using the viscous regime, the relation could be simplified as β − 1 ∝ Re0.2.50 The inertial regime leads to the scaling law of β ∝ We0.25.50 All these models agree well with the experimental data, and it is hard to discriminate among them. To express the maximum spreading factor on hydrophobic surfaces with microcavities in our experiments, we fitted the maximum spreading factor β as an exponential function of Re using the least-squares method as shown in Figure 8. The relationship between β and Re in our experiments can be expressed as β = 0.51Re 0.30 − 3.0
(3)
5. CONCLUSIONS An intriguing phenomenon of the center-assisted recoil was presented in this paper on hydrophobic surfaces with closed microcells at high-speed collisions, which effectively reduced the contact time between liquid and solid surfaces. The central
Substituting eq 3 in eq 2, we can obtain the critical Reynolds number Rec of impact in our experimental conditions as an implicit function of the hole radius r*1 and the receding contact angle θr. Because the receding contact angle of the hydrophobic surfaces in our experiments is approximately 124.9° ± 5.0°, we 9972
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Figure 9. Prediction of the critical Reynolds number Rec of impact, above which the hole would grow. (a) Evolution of the critical Reynolds number Rec with the dimensionless initial radius r1* of the hole. Red stars refer to the rupture of the liquid film due to hole growth; blue crosses indicate the integrity of the liquid lamella when the holes close without growth. (b) The critical Reynolds number Rec versus the receding contact angle θr for varied nondimensional hole radii r1*. The dispersion points demonstrate the results with film rupture: blue circles (0.05 < r1* < 0.1) and red crosses (0.1 < r*1 < 0.15), all located in the unstable region. The smallest unstable critical Reynolds number Rec appears at the receding contact angle of θr ≈ 125°, which coincides with that of the microcavity surfaces in our experiments. (6) Minemawari, H.; Yamada, T.; Matsui, H.; Tsutsumi, J.; Haas, S.; Chiba, R.; Kumai, R.; Hasegawa, T. Inkjet printing of single-crystal films. Nature 2011, 475, 364−367. (7) van Dam, D. B.; Clerc, C. L. Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys. Fluids 2004, 16, 3403−3414. (8) Roisman, I. V.; Horvat, K.; Tropea, C. Spray impact: Rim transverse instability initiating fingering and splash and description of a secondary spray. Phys. Fluids 2006, 18, 102104. (9) Attinger, D.; Moore, C.; Donaldson, A.; Jafari, A.; Stone, H. A. Fluid dynamics topics in bloodstain pattern analysis: Comparative review and research opportunities. Forensic Sci. Int. 2013, 231, 375− 396. (10) Li, J.; Luo, Y.; Zhu, J.; Li, H.; Gao, X. Subcooled-water nonstickiness of condensate microdrop self-propelling nanosurfaces. ACS Appl. Mater. Interfaces 2015, 7, 26391−26395. (11) Liu, T. L.; Kim, C.-J. C. Turning a surface superrepellent even to completely wetting liquids. Science 2014, 346, 1096−1100. (12) Tuteja, A.; Choi, W.; Mabry, J. M.; McKinley, G. H.; Cohen, R. E. Robust omniphobic surfaces. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 18200−18205. (13) Reyssat, M.; Pardo, F.; Quéré, D. Drops onto gradients of texture. Europhys. Lett. 2009, 87, 36003. (14) Lembach, A. N.; Tan, H.-B.; Roisman, I. V.; GambaryanRoisman, T.; Zhang, Y.; Tropea, C.; Yarin, A. L. Drop impact, spreading, splashing, and penetration into electrospun nanofiber mats. Langmuir 2010, 26, 9516−9523. (15) Josserand, C.; Thoroddsen, S. T. Drop impact on a solid surface. Annu. Rev. Fluid Mech. 2016, 48, 365−391. (16) Yarin, A. L. Drop impact dynamics: Splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 2006, 38, 159−192. (17) Shen, Y.; Tao, J.; Tao, H.; Chen, S.; Pan, L.; Wang, T. Relationship between wetting hysteresis and contact time of a bouncing droplet on hydrophobic surfaces. ACS Appl. Mater. Interfaces 2015, 7, 20972−20978. (18) Schutzius, T. M.; Graeber, G.; Elsarkawy, M.; Oreluk, J.; Megaridis, C. M. Morphing and vectoring impacting droplets by means of wettability-engineered surfaces. Sci. Rep. 2014, 4, 7029. (19) Range, K.; Feuillebois, F. Influence of surface roughness on liquid drop impact. J. Colloid Interface Sci. 1998, 203, 16−30. (20) Latka, A.; Strandburg-Peshkin, A.; Driscoll, M. M.; Stevens, C. S.; Nagel, S. R. Creation of prompt and thin-sheet splashing by varying surface roughness or increasing air pressure. Phys. Rev. Lett. 2012, 109, 054501. (21) Xu, L.; Barcos, L.; Nagel, S. R. Splashing of liquids: Interplay of surface roughness with surrounding gas. Phys. Rev. E 2007, 76, 066311. (22) Liu, Y.; Tan, P.; Xu, L. Kelvin−Helmholtz instability in an ultrathin air film causes drop splashing on smooth surfaces. Proc. Natl. Acad. Sci. U.S.A. 2015, 112, 3280−3284.
air bubbles trapped at the collision moment are found to trigger the formation of holes in the center of the liquid film and effectively modify the retraction dynamics of the drop impacts. At certain conditions, holes that are large enough can grow whereas small ones die out. It is concluded that hydrophobic surfaces with microcavities used in the present study are in the most unstable state under high-speed impacts. Holes on these surfaces are more likely to occur and grow. Drops impacting at high speeds on these surfaces could achieve an approximately 50% reduction in the contact time compared with those with low-speed impacts. Unlike in previous studies on surfaces with macrotextures, our substrates could be designed to reduce the contact time of high-speed colliding drops independent of the collision position. This could be of great value for applications where suppressing wetting under high-speed impacts is beneficial, such as the design of self-cleaning and anti-icing surfaces.
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*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to Cunjing Lv for helpful discussions. We acknowledge support from National Natural Science Foundation of China (Grant No. 11072126, 111721156).
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