Drop Impact on Oblique Superhydrophobic Surfaces with Two-Tier

Mar 22, 2017 - The comparison of the capillary emptying time of the tail, center, and front positions of the drop in each case is also plotted in the ...
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Drop Impact on Oblique Superhydrophobic Surfaces with Two-Tier Roughness Rui Zhang, Pengfei Hao, and Feng He* Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China ABSTRACT: This paper investigates the complex physical phenomenon of oblique drop impact on superhydrophobic substrates with two-tier roughness (patterned with varied submillimeter-scale posts and coated with nanoparticles). Experimental results show that the impact Weber number of drops and the solid fraction of the submillimeter-scale post structures are crucial for the outcomes of oblique drop collisions. Water droplets with 10 < Wen < 245 are found to rebound on all the test substrates. As the surface solid fraction decreases, four possible bouncing patterns occur in sequence: sliding rebound, stretched rebound, penetration rebound, and breakup rebound. We demonstrate that the stretched rebound, in which the drops bounce off the surface rapidly in an elongated shape without tangential retraction, allows a 10%∼30% reduction of contact time compared with conventional sliding rebound on oblique surfaces. Three types of stretched rebound are observed on substrates with moderate solid fraction (0.1 < φ < 0.5), in which the liquid detachment starts from front, center, and tail, respectively. A simple analytical argument is presented to explain the occurrence of distinct patterns. These findings are believed to provide valuable guidance to the design of self-cleaning and antiicing surfaces under oblique liquid impacts where rapid drop shedding is profitable.

1. INTRODUCTION The study on the collision between liquid drops and solid surfaces has a history of over a hundred years.1,2 Much research has been done on the perpendicular drop impacts on solid surfaces with varied morphology to reveal the complicated physical mechanism behind this delicate interplay among liquid, gas, and solid.3−16 However, in most engineering problems, the liquid impingement on moving vehicles, turbine blades, and crop leaves is oblique. It is important to study the drop impact behaviors on inclined solid surfaces to promote self-cleaning and prevent ice accretion.17−19 Owing to the rapid development of the micro- and nanoassembly technique, superhydrophobic surfaces with a variety of textures have been fabricated to achieve better mechanical and pressure stability under liquid impingement,20−24 except for the interesting hydrodynamic focusing or inversed Leidenfrost phenomenon observed on nanofiber surfaces.24−28 Many researchers have been working on the characteristics of drop impact on superhydrophobic surfaces which can promote rapid drop shedding.29−33 The most effective method proposed so far to achieve rapid drop repelling should be the pancake bouncing with a contact time of ∼0.2τ,34 in which the liquid could directly rebound from a superhydrophobic surface at its maximum extension before lateral retraction.31 This is different from the characteristics of drop bouncing on ordinary superhydrophobic surfaces, in which the receding contact angle and the motion of the contact line play an essential role in the retraction and rebound of colliding droplets.35,36 Pancake bouncing was found to result from the rectification of capillary © 2017 American Chemical Society

energy stored in the penetrated liquid into the upward energy adequate to lift the whole drop and require the application of superhydrophobic surfaces with submillimeter-scale posts decorated with nanotextures,31 which differed from the conventional superhydrophobic textured surfaces with small roughness (100 μm). In this paper, we systematically investigate the intriguing oblique impact dynamics of drops impacting on superhydrophobic surfaces patterned with various submillimeterscale posts decorated with nanoparticles (roughness >100 μm). We found a distinct outcome of stretched rebound with respect to traditional sliding rebound, in which the drops rebound more rapidly without tangential retraction, with a 10%∼30% reduction of colliding time. We attribute the occurrence of stretched rebound to the magnification of the aspect ratio between tangential and horizontal extensions. We also provide a simple analysis to elucidate and discuss the influence of the solid fraction of submillimeter-scale structures on three kinds of distinct stretched bouncing patterns.

cos θC = f (cos θ + 1) − 1

(1)

where θC is the Cassie−Baxter contact angle, θ is the intrinsic contact angle of the flat surface with the same chemical characteristics, and f is the fraction of the solid surface in contact with the liquid. Wenzel proposed another model to predict the wetting behavior of a rough surface, in which the increment of the contact area between the penetrated liquid and the solid tends to improve the hydrophobicity of the surface.57 The Wenzel model is described as follows:

cos θW = r cos θ

2. EXPERIMENTAL SECTION

(2)

where θW is the Wenzel contact angle and r is the roughness factor defined as the ratio of the actual surface area of the solid−liquid contact to the geometric projected area. The experimental contact angles of a 5 μL droplet on the various superhydrophobic surfaces coated with nanoparticles and the theoretical contact angles obtained from both Cassie−Baxter and Wenzel models are plotted as a function of the post spacing, as shown in Figure 2. The rolling angle of a 5 μL droplet on each surfaces are also illustrated in Figure 2. The experimental contact angles of the superhydrophobic surfaces with two-tier roughness locate between the two thresholds of Cassie− Baxter model and Wenzel model. This might result from the partial liquid penetration into the large gaps between pillars, which leads to the hybrid wetting state of the droplet. Thus, the rolling angles of the two-tier superhydrophobic surfaces are found to be much larger than superhydrophobic silicon surfaces with nanoparticles. Besides, the water liquid might also penetrate into the interspace between submicrometer rough features on the top of the pillars and shows a Wenzel-type wetting behavior.58,59 2.2. Experimental Setup. In the present study, the experiments were performed by dripping deionized water droplets with millimetric size (D0 = 1.5 mm ± 0.1 mm) onto the inclined sample substrates tilted at varied angle α, as shown in Figure 3. The droplets were generated from a fine capillary tube which was equipped with a syringe pump. The height of the tube was adjusted to vary the impact speed. The impact velocity ranges from 0.9 m/s to 4.85 m/s, corresponding

2.1. Material Preparation and Performance Measurement. This study focuses on the different impact outcomes by releasing water drops with varied velocities on superhydrophobic silicon surfaces with and without submillimeter-scale posts. The substrates with submillimeter-scale posts were fabricated using standard photolithography technology and etching of inductively coupled plasma (ICP) as shown in Figure 1a. The geometrical parameters of the designed textured surfaces and the silicon surface are shown in Table 1 and Figure 1d describes the schematic diagram of the cross-sectional parameters of

Figure 1. Scanning electronic micrograph (SEM) of the prepared surfaces. (a) Submillimeter-scale post surfaces: the posts have an edge length, spacing, and depth of 100 μm, 100 μm, and 330 μm, respectively. (b) Superhydrophobic surfaces patterned with submillimeter-scale posts coated with nanoparticles. (c) Superhydrophobic silicon surfaces coated with nanoparticles. (d) Cross-sectional parameters of submillimeter-scale post surfaces. 3557

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Table 1. Geometric Parameters of Prepared Surfaces with and without Submilimeter-Scale Posts and Wettability Measurement of the Experimental Substrates Coated with Nano-Particlesa substrate

edge length P (μm)

spacing S (μm)

height h (μm)

solid fraction (before nanotreatment) φ

nano-Si P100S25 P100S50 P100S100 P100S200 P100S300 P100S500

− 100 100 100 100 100 100

− 25 50 100 200 300 500

− 330 330 330 330 330 330

1 0.64 0.444 0.25 0.111 0.063 0.028

contact angle 149.4° 150.8° 152.9° 155.5° 159.4° 157.0° 147.5°

± ± ± ± ± ± ±

contact angle hysteresis

1.2° 1.9° 1.8° 1.6° 1.4° 1.8° 2.1°

10.9° 28.2° 22.3° 27.5° 23.4° 21.2° 20.7°

± ± ± ± ± ± ±

0.5° 1.9° 1.8° 1.5° 0.9° 1.5° 1.4°

Notes: φ is the initial geometric solid fraction of the submillimeter-scale posts without nanocoatings, which is defined as the ratio between the top area of the primary structure and the apparent area of the surface, which indicates φ = P2/(P + S)2 here. The final solid fraction of the substrates after nanoparticle treatment is smaller than the initial geometric solid fraction φ. We just use the initial geometric solid fraction φ to express and emphasize the characteristics of the submillimeter-scale structure, which are essential to the oblique impact outcomes below. a

hydrophobic surfaces with two-tier roughness tilted at an angle of 45°. Investigation of the possible outcomes of drop impact on the inclined prepared substrates is shown in Figure 4. Droplets rebound on every inclined superhydrophobic substrate at normal Weber number ranging from 10 to 245, in four diverse pathways, sliding rebound, stretched rebound, penetration rebound, and breakup rebound. Figure 4a shows the sliding rebound of drops (Wen = 20, D0 = 1.5 mm, U0 = 1.4m/s) impacting on superhydrophobic silicon surfaces coated with nanoparticles. The drop collides with the surface, spreads to a pancake shape, retracts and bounces off the substrate at 6.56 ms in a contracting shape. Due to the existence of the tangential velocity, the collision process occurs together with the drop sliding along the wall and the location of detachment is far from the impinging position, as shown in the last snapshot in Figure 4a. Drops (Wen = 120, D0 = 1.5 mm, U0 = 3.43m/s) colliding with superhydrophobic surface P100S50 (φ = 0.44) bounce off in a stretched shape with a shorter contact time of 4.48 ms, as shown in Figure 4b. As the solid fraction of the substrates decreases, the perturbation of the structure to the liquid strengthens and drops could penetrate into the solid. Low Weber number drops (Wen = 10, D0 = 1.5 mm, U0 = 1m/ s) undergo penetration and capillary emptying24,31,60,61 before bouncing off the substrate P100S200 (φ = 0.111) at 4.8 ms, as shown in Figure 4c, while high-speed drops (Wen = 161, D0 = 1.5 mm, U0 = 3.96m/s) impregnate the structures and break up into smaller pieces before rebounding on substrate P100S500 (φ = 0.028) at 4.16 ms, as illustrated in Figure 4d. Extensive experiments were performed by releasing water droplets with varied Weber numbers impacting on superhydrophobic substrates patterned with submillimeter-scale posts with different solid fractions. Many researchers classify the outcomes of the oblique drop impacts in terms of the Weber number Wen based on the normal component of the impacting velocity (i.e., Wen=ρD0U2n/σ).17,19,44,47 Therefore, we present in Figure 5 the possible patterns of oblique drop collisions as a function of the normal Weber number Wen and the solid fraction φ of the submillimeter-scale structure. A variety of rebound patterns are demonstrated with symbols of varied shapes and colors. The subregions colored in red, yellow, and green indicate the partition between sliding rebound, stretched rebound, and breakup rebound. Sliding rebound tends to occur between superhydrophobic substrates with large solid fraction and drops with low Weber numbers, as shown with the ● in Figure 5. As the solid fraction of the substrates decreases, stretched rebound begins to appear on submillimeter-scale post surface with two-tier roughness (see the green

Figure 2. Evolution of the experimental and theoretical contact angles and rolling angles with the post spacing on superhydrophobic surfaces with two-tier roughness. The blue and green solid lines indicate the experimental data of apparent contact angles and rolling angles of a 5 μL droplet. And the black and red dashed lines signify the theoretical contact angles from the Cassie−Baxter model and Wenzel model, respectively. At the post spacing below 200μm, the Wenzel contact angles could not be figured out, which are not presented here.

Figure 3. Schematic of the experimental equipment. to 1400 < Re < 7300 and 20 < We < 500, respectively. Here Re = ρD0U0/μ is the Reynolds number and We = ρD0U20/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 dynamical process of drop oblique impact was recorded using a high-speed camera (FASTCAM Mini UX100, Photron) at the frame rate of 6250 fps with a shutter speed 1/50000 s. 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 residue of water drops.

3. RESULTS AND DISCUSSION 3.1. Outcomes of Oblique Drop Impact. We observed the oblique collision behaviors of drops with varied normal Weber numbers impacting on different prepared super3558

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Figure 4. Outcomes of drop impact on various inclined superhydrophobic surfaces with α = 45°. (a) Selected side-view snapshots showing drop sliding rebound (Wen = 20, D0 = 1.5 mm, U0 = 1.4m/s) on superhydrophobic silicon surfaces with nanoparticles. (b) Selected side-view high-speed images demonstrating drop stretched rebound (Wen = 120, D0 = 1.5 mm, U0 = 3.43m/s) on superhydrophobic submillimeter-scale post surface P100S50 (φ = 0.44). (c) Selected high-speed images of drop penetration rebound (Wen = 10, D0 = 1.5 mm, U0 = 1m/s) on superhydrophobic submillimeter-scale post surface P100S200 (φ = 0.111) captured from side-view. (d) Selected side-view snapshots of drop breakup rebound (Wen = 161, D0 = 1.5 mm, U0 = 3.96m/s) on superhydrophobic submillimeter-scale post surface P100S500 (φ = 0.028). The red dots indicate the impinging position of the drop, and the blue dot lines manifest the center position of the drop at each instant. The distance from the center of the drop to the impinging position in the last snapshot in Figure 4 (panels a−c) indicates the displacement of the bouncing drop. The scale bars: 1 mm.

Figure 5. Partition map of drop oblique impact outcomes on superhydrophobic surfaces tilted at 45° as a function of impact Weber number and surface solid fraction φ of the primary structure. Six possible experimental results [sliding rebound (with rim breakup), stretched rebound (with rim breakup), penetrated rebound, and breakup rebound] are indicated with different symbols in various colors, as shown in the legend. The experimental data of oblique drop impact on different superhydrophobic surfaces from ref 19 and ref 17 are also plotted in this figure. The four subregions colored in red, yellow, blue, and green indicate four typical patterns of drop bouncing: sliding rebound, stretched rebound, penetration rebound, and breakup rebound. Sliding rebound tends to occur between substrates with large solid fraction (φ > 0.5) and droplets with low impact Weber number. Stretched rebound is observed on substrates with moderate solid fraction (0.1 < φ < 0.5). Impacting drops penetrate the substrates at low Weber number and break up from rim or interior at high Weber number on substrates with very low solid fraction (φ < 0.1). The green dash dotted curve indicates the contour line of e = 50, which is explained below.

★). Larger impact Weber number would lead to the rim breakup of the stretched liquid film as shown with the green ■ in Figure 5. Low Weber number drops penetrate the sparse post arrays on substrate P100S300 and P100S500 with very small solid fraction (φ < 0.1) and bounce off the surface after evacuation (see the red ◆). High Weber number drops are strongly perturbed by the sparse posts and rapidly break up from either interior or rim into pieces (see the red ▲). This bouncing regime on submillimeter-scale posts was named the breakup rebound in our study. There was always some leftover of liquid at the surfaces, however, the liquid residue on most of the tested substrates was very few ( 0.25. As the Weber number increases, the aspect ratios on substrates with φ < 0.5 increase rapidly, which accompanies with the occurrence of the stretched rebound (see the yellow zone). On substrates with the lowest solid fraction (φ = 0.111), penetration rebound occurs at We < 40 and rim breakup appears at Wen ≥ 60. The aspect ratio decreases slightly at Wen ≥ 60, as shown in Figure 9b, which might be caused by the rupture of the liquid rim. On the basis of the above analysis, due to the large collision kinetic energy and appropriate spacing of the posts, the impinging liquid penetrates into the structure of inclined surfaces with two-tier roughness in a stretched bouncing pattern. Since it takes a period of time for the penetrated liquid to evacuate, which was called the capillary emptying process in the previous work,31 the penetrated tail of the drop is pinned at the impinging position for a few microseconds and the drop gradually deforms into an elongated shape. The lateral spreading is confining and the transversal retraction process is accelerated as a result. The droplet is found to rebound rapidly without an obvious tangential retraction, which is reflected by the amplification of the aspect ratio between the drop tangential and horizontal extensions. To better illuminate the regime behind this counterintuitive bouncing behavior, we propose a simple analytical argument to elucidate the stretched rebound observed on superhydrophobic surfaces with two-tier roughness. The deceleration process of the drop impinging moment is dominated by the interaction between inertial force, capillary force, and viscous force. Since the Ohnesorge number in the experiments is 0.0026 which is far less than 1, the effect of the viscous dissipation in our analysis is neglected. Supposing the penetrated area of the surface is independent of the impact Weber number but equivalent to the maximum transversal area of the impacting drop, the drop motion is impeded by the capillary force which could be approximated to Fc ∼ -σ cos D20P/(P + S)2,32,62,63 where D0 denotes the initial diameter of the drop and θ denotes the apparent contact angle of the submillimeter-scale post surface. Since the liquid hitting on top of the structure was immediately stopped by the elastic force from the solid, we suppose the capillary force at the three-phase contact line mainly decelerates the liquid not in direct contact with the top of the solid structure. The deceleration of the liquid could be estimated as ac ∼ Fc/ρD30(1 − φ) ∼ -σφ cos θ/[ρPD0(1 − φ)], where ρ denotes the density of the liquid. Since the depth of penetration of the liquid varies with the position, we suppose the depth of the posts are large enough, which allows the liquid with the deepest penetration to slide downward before contacting the bottom of the substrate. The ideal deepest depth of the drop penetration is expressed as sc ∼ U2n/ac ∼ −Wen[(1 − φ)/φ](P/cos θ), where Un denotes the initial normal velocity of the drop and Wen = ρD0U2n/σ denotes the normal Weber number of the impacting drop. And we obtain the dimensionless depth of penetration sc/P ∼ −(Wen/

e=−

Ec kσD02 P cos θ

= Wen

(1 − φ) φ

2

(3)

where k is a dimensionless factor. The theoretical emptying time scale for the penetrated liquid to release scales as tc ∼ Un/ ac ∼ −ρD0UnP(1 − φ)/(σφ cos θ). The contact time of a bouncing drop on superhydrophobic surfaces scales as τ ∼ ρD03 /σ . Comparing these two time scales, we obtain the nondimensional time scale of the capillary emptying process

n=−

tc τ

j cos θ

=

Wen

1−φ P φ D0

(4)

which scales as Wen , (1 − φ)/φ and P/D0, where j is a dimensionless factor and φ = P2/(P + S)2 denotes the solid fraction of the submillimeter-scale post surface. In our experiments, both the high Weber number of droplets and the small solid fraction of substrates could lead to the direct contact between the liquid with the deepest penetration and the bottom of substrates. However, the ideal dimensionless surface energy stored e could express the maximum surface energy which is possible to be stored by the penetrated liquid and reflect the ability of the upward motion to lift the whole droplet. We found a fitting value of e = 50 according to the boundary line between stretched rebound and other bounding patterns in Figure 5, as shown with the green dash dot line. Besides, the solid fraction of the substrates also confines the occurrence of stretched rebound. Too small solid fraction (φ < 0.1) of the substrates leads to too late completion of capillary emptying of penetrated liquid (large n). Most of the liquid spreads between the post arrays instead of on top of the structure, which results in the rupture of the liquid film (see the red dots in Figure 5). While too large solid fraction (φ > 0.5) would promote too early liquid lifting (small n) which fails to provide enough time for the lateral retraction of liquid lamella, so the liquid film slides along the wall and rebounds in a conventional pathway (see the black dots in Figure 5). Therefore, the stretched rebound locates in the region above the contour line of e = 50 and between the interval of 0.1 < φ < 0.5 in the Wen − φ phase diagram in Figure 5. The receding contact angle and the dynamics of receding contact line was proposed to play an essential role in the drop bouncing dynamics.35,36 However, in the oblique impact on superhydrophobic surfaces with two-tier roughness, no tangential retraction process was observed for the stretched rebound droplets. The drops depart from the surface in the maximum tangential extension shape without retraction along the wall. Thus, the liquid penetration and capillary emptying process, instead of the receding contact angle and the dynamics of receding contact line, becomes the essential factor influencing the rapid drop bouncing in stretched rebound on inclined superhydrophobic surfaces with two-tier roughness. We also measured the maximum tangential spreading diameter of drops on different inclined superhydrophobic surfaces in the experiment and compared the results with the previous normal impact data obtained by Bayer,36 as shown in 3562

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compared with each other. The elevation of the liquid lamella was found to start from distinct positions, shown in Figure 11. On substrate P100S50 with φ = 0.44, a drop (Wen = 120, D0 = 1.5 mm, U0 = 3.43m/s) spreads into a pancake shape, and the tail first departs from the substrate at 2.4 ms, before it completely bounces off the surface at 4.48 ms, as shown in Figure 11a. On substrate P100S100 with a smaller solid fraction φ = 0.25, a drop (Wen = 120, D0 = 1.5 mm, U0 = 3.43m/s) rebounds starting from the center of the stretched liquid film, as illustrated in Figure 11b. Figure 11c exhibits the stretched rebound of a drop (Wen = 40, D0 = 1.5 mm, U0 = 1.98m/s) starting at the front end on substrate P100S200 with the smallest solid fraction φ = 0.111. To better illustrate and analyze the cause of the three types of stretched rebound on superhydrophobic surfaces with twotier roughness, we plot the experimental data as a function of solid fraction and the normal Weber number, as shown in Figure 12a. The experimental data of stretched rebound from tail, center, and front part of the drop are found to locate right above the fitting curves of n = 0.8, 1.6, 3.2, respectively, where 1−φ P n = Wen φ D signifies the nondimensional capillary

Figure 10. The experimental data of dimensionless maximum tangential extension is shown with various solid symbols in

Figure 10. Influence of surface wettability on the maximum tangential drop extension on varied superhydrophobic surfaces. The varied solid symbols indicate the oblique experimental results of dimensionless maximum tangential extension of drops on different superhydrophobic substrates in our experiments. The different open symbols demonstrate the normal impact results on substrates with various wettability from Bayer.36 The solid line represents a regression fit to 0.313 , whereas the the present experimental data Dm/D0 ∼ (RenWe0.5 n ) 0.14 by dashed line depicts the correlation of Dm/D0 ∼ (RenWe0.5 n ) Bayer.36

0

emptying time of the penetrated liquid. The schematic evolution of the dimensionless emptying time of drops in different partitions in Figure 12a with different positions (tail, center, and front) is plotted in Figure 12b. The penetration of the tail of the drop is the deepest and the emptying time is the longest since it first touches the substrate with the largest impact kinetic energy, as shown with the green columns in Figure 12b. Due to the effect the air cushion between the liquid and the solid surface,64−69 the inertial force of the tail, center, and front part of the drop colliding with the surface decreases successively. Thus, both the depth of penetration and the time required for the penetrated liquid to empty gradually decreases from tail to front. Besides, the emptying time of the tail part of drop decreases from A to C, since the surface energy stored of the penetrated liquid (e) is positively correlated to the capillary emptying time (n) (i.e., the stored energy (e) also declines from A to C and from tail to front, as shown in Figure 12b). Therefore, a critical line of the surface energy stored (e) exists, above which the liquid penetration is deep enough and the capillary energy stored is sufficient to rectificate into the upward

Figure 10, which could be predicted with a regression fitting of 0.313 , as shown with the solid line in Figure Dm/D0 ∼ (RenWe0.5 n ) 10. While the open symbols in Figure 10 display the normal collision results from Bayer,36 and the dashed line represents the regression fit Dm/D0 ∼ (Re We0.5)0.14 of their data. The exponential growth rate of Dm/D0 as a function of RenWe0.5 n in oblique impact is larger than in normal impact, which derives from the development of the asymmetry of the tangential and horizontal extension of drops on inclined superhydrophobic surfaces. The maximum lateral spreading is smaller, and the lateral retraction finishes earlier in oblique impact, compared with the tangential motion of drops. Therefore, the maximum tangential extension Dm/D0 grows more rapidly with enhancing Re and We in the oblique impact in our experiments. 3.2. Three Types of Stretched Rebound. The stretched rebounds observed in oblique impact experiments under various conditions were found to perform obvious differences

Figure 11. Three typical mechanisms of drop stretched rebound on superhydrophobic surfaces with two-tier roughness. (a) Stretched rebound starting from the tail of a drop (Wen = 120, D0 = 1.5 mm, U0 = 3.43m/s) impacting on substrate P100S50 (φ = 0.44) at 45° tilt. (b) Stretched rebound starting from the center of a drop (Wen = 120, D0 = 1.5 mm, U0 = 3.43m/s) colliding with tilted substrate P100S100 (φ = 0.25) at 45°. (c) Stretched rebound starting from the front of a drop (Wen = 40, D0 = 1.5 mm, U0 = 1.98m/s) impinging on substrate P100S200 (φ = 0.111) tilted at 45°. The red dots indicate the impinging positions and the red dotted circles signify the initial emptying regions. The displacement in the last image indicates the distance from the bouncing position to the impinging position. The scale bars: 1 mm. 3563

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Figure 12. Comparison and simple illustration of three types of stretched rebound. (a) Partitions of three types of stretched rebound as a function of normal impact Weber number and the surface solid fraction. The black ■, red ●, and blue ▲ indicate the stretched rebound starting from tail, center, and front, respectively. The black dash, red dot, and blue dash dot curves indicate the dimensionless capillary emptying 1−φ P timen = Wen φ D equaling to 0.8, 1.6, 3.2, respectively. The experimental data points for stretched rebound from front, center, and tail 0

positions lie above the envelope curves of n = 3.2, 1.6, 0.8, respectively, as shown with the colored regions numbered with A, B, and C. (b) Schematic comparison of the dimensionless emptying time (n) and the surface energy stored (e) of different positions of the drop in different partition zones (A, B, and C) in (a). The green, red, and blue color indicates the data for tail, center, and front part, respectively, which decreases successively. The red dashed piecewise line signifies the line of critical surface energy (e = 50) for varied regions above which the capillary energy stored of penetrated liquid is sufficient to convert to the vertical motion of the drop bouncing off the substrates.

motion to lift the whole drop off the substrate. While penetrated liquid with insufficient surface energy would just spread and retract in a conventional pathway on top of the posts. A schematic critical line of e = 50 is plotted in Figure 12b, above which the liquid penetration and upward emptying P motion occurs. Since n = e/φ D denotes the relationship 0

between n and e, the value of n which corresponds to the critical contour line of e = 50, decreases with the increment of solid fraction from subregion A to C, as shown with the red dashed piecewise line in Figure 12b. For substrates in subregion A, the tail, center, and front parts of the drop all penetrated into the structure with varied depths and the front part of the liquid first bounces off, due to the shortest dimensionless emptying time. The schematic diagram illustrating this stretched rebound process is shown in Figure 13a. The red dashed circle indicates the bouncing starting position. The superhydrophobic substrates in subzone B is permeated by the liquid from both the tail and the center positions, and the center part of the drop is first released from the substrate due to the smaller capillary emptying time, as shown in Figure 13b. Only the tail of the droplet could penetrate into the structures in partition C, which results in the lifting of the tail part of the drop. And the upward motion of the tail drives the whole drop to bounce rapidly, as shown in Figure 13c. 3.3. Contact Time. Due to the asymmetric property between the tangential and lateral motion of the liquid in oblique impact, the transversal extension and retraction process is accelerated and the contact time of impacting drops is shortened by approximately 40% compared with that in normal impact with the same impact Weber number.45 In this study, we found that the stretched rebound on submillimeter-scale posts could further reduce the contact time compared with traditional sliding rebound due to the enhanced asymmetric aspect ratio. Since the initial liquid penetration on submillimeter-scale post surfaces with two-tier roughness could pin the tail of the drop at the impinging position for several microseconds, the drop elongates in the tangential direction and enhances the asymmetry of the spreading drop. The maximum lateral spreading is limited, and the transverse retraction finishes rapidly while the drop is still outstretched in the tangential

Figure 13. Schematic diagram illustrating three types of stretched rebound occurred on varied superhydrophobic surfaces with two-tier roughness. (a) Stretched rebound from the front on substrate P100S200. (b) Stretched rebound from the center on substrate P100S100. (c) Stretched rebound from the tail on substrate P100S50. T, C, and F in each figure denotes the tail, center, and front part of the drop. The figures in the first row demonstrate the cross-sectional patterns of the drop during the penetration process and the different liquid penetrated positions on varied substrates, as shown with the white bold letters. The figures in the second row exhibit the first rebounding positions of drops (see the black bold letters) on superhydrophobic surfaces with various solid fraction. The comparison of the capillary emptying time of the tail, center, and front positions of the drop in each case is also plotted in the center of each figure.

direction. The drop quickly bounces off the substrate in an elongated shape on superhydrophobic surfaces with two-tier roughness with moderate solid fraction 0.1 < φ < 0.5. The contact time of drop impact on 45° tilted superhydrophobic surfaces with varied structures is plotted as a function of normal impact Weber number in Figure 14. The ★ indicate the data measured on superhydrophobic silicon surfaces (φ = 1) coated with nanoparticles, and the open symbols in different colors and shapes magnify the results on distinct submillimeter-scale posts with solid fraction 0.028 ≤ φ ≤ 0.64. Sliding rebound occurs on inclined superhydrophobic silicon substrates and two-tier rough surface P100S25 (φ > 0.5), and stretched rebound is observed on tilted substrates P100S50 ∼ P100S200 (0.1 < φ < 0.5). On slant substrates P100S300 and P100S500 (φ < 0.1), the drop is perturbed by the posts and breaks up from interior into pieces before 3564

DOI: 10.1021/acs.langmuir.7b00569 Langmuir 2017, 33, 3556−3567

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drop deformation and contact time in oblique impacts taking advantage of the drop penetrating and emptying process. This study is believed to provide a better understanding of the drop dynamics of stretched rebound on inclined surfaces and a valuable guidance on the equipment of self-cleaning surfaces under oblique liquid impact.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID Figure 14. Comparison of the nondimensional contact time of drops on varied superhydrophobic surfaces as a function of normal Weber number (10 < Wen < 245). The ★ indicate the contact time on superhydrophobic silicon surfaces with nanoparticles. And the open symbols signify the contact time on varied superhydrophobic submillimeter-scale post surfaces with two-tier roughness. Stretched rebound on substrate P100S50, P100S100, and P100S200 with moderate solid fraction (0.1 < φ < 0.5) could effectively reduce the contact time by 10%∼30% compared with sliding rebound on superhydrophobic silicon substrates with nanoparticles and substrate P100S25 with two-tier roughness (φ > 0.5).

Pengfei Hao: 0000-0002-7181-4322

bouncing off the surfaces. The contact time presents a declining trend with the Weber number on all test superhydrophobic surfaces. The evolution of the contact time of colliding drops on submillimeter-scale post surface with the largest solid fraction (φ = 0.64) is similar to that on superhydrophobic silicon surfaces at 10 < Wen < 245, since the initial Weber number of the drop is not sufficient for the penetration of liquid. The stretched rebound on submillimeter-scale post substrates with moderate solid fraction (0.1 < φ < 0.5) results in a 10%∼30% reduction of contact time compared with traditional sliding rebound on superhydrophobic surfaces with a larger solid fraction.

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 11635005 and 11632009) and the State Key Project of Research and Development (Grant 2016YFC1100300).

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4. CONCLUSIONS In this paper, we present four possible outcomes of drop impact with different normal Weber numbers on inclined superhydrophobic surfaces with two-tier roughness and with varied solid fractions through both side-view and top-view snapshots, which are sliding rebound, stretched rebound, penetration rebound, and breakup rebound. Drops undergo an asymmetric spreading and retracting process due to the tangential relative velocity to the wall in oblique impacts. The solid fraction of the submillimetre-scale posts and the normal Weber number of the drop are found to be the determinants of the bouncing patterns. Sliding rebound usually occur on superhydrophobic substrates with large enough solid fraction (φ > 0.5). Two-tier rough substrates with moderate solid fractions (0.1 < φ < 0.5) are found to contribute to rapid drop detachment owing to the ability to promote stretched rebound of colliding drops. Colliding drops tend to break up either from rim or from center before bouncing off the superhydrophobic substrates with the lowest solid fraction (φ < 0.1). The stretched rebound is classified into three typical categories according to the initial lifting position observed in experiments, which are governed by both the surface energy stored during penetration and the capillary emptying time. The contact time of stretched rebound is reduced by 10%∼30% compared with that of the conventional sliding rebound. Fabrication superhydrophobic surfaces with appropriate submillimetre-scale posts and coated with nanoparticles is found to be an effective method to control the 3565

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