Research ArticleMATERIALS SCIENCE

Compact nanoscale textures reduce contact time of bouncing droplets

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Science Advances  17 Jul 2020:
Vol. 6, no. 29, eabb2307
DOI: 10.1126/sciadv.abb2307

Abstract

Many natural surfaces are capable of rapidly shedding water droplets—a phenomenon that has been attributed to the presence of low solid fraction textures (Φs ~ 0.01). However, recent observations revealed the presence of unusually high solid fraction nanoscale textures (Φs ~ 0.25 to 0.64) on water-repellent insect surfaces, which cannot be explained by existing wetting theories. Here, we show that the contact time of bouncing droplets on high solid fraction surfaces can be reduced by reducing the texture size to ~100 nm. We demonstrated that the texture size–dependent contact time reduction could be attributed to the dominance of line tension on nanotextures and that compact arrangement of nanotextures is essential to withstand the impact pressure of raindrops. Our findings illustrate a potential survival strategy of insects to rapidly shed impacting raindrops, and suggest a previously unidentified design principle to engineering robust water-repellent materials for applications including miniaturized drones.

INTRODUCTION

In 1945, Cassie and Baxter (1) proposed that the water-repellent function of many natural surfaces was attributed to the low solid fraction of surface textures. Specifically, the classical Cassie-Baxter theory suggested that low solid fraction, Φs, of the textures (i.e., Φs ~ 0.01) is essential for effective water repellency (1, 2). As a result, the use of low solid fraction textures has become the key principle for the design of water-repellent surfaces over the past few decades (3). However, recent high-resolution electron microscopy observations revealed that many water-repellent insect surfaces (4, 5), such as mosquito eyes (6), springtails (7), and cicada wings (8), have unexpectedly high solid fraction surface textures (i.e., Φs ~ 0.25 to 0.64) and textures that are typically within the range of 100 to 300 nm in size (Fig. 1). These observations raise two questions that cannot be answered by the Cassie-Baxter theory: (i) Why do insects use high solid fraction textures to achieve water repellency? And, (ii) why do these insect surfaces consistently exhibit textures that are on the scale of ~100 to 300 nm?

Fig. 1 Examples of water-repellent insects equipped with high solid fraction nanoscale surface textures.

(A) Optical and scanning electron microscopy (SEM) images of mosquito eyes, a springtail, and cicada wings showing the presence of high solid fraction nanoscale surface textures (Photo credit: L.W., Pennsylvania State University). (B) A plot summarizing the solid fraction Φs and the corresponding texture size D for various water-repellent insects (4, 7, 8, 37, 38). Note that the solid fraction of different insect surfaces is in the range of ~0.25 to ~0.64, which is substantially higher than that of the plant surfaces (e.g., Φs ~ 0.01). Error bars indicate SDs for five independent measurements.

Nanoscale textures serve a number of different functions related to insect survival (9), including antireflection (e.g., moth eyes) (10), antifogging (e.g., mosquito) (6, 11), self-cleaning (e.g., cicada and springtail) (7, 12), and antibiofouling (e.g., dragonfly) (13). One of the important functions critical to the survival of flying insects is the rapid detachment from impacting raindrops before these insects collide with the ground or plunge into pools of water and suffocate (14). Specifically, the impact duration of raindrops with flying mosquitos ranges from ~0.5 to 10 ms, a time frame that could be attributed to the combination of active (e.g., shifting body positions) and passive (e.g., water-repellent surface) droplet shedding mechanisms (14). It is suggested that certain plant leaves and butterfly wings use low solid fraction, microscale patterns to break up the impacting droplets into smaller pieces to reduce the droplet contact time (15). Other conventional mechanisms of reducing droplet contact time also require the low solid fraction Φs ~ 0.01 (16, 17). However, it remains unknown how high solid fractions (i.e., Φs ~ 0.25 to 0.65) and nanoscale textures (~100 to 300 nm) of water-repellent insect surfaces play a role in the rapid detachment of impacting raindrops.

Here, we demonstrate that the contact time of bouncing droplets on high solid fraction surfaces can be reduced by reducing the texture size to nanometer scale. Specifically, we discovered that high solid fraction surfaces (Φs ~ 0.44) with texture size ~100 nm could reduce the contact time by ~2.6 ms compared with that with texture size >300 nm. This texture size–dependent contact time reduction on solid surfaces has not been observed previously and cannot be accounted for by existing surface wetting theories (1, 2, 15–19). We showed theoretically that the reduction in droplet contact time can be attributed to the dominance of three-phase contact line tension (20) on compact nanoscale textures. Through pressure stability analysis and experiments, we have also shown that high solid fractions (Φs > 0.25) are required for insects to withstand impacting raindrops. Our results suggest that the compact and nanoscale textures on water-repellent insect surfaces may work synergistically to rapidly repel and shed impacting raindrops, which could be an important survival strategy for flying insects.

RESULTS

Measurements of contact time of bouncing droplets on textured surfaces

To explore how the texture size affects the liquid-solid interactions, we fabricated a series of textured surfaces at solid fractions that are similar to the insect surfaces (Fig. 1). In particular, reentrant pillars were used to avoid the intrusion of test liquid droplets into the textures and to ensure that the droplets maintain the Cassie-Baxter state (21, 22). The texture size D was varied from ~100 nm to 30 μm, and the solid fraction Φs was maintained at either 0.25 or 0.44 (section S2). The undercut and height of each reentrant pillar were carefully designed (section S3) to avoid possible liquid sagging failure (figs. S1 and S2) (21–23). The fabricated surfaces were then coated with a silane monolayer to render the surface hydrophobic (sections S4 and S5 and figs. S3 to S5). We conducted water droplet bouncing tests by releasing droplets of radius R = 1.15 mm at a height h = 5 cm onto the fabricated textured surfaces and recorded the droplet spreading and retracting processes from the side view using a high-speed camera operating at a frame rate of 10,000 Hz (Fig. 2, A and B). The terminal impacting velocity v is ~1.0 m/s, which corresponds to a Weber number We ~31.6, where We = 2ρv2Rγ and ρ and γ are the density and surface tension of water, respectively.

Fig. 2 Comparison of contact time of bouncing water droplets on textured surfaces.

(A) Time-lapse images of bouncing water droplets (diameter d0 ~ 2.3 mm, Weber number We ~ 31.6) on surfaces with solid fraction Φs = 0.44. The droplet detached faster from ~100 nm textures than the one from ~300 nm textures. D denotes the texture cap size of each reentrant pillar, and tc denotes contact time. (B) Identical drop impact experiments on surfaces with solid fraction Φs = 0.25. Droplets detached simultaneously from both surfaces. Insets showing the SEM images of fabricated nanoscale reentrant textures. Scale bars in all SEM images, 200 nm; scale bar in the optical image, 1 mm. See also movies S1 and S2.

Our measurements showed that the contact time tc of bouncing droplets decreases with the texture size on textured surfaces when the textures are smaller than ~300 nm at Φs = 0.44. Specifically, the droplet contact time tc on a surface with ~100 nm textures is 16.2 ± 0.2 ms, which is ~2.6 ± 0.2 ms shorter than those with ~300 nm to 30 μm textures (18.8 ± 0.4 ms) (Figs. 2A and 3A and movie S1). In comparison, the contact time on surfaces with Φs = 0.25 remains 14.1 ± 0.2 ms regardless of the texture size (i.e., ~150 nm to 30 μm) (Figs. 2B and 3A and movie S2). This texture size–dependent contact time reduction on solid surfaces has not been observed previously and cannot be accounted for by existing surface wetting theories (1, 2, 15–19).

Fig. 3 Experimental measurements and theoretical predictions of contact time of bouncing water droplets on textured surfaces.

(A) Comparison between the measured contact time tc (scatter dots) of bouncing droplets and those predicted by Eq. 2 (dash lines) on textured surfaces. The purple circles and the orange triangles represent the measured contact time obtained from surfaces with solid fractions Φs = 0.25 and Φs = 0.44, respectively. Error bars represent the SDs of three independent measurements. (B) A phase map showing the ratio (E*) of line energy to surface energy as a function of texture size and solid fraction. The line energy begins to dominate over the surface energy in dictating the macroscopic surface wettability when the surface texture size approaches ~100 nm at Φs > 0.25.

Theoretical predictions of contact time of bouncing droplets on textured surfaces

Previous studies indicated that the contact time tc scales with the inertial-capillary time scale and is only a function of droplet radius R for a given liquid. Specifically, the contact time can be predicted by the expression (16)tc=aρR3/γ(1)where ρ and γ are the density and surface tension of water, respectively, and a is an empirical prefactor determined from experiments. Studies showed that a =2.6 ± 0.1 on superhydrophobic surfaces with low solid fraction (Φs ~ 0.01) (16). Larger values of a were reported when surfaces with higher solid fraction were used (24). In our experiments, we find that a = 4.1 ± 0.1, 3.1 ± 0.1, and 2.6 ± 0.1, for surfaces with Φs = 0.44, 0.25, and ~0.01, respectively (section S6). In our experiments, Eq. 1 can successfully predict the contact time of droplets on all surfaces at Φs = 0.25 and those on surfaces at Φs = 0.44 with texture size >300 nm. However, it fails to predict the contact time on surfaces at Φs = 0.44 with texture size <300 nm (fig. S6).

When a liquid droplet impacts a textured surface, it spreads to a maximum diameter and then retracts from the surface analogous to a “liquid spring” (16). On low solid fraction textured surfaces (i.e., Φs ~ 0.01), the “spring constant” of the liquid spring is dominated by the liquid-air interfacial tension of the droplet, and contribution from the liquid-solid interaction can be regarded as negligible. However, on high solid fraction textured surface (i.e., Φs = 0.44), the liquid-solid interaction can no longer be ignored because the additional energy resulting from the formation of three-phase contact lines underneath the droplets could be substantial enough to influence the droplet bouncing energetics.

We found that the reduced contact time tc on surfaces with Φs = 0.44 and textures smaller than 300 nm could be rationalized by taking into account the three-phase contact line tension τ, which was first introduced by Gibbs in the 1870s (20). Specifically, τ is a one-dimensional analogy of surface tension γ and is defined as the excess free energy of a solid-liquid-vapor system per unit length of a three-phase contact line (20, 25, 26). Experimental measurements reported that τ is on the order of 10−11 to 10−5 J/m, depending on the specific experimental systems under investigation (26). A recent study has shown that τ is on the order of 10−9 to 10−8 J/m based on the experimentally measured water contact angles on springtail surfaces with reentrant textures (27). This magnitude of τ is consistent with a theoretical study that predicted that the upper limit of τ would be 5 × 10−9 J/m (28). Because of its small magnitude, τ usually can be ignored for macroscopic wetting systems (29). However, numerous three-phase contact lines are formed underneath the droplet on a nanoscale textured surface with high solid fraction, and the collective line energy can be substantial enough to influence the macroscopic wetting behaviors (19). By incorporating the additional line energy, Eq. 1 can be modified as (section S7)tc=aρR3/(γ+Λτ)(2)where Λ is the contact line density, expressed as Λ=4ΦsD. Predictions from Eq. 2 are in good agreement with our experimentally measured tc on surfaces at both Φs = 0.44 and Φs = 0.25 with τ = 10−9 J/m (Fig. 3A).

The effect of τ on tc becomes notable only if the cumulative line energy is on the same order as the surface energy, which requires the contact line density Λ > 107 m−1. This high contact line density can only be achieved on surfaces with both high solid fraction and nanoscale textures. To quantitatively explore the importance of line tension, we constructed a phase map by plotting the dimensionless energy E*—the ratio between line energy and surface energy—as a function of texture size and solid fraction (Fig. 3B). On conventional superhydrophobic surfaces with low solid fraction (i.e., Φs ~ 0.01), the effect of line energy can be ignored because of the low contact line density (i.e., Λ << 107 m−1). However, the effect of line energy begins to dominate on surfaces with high solid fraction (i.e., Φs = 0.44) when the texture size is reduced to ~100 nm as the contact line density Λ approaches to 107 m−1. This indicates that the effect of line tension cannot be neglected for macroscopic wetting phenomena on high solid fraction nanoscale textured surfaces.

Kinematics of bouncing droplets on textured surfaces

To gain further insight on the reduction in contact time of impacting drops on compact nanoscale textured surfaces, we investigated the kinematics of bouncing droplets by observing their spreading and retracting processes on different surfaces (Fig. 4A). Specifically, the bouncing process could be quantified by plotting the dimensionless contact length L*—the ratio between the contact length lc and drop initial diameter d0—as a function of time. Inspection of lc/d0 on different surfaces showed that the droplets spread outward and reached the maximum contact length within the same time ts = 2.6 ± 0.1 ms upon impacting surfaces with different solid fractions (i.e., Φs ~ 0.01, Φs = 0.25, and Φs = 0.44). During this phase, the spreading velocities were the same on these surfaces, as the spreading motion is dictated primarily by the kinetic energy of the droplet. The maximum dimensionless length during this phase can be predicted by L*=lcdo∼(2ρv2Rγ)1/4 (30). During the retracting phase, however, it took longer for the droplets to fully retract from surfaces with higher solid fractions. For example, it took ~11.5 ms for a droplet to fully retract from a surface with solid fraction Φs = 0.25, while it only took ~9.1 ms for the droplet to fully retract from a superhydrophobic black silicon surface (Φs ~ 0.01). These observations indicate that increased solid fraction leads to increased retraction time.

Fig. 4 Droplet bouncing and wetting kinematics on textured surfaces.

(A) Spreading and receding kinematics of bouncing water droplets on various surfaces. Black silicon with Φs ~ 0.01 showed a superhydrophobic bouncing behavior with a constant receding velocity. Surfaces with 150 and 400 nm textures at Φs = 0.25 showed a characteristic bouncing behavior in which the receding velocity reached a plateau at ~10 to 12 ms. The surface with 300 nm textures at Φs = 0.44 showed a similar bouncing behavior in which the receding velocity reached a plateau at ~11 to 14 ms, while the surface with 100 nm textures at Φs = 0.44 showed a superhydrophobic bouncing behavior with a constant receding velocity similar to that on the black silicon. (B) Comparison of the receding angle θr between surfaces with texture sizes of ~100 and ~300 nm at Φs = 0.44 during the receding process. Scale bar, 2 mm. (C) Measured contact angle hysteresis on surfaces with texture size ranging from ~100 nm to 30 μm and Φs = 0.25 or 0.44. Error bars indicate SDs for three independent measurements. Our measured contact angle hysteresis data are in good agreement with those reported in the literature (11, 31).

Specifically, we found that on a superhydrophobic black silicon surface (i.e., Φs ~ 0.01), the droplet retracted at a constant velocity, which enabled the droplet to retract in the fastest possible manner (i.e., “superhydrophobic bouncing”). However, on surfaces with higher solid fraction (e.g., Φs = 0.25, D = 150 nm, or 400 nm), the droplet retraction was delayed as the retracting velocity reached a plateau at ~10 to 12 ms, which was notably deviated from the superhydrophobic bouncing behavior. Unexpectedly, a superhydrophobic bouncing behavior was observed on 100 nm textures even though the solid fraction Φs is 0.44 (Fig. 4A), which enabled the droplet to retract without delay. Therefore, it is evident that the contact time on 100 nm textures with Φs = 0.44 may have reached the minimal possible contact time at that specific solid fraction. These observations indicate that the nanoscale textures could compensate for the increased contact time, which results from the high solid fraction.

Contact angle hysteresis measurements

We found that the absence of the velocity plateau on surfaces with 100 nm textures is resulted from the reduced contact angle hysteresis (Fig. 4B). To precisely quantify the contact angle hysteresis, we developed a method that systematically measures the advancing and receding contact angles on the fabricated surfaces (Fig. 4C and fig. S4). We found that the water contact angle hysteresis on surfaces with Φs = 0.25 and texture size ranging from ~150 nm to 30 μm is 25.3 ± 2.1°, which is in good agreement with those reported in the literature (11, 31). In comparison, the water contact angle hysteresis on surfaces with Φs = 0.44 and texture size ranging from ~300 nm to 30 μm is 41.2 ± 0.4°.

However, the contact angle hysteresis on surfaces with Φs = 0.44 decreases substantially when the texture size is smaller than ~300 nm (i.e., 29.0 ± 0.5° and 34.9 ± 0.8° for texture sizes of 100 and 200 nm, respectively). These experimental measurements support our hypothesis that the absence of the velocity plateau is attributed to the reduction in contact angle hysteresis on smaller textures. Recent theoretical predictions and experimental observations (19, 27) have shown that the effect of line tension may play an important role in enhancing both the apparent advancing and receding contact angles on high solid fraction nanoscale textures, thereby reducing the overall contact angle hysteresis.

Pressure stability analysis and experiments

While we have shown that water-repellent surfaces with high solid fraction nanoscale textures can lead to reduced contact time of bouncing droplets compared with their microscopic counterparts, the contact time on these surfaces is still longer than that on lower solid fraction surfaces. An interesting question that arises is: Why do water-repellent insect surfaces not adopt textures with lower solid fraction instead? We further investigated this by considering the pressure stability of the textured surfaces against impacting droplets.

When water droplets impact on a solid surface, there are two modes of impacting pressure. The first mode is the water hammer pressure, PH = 0.2ρCv, at the liquid-solid contact stage, and the second mode is the dynamic pressure, PD = 0.5ρv2, at the spreading stage, where ρ is the density of water, C is the sound speed in water (1497 m/s), and v is the impact velocity (32). To completely shed impacting droplets, the capillary pressure PC, which is the critical pressure preventing droplets from penetrating into the textures (33), has to be greater than both PH and PD. Specifically, PC can be expressed as PC=4Φs1−ΦsγD for textures with reentrant pillars (section S8). For free-falling raindrops of size dr, the terminal velocity can be expressed as v=ρρagdr, where ρa is the density of air and g is the gravitational acceleration (34). A typical raindrop ranges from 1 to 3 mm in size (34), so the terminal velocity is ~2.9 m/s ≤ v ≤ ~4.9 m/s, and therefore, the water hammer pressure of raindrops is in the range of ~0.9 MPa ≤ PH ≤ ~1.5 MPa. Note that the water hammer pressure of raindrops is much higher than the dynamic pressure (i.e., PH ≫PD ~ 8 kPa). Therefore, the raindrop will remain in the Cassie-Baxter state as long as the capillary pressure sustained by the textured surface is greater than the water hammer pressure. Otherwise, the raindrop will transit to a complete or partial Wenzel state, in which droplets typically remain stuck to the surface (fig. S8) (32).

We further explored the pressure stability of textured surfaces by plotting the dimensionless pressure P*—the ratio of capillary pressure and raindrop water hammer pressure—as a function of texture size and solid fraction (Fig. 5 and fig. S9). We found that to produce sufficient capillary pressure on a textured surface to withstand the water hammer pressure of raindrops (i.e., an average of PH is ~1.2 MPa), the texture size has to be <1 μm and Φs has to be >0.25 for both reentrant and straight pillars (section S8 and fig. S9). To validate this, we have performed droplet impact tests on four surfaces with reentrant textures with different geometrical parameters (i.e., texture sizes D are 200 nm and 10 μm; solid fraction Φs are 0.25 and 0.44). In these tests, water droplets of radius R = 1.15 mm at a height h = 83 cm were released to simulate free-falling raindrops (section S9). The terminal velocity v was ~4.0 m/s, which corresponded to a water hammer pressure PH ~ 1.2 MPa and a Weber number We ~ 505.5. Among the four surfaces, only the surface with pillar size of 200 nm and solid fraction of 0.44 was able to maintain the droplet in the Cassie-Baxter state throughout the impact process, while droplets on other surfaces transited to partial Wenzel state (Fig. 5B and movies S3 to S6). As shown in Fig. 5A, the combination of pillar size of 200 nm and solid fraction of 0.44 can sustain a capillary pressure PC comparable to the water hammer pressure PH of raindrops (i.e., P* = PC/PH ≅ 1). Decreasing the solid fraction or increasing the texture size would reduce the pressure stability (i.e., P* ≪ 1). Furthermore, it is important to note that the texture size and solid fraction of representative water-repellent insects fall within or near the pressure stable regime. The high solid fraction represents an important requirement for these insects to withstand the impact pressure of raindrops to shed them completely.

Fig. 5 Pressure stability of reentrant textured surfaces against impacting raindrops.

(A) A phase map showing the pressure stability of reentrant textured surfaces against impacting raindrops as a function of texture size and solid fraction. To repel impacting raindrops, it requires a sufficient capillary pressure PC on textured surfaces to withstand the raindrop hammer pressure PH. P* is defined as the ratio between PC and PH, i.e., P* = PC/PH. Note that the textured surfaces are pressure stable when texture size D is small at high solid fraction Φs. It is shown that all the geometrical parameters of the surface textures on water-repellent insects fall within or near the pressure stable regime. (B) Experimental results showing droplets impacting on reentrant textured surfaces with different geometrical parameters (movies S3 to S6). Water droplets with terminal velocity ~4.0 m/s impacted the reentrant pillars, resulting in a water hammer pressure PH ~ 1.2 MPa and We ~ 505.5. The surface with texture size of 200 nm and solid fraction of 0.44 was able to maintain the droplet at the Cassie-Baxter state (solid star symbol), while the droplets on other surfaces were in partial Wenzel state (empty star symbols). Scale bar, 2 mm.

DISCUSSION

For over 75 years, water-repellent surfaces have been designed on the basis of the principle of minimizing the solid fraction of textures, as inspired by many natural species (3); however, our study shows that the use of nanoscale textures on high solid fraction surfaces reduces the water contact angle hysteresis and leads to a reduction in the contact time of bouncing droplets. These findings uncover a previously unidentified strategy to reduce droplet contact time on solid surfaces, which could be attributed to the dominance of line energy on compact nanoscale textures. Furthermore, our experimental results suggest that the superhydrophobic bouncing behavior can be achieved on high solid fraction surfaces (i.e., Φs = 0.44) when the texture size approaches ~100 nm. We anticipate that similar bouncing behavior could be preserved at smaller texture size on high solid fraction surfaces. Therefore, our theory (i.e., Eq. 2) may predict the smallest possible contact time of bouncing droplets for sub–100 nm textures at high solid fraction (i.e., Φs > 0.25), which will be a subject of future study.

From a biological perspective, our findings provide new insights on how compact nanoscale textures may reduce contact time of bouncing droplets and thereby may help insects escape from high-speed impact of raindrops before colliding with the grounds or pools of water. Specifically, our results showed that high solid fraction surfaces (Φs ~ 0.44) with texture size ~100 nm could reduce the contact time by ~2.6 ms compared with that with texture size >300 nm. If a mosquito is attached to a falling raindrop at a velocity of ~2.9 to 4.9 m/s, then a contact time reduction of ~2.6 ms will reduce the travel distance by ~7.5 to ~12.7 mm, which is equivalent to ~2 to 5 body lengths of the mosquito (14). Our study also provides experimental evidence that the high solid fraction textures are required to provide sufficient capillary pressure to counter the impact pressures of raindrops. Therefore, the use of compact nanoscale textures can be utilized to repel raindrops completely and rapidly, which could serve as a passive mechanism to help flying insects mitigate complex environmental perturbations. Technologically, the ability of compact nanoscale textured materials to repel high-speed impact of liquid droplets with reduced contact time may find use in a range of applications, including fouling-resistant personal protective equipment (35) to insect-sized flying robots and miniaturized drones (36).

MATERIALS AND METHODS

Materials

The mosquito, springtail, and cicada specimens were purchased from www.deadinsects.net, which were kept in a 70% ethanol solution at −26°C before use. Silicon wafers with a thermally grown oxide layer were purchased from Addison Engineering Inc., USA. 1H,1H,2H,2H-perfluorooctyltriethoxysilane (i.e., FAS-17) was purchased from Sigma-Aldrich and was used as received.

Characterization of the insect surfaces

The optical images of insects were photographed by a digital camera using a macro lens (700D, Canon, Japan). The nanoscopic view of the insect surfaces was observed by a field emission scanning electron microscope (Merlin, Zeiss, Germany), operating at 5-kV acceleration voltage. To avoid the electron charging on the nonconductive biological specimens, a layer of 5 nm gold was sputtered. The specimens were brought to room temperature (~22°C) before characterization.

Fabrication of nano- and micro-reentrant structures

The process involved two-step inductively coupled plasma etching on thermally oxidized silicon wafers, which was developed on the basis of protocols from literature (21, 22). Briefly, the silicon dioxide with a defined mask was etched directionally to expose the underlying silicon, and then isotropic etching over silicon was conducted to create reentrant structures. Detailed information of this fabrication process is provided in section S2.

Fluorosilanization

The fabricated reentrant structures were rendered hydrophobic by chemical vapor phase deposition of FAS-17 at 120°C in a vacuum oven. Before silanization, the structures were cleaned by oxygen plasma for 3 min. Detailed description of the silanization process is provided in section S4.

Contact angle measurements

Contact angle hysteresis was determined by measuring the difference between advancing and receding angles using a goniometer (ramé-hart, model 295, USA). To ensure the measurement accuracy, we have developed a methodology to repeatedly increase and decrease the sessile drop volume sinusoidally and plotted the contact angle as a function of time to measure the advancing and receding angles (section S5 and fig. S4).

Droplet bouncing and imaging

Side view of the droplet bouncing process on textured surfaces was captured by a high-speed camera (MIRO M320s, Phantom, USA) filming at 10,000 frames/s. Deionized water droplets with diameter ~2.3 mm were released from a fine needle connected to a microfluidic pump (New Era Pump Systems Inc.) at predetermined heights (5 or 83 cm). All experiments were conducted at room temperature ~22°C, and the relative humidity was ~46%. The contact length of bouncing droplets with solid surfaces was analyzed using ImageJ and MATLAB.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/29/eabb2307/DC1

https://creativecommons.org/licenses/by-nc/4.0/

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

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Acknowledgments: We thank B. Boschitsch for the help with manuscript preparation. We also thank B. Liu, C. Eichfeld, G. Lavallee, K. Gehoski, M. Labella, and S. Miller from the Materials Research Institute at Penn State University for the help with sample preparation. Funding: We acknowledge funding support by the NSF (CAREER Award# 1351462), the Wormley Family Early Career Professorship, PPG Foundation, the Department of Materials Science and Engineering at Penn State, and the Humanitarian Materials Initiative Award sponsored by Covestro and the Materials Research Institute at Penn State. Part of the work was conducted at the Penn State node of the NSF-funded National Nanotechnology of Infrastructure Network. Author contributions: L.W. and T.-S.W. conceived the overall experiments. L.W. took the optical and SEM images of the insects. L.W. designed and fabricated the reentrant textured samples. J.W. fabricated the black silicon samples. L.W. and J.W. performed the bouncing tests. L.W. and R.W. measured the contact angle hysteresis and collected the contact time and contact length data. L.W., R.W., and T.-S.W. processed and analyzed the data. L.W. and T.S.W. wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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