Bioinspired Drag Reduction of Cavities Induced by Janus Nanostructure Interfaces on Hydrophobic Spheres Plunging into Water with a Low Speed

Form drag of the blunt object occurs from the pressure difference due to the physical dimensions of the object obstructing and altering the flow of the fluid. The innovative approach of form drag reduction is realized by changing the shape of the blunt object to a streamlined body by introducing a cavity. The construction of superhydrophobic interfaces is widely considered as the best solution for introducing a cavity, because water is prevented from penetrating the space between the nanoscale structures, leading to a Cassie–Baxter wetting regime and then water splashing outward. Here, by introducing Janus nanostructure coating on hydrophobic spheres, it is found that the position (impacting direction) and coverage ratio (r) of the nanostructures, accurately manipulate the performance of water film on the sphere surface. When the nanostructure faces upward, the detached thin film develops to a splash crown only if r increases to 1/3 or even above. Correspondingly, the remaining open aperture aids in increasing the subsequent air entrainment, and an air‐entrainment cavity is trapped on the sphere surface. However, if the nanostructure faces downward, only a tiny region of the nanostructures (r ≤ 1/8) can help a thin liquid film directly develop into a splash crown and cavity.


Bioinspired Drag Reduction of Cavities Induced by Janus Nanostructure Interfaces on Hydrophobic Spheres Plunging into Water with a Low Speed
Jingjing Xie, Changzhuang Yao forces are always experienced. Thus, hydrodynamic drag reduction is crucial for avoiding speed loss and improving energy efficiency. [1] In general, there are two main forms of hydrodynamic drag resistance, i.e., skin friction (friction drag force) and the form drag force. Skin friction is the friction between a fluid and the surface of a solid moving through it or between a moving fluid and its enclosing surface as a result of fluid viscosity. Skin friction is the key factor for a streamlined body, such as a submarine or torpedo. [2] Form drag occurs from the pressure difference due to the physical dimensions of the object obstructing and altering the flow of the fluid (i.e., flowseparation phenomena). On a blunt body, the form of drag underwater is much greater than the skin friction. [3,4] Consequently, for hydrodynamic drag reduction, it is essential to reduce the form of drag on a blunt body.
The innovative approach of form drag reduction is realized by changing the shape of the blunt body to a streamlined body through introducing a cavity. [3][4][5][6][7] The cavity can be generated by the principle of natural cavitation on underwater objects because the water near the head of the object is vaporized to generate cavitation when the speed of the object is high enough. [8,9] However, at low speeds, the cavity greatly depends on the air-capture process when the object impacts the water surface. [10,11] If the water disturbance and water splashing outward along the object create an open splash crown for air to enter during the impacting process, more air is drawn into the cavity with the object continuously falling. Then, due to the hydrostatic pressure of the surrounding water and the capillary force, the middle of the cavity gradually shrinks until it is clipped, and then a streamlined cavity form. [12] The behavior of water regulation on the object interfaces (i.e., water disturbance and water splashing outward) is significantly relayed on the characteristics of the object interface, including wettability, [13][14][15] microstructure, [16,17] and surface energy distribution. The static unwetted interfaces, such as the superhydrophobic [18][19][20][21][22][23][24][25] and Leidonfrost [26][27][28][29] interfaces, prevent water from penetrating the space between the microscale and/or nanoscale structures, leading to a Cassie-Baxter wetting regime and then water splashing outward. A superhydrophobic interface is generally characterized by low surface free energy Form drag of the blunt object occurs from the pressure difference due to the physical dimensions of the object obstructing and altering the flow of the fluid. The innovative approach of form drag reduction is real ized by changing the shape of the blunt object to a streamlined body by introducing a cavity. The construction of superhydrophobic interfaces is widely considered as the best solution for introducing a cavity, because water is prevented from penetrating the space between the nanoscale structures, leading to a Cassie-Baxter wetting regime and then water splashing outward. Here, by introducing Janus nanostructure coating on hydrophobic spheres, it is found that the position (impacting direc tion) and coverage ratio (r) of the nanostructures, accurately manipulate the performance of water film on the sphere surface. When the nano structure faces upward, the detached thin film develops to a splash crown only if r increases to 1/3 or even above. Correspondingly, the remaining open aperture aids in increasing the subsequent air entrain ment, and an airentrainment cavity is trapped on the sphere surface. However, if the nanostructure faces downward, only a tiny region of the nanostructures (r ≤ 1/8) can help a thin liquid film directly develop into a splash crown and cavity. chemicals and a rough hierarchical structure. [30][31][32][33][34][35][36] Thus, the rough structure acts as an important role in the water splashing outward. [16,[37][38][39][40] However, how a rough structure, especially the position and coverage ratio of a rough structure, promotes water splashing at smooth interfaces with low surface free energy chemicals has been ignored.
Janus micro/nanostructured interfaces are often exploited by natural species. The lotus leaf structure is a typical example of a Janus micro/nanostructured interface. Its upper side is decorated by micropapillae with nanocrystals, while the lower side is covered by tabular papillae with nanogroove structures. Benefiting from Janus micro/nanostructures, the lotus leaf achieves in-air superhydrophobicity on the upper side and underwater superoleophobicity on the lower side. [41] The concept of Janus materials was first proposed by P. G. Gennes in his prophetic 1991 Nobel Laureate Lecture entitled Soft Matter. [42] Janus nanomaterials are so named in reference to Janus, the Roman god of doorways, gates, beginnings and endings, typically depicted as having two faces. Like the ancient deity, Janus nanomaterials also have two faces, each consisting of different chemistry, size, morphology, material, etc. [43,44] Inspired by the above, the Janus nanostructure interfaces, i.e., nanostructural regions with different coverage ratios were prepared on spheres. The nanostructural region was superhydrophobic and the nonnanostructural region was hydrophobic. The spheres were released with the nanostructural region facing two opposite directions, i.e., facing upward and downward at different heights. When the sphere was released with the nanostructural region facing up, if the nanostructural region was very small, for example, if the coverage ratios of the nanostructures were 1/8 or 1/6, the opened aperture was easy to close and it was difficult for the air to enter. A relatively complete air-entrained cavity could only form in the spheres if the nanostructure ratio reached 1/3. However, when a sphere entered the water with the nanostructural region facing down, the water film detached from the sphere before reaching the pole. Then the opened aperture left at the top of the sphere led to cavity formation and air entrainment. This research provides a new idea for manipulating the behavior of water film on sphere interfaces and the capture and shapes of cavities by only designing the positions and coverage ratios of nanostructures.

Characterization of The Spheres with Janus Nanostructure Coatings
Spheres with different Janus nanostructured coatings were prepared at first. We used the nanostructural coverage ratio value (r) to represent the percentage of the completely etched region, i.e., the ratio of the spherical cap height where the fully etched area covered the sphere diameter. The coverage areas of the nanostructural region are illustrated in royal blue, which gradually increases from left to right. The nanostructural coverage ratios were 0, 1/8, 1/6, 1/3, 1/2, 2/3, and 1 ( Figure S1a, Supporting Information).
The surface of the unetched region on the sphere was relatively smooth. There were some tiny bulges irregularly distributed on the unetched region. This region exhibited hydrophilicity. The scanning electron microscopy (SEM) images of the etched region were covered with numerous Cu(OH) 2 clusters of several neighboring incline nanoneedles with the diameter of 100 nm, which was in the similar range of the nanospikes found on insect wings (i.e., cicada and dragonfly wings). [45][46][47][48] The tilted and staggered nanoneedles formed microclusters. On the top of each microcluster, there usually is a nanoflower with several nanopores. The diameters of the nanoflowers ranged from 0.3 to 1.0 µm. The cluster-to-cluster spacing is about 3-5 µm. The nanopores on the flowers are in the range of 50-100 nm. The length of the longest nanoneedles is 18.13 ± 1.29 µm. The aspect ratio was 181 ( Figure S4, Supporting Information). The Gaussian curvature K of the spheres is 1/R 2 , i.e., 0.0248 mm −2 . This region exhibited superhydrophilicity with a CA of 6.6 ± 2.1°. The boundary line between the unetched and etched region of the sphere was relatively clear. There was transition region with a microstructure gradient at the boundary area. There was little difference between the roughness on the etched region of the spheres when the nanostructural ratios were smaller than 1 (Supporting Information S1 and S2).
After modification of chemical components with low surface energy (n-hexadecane thiol), the SEM and energy-dispersive X-ray spectroscopy (EDX) images at different regions (i.e., unetched, etched, and boundary regions) on the spheres with the nanostructure coverage ratio of 1/3, 1/6, and 1/8 are shown in Figure 1 and Figures S10 and S11 (Supporting Information). After modification with n-hexadecane thiol, the coverage areas of the nanostructural region changed to steel blue ( Figure 1a). The surface of the unetched region on the sphere with the nanostructure coverage ratio of 1/3 was still relatively smooth ( Figure 1b). There was a great deal of nanoparticles densely stacked together on the unetched region. The typical EDX spectrum and images of uniform distribution of C and S element illustrated that n-hexadecane thiol had been successfully modified in this region. This region exhibited hydrophobicity with a CA of 105.9 ± 1.2°. The SEM images of the etched region were covered with numerous porous microflowers constructed by nanosheets with the thickness of ≈100 nm, as shown in Figure 1c and Figure S6 (Supporting Information). The diameter of microflowers was about 6.0 µm. The pores on and between the microflowers were 200 nm-4.0 µm and 3.0-20.0 µm, respectively. There were numerous micropores existing underneath the pores between the microflowers. This region exhibited superhydrophobicity with a CA of 151.1 ± 1.2°. The morphology of the boundary between the unetched and etched region of the sphere is shown in Figure 1d and Figure S7 (Supporting Information). The further magnified SEM images illustrated that the porous microstructures took on the shape of a sponge with gradient and multilevel pores. The microflowers and micropores grew on the clusters of nanoneedles (Supporting Information S3). The thickness of the microsponge was about 5.0-8.0 µm. The advancing and receding contact angles results illustrated little CA hysteresis (Supporting Information S4). The boundary line was relatively clear. The further magnified SEM images illustrated that the porous www.advmatinterfaces.de microstructures were grown above the clusters of nanoneedles. The nanostructures acted as nucleation sites for crystallization of n-hexadecane thiol. The SEM and EDX images at different regions (i.e., unetched, etched, and boundary regions) on the spheres with the nanostructure coverage ratio of 1/6 and 1/8 after modification illustrated the similar results (Supporting Information S5).
Besides, two damage methods had been adopted to investigate the mechanical damage of nanostructures. They were droplet bounce process on the spheres and the sphere impacting process on water surfaces, respectively. After the two damage methods, the microstructures of the unetched, etched, and boundary regions changed little. Thus, the nanostructures on Janus interfaces were not damaged after droplet bouncing process (Supporting Information S6).

Impacting Process of Spheres with Different Janus Nano structured Coatings Facing in Two Opposite Directions
To investigate the influence of the processes of the Janus nanostructures impacting the water surface, five kinds of spheres, each exhibiting different nanostructural coverage ratio values of 1/8, 1/6, 1/3, 1/2, and 2/3, were prepared. The Janus nanostructured coatings of the spheres faced two opposite directions when impacting the water surface, i.e., the etched region with nanostructures facing upward and downward. We took the geometric center of the rough structure region as the coordinate origin O. When the nanostructures faced upward, the nanostructures were under the origin O, and the nanostructure regions were in the negative regions. Conversely, when the nanostructures faced downward, the nanostructures were above Figure 1. Characterization of the spheres with Janus nanostructured coatings after modification with n-hexadecane thiol. a) Optical photographs of the Janus spheres with seven nanostructural coverage ratios (0, 1/8, 1/6, 1/3, 1/2, 2/3, and 1). b) Scanning electron microscopy (SEM) images and energy-dispersive X-ray spectroscopy (EDX) spectrum of the unetched region on the sphere with the nanostructural coverage ratio of 1/3. A detailed nanostructure analysis showed that there was a great deal of nanoparticles densely stacked together on the unetched region. This region exhibits hydrophobicity with a CA of 105.9 ± 1.2°. c) SEM images and EDX spectrum of the etched region with a nanostructural coverage ratio of 1/3. A detailed nanostructure analysis showed that this region covered with numerous porous microflowers. This region exhibited superhydrophobicity with a CA of 151.1 ± 1.2°. d) SEM images of the boundary between the unetched and etched regions. The boundary was very clear. Further magnified SEM images illustrated the porous microstructures were grown above the clusters of nanoneedles.
www.advmatinterfaces.de the origin O, and the nanostructure regions were in the positive region. Thus, the negative "−" and positive "+" signs could be used to indicate the falling direction of the Janus nanostructured interfaces, as shown in Figure 2a.
As shown in Figure 2b, the spheres impacted the water surface with the nanostructures facing upward. After the spheres with the nanostructural coverage ratio values of −1/8 and −1/6 passed through the free water surface, no air entrainment was observed on the impacting sphere. Instead, large amounts of tiny bubbles gathered at the end of the spheres, and only a vertical jet was observed above the free water surface. With the spheres continuously falling in the water, tiny bubbles were shed from the end of the spheres. This was because flow separation occurred behind the blunt tail, and the strong turbulence in the wake made the tiny bubbles instable. When the nanostructural coverage ratio value of the spheres reached −1/3, an air-entrained cavity was trapped on the sphere interface. At the very beginning of the impact process (10 ms), the hydrophobic sphere pulled the free water surface downward, generating gasliquid interface deformation and air entrainment. The hydrophobic sphere further pulled and stretched the cavity in the vertical direction with time. Then, the whole part of the cavity was pinched off almost at the water surface with the cavity attached. As the nanostructural coverage ratio value increased to −1/2 or even larger than −1/2, the pinched-off position moved downwards to the tail part of the cavity. At the same time, the tail cavity gradually developed completely, showing a water-drop outline shape (Supporting Information Movies S1 and S2). The hydrophobic sphere with a nanostructural coverage ratio value of −2/3 and an attached cavity exhibited a total length of 54.9 mm, which was more than four times the diameter of the sphere (i.e., 12.7 mm).
If the spheres impacted the water surface with the nanostructures facing downward, as shown in Figure 2c, airentrained cavities were observed on the sphere with the nanostructural coverage ratio values of +1/8, +1/6, +1/3, +1/2, and +2/3. The process of entering the water with the nanostructural coverage ratio of +1/3 was taken as an example. At the very beginning of the impact process (10 ms), the sphere pulled the free water surface downward, generating the gas-liquid interface deformation and air entrainment. Additionally, an open splash crown was observed above the water surface. The sphere further pulled and stretched the cavity in the vertical direction with time, thus thickening the splash crown wall. At 35 ms, the middle part of the cavity started to shrink because of the hydrostatic pressure of surrounding water and the capillary force. The morphology of the cavity was changed and was gradually elongated by the sphere. The volume of the tail cavity and the splashing liquid film also increased. At 55 ms, the middle part of the cavity was pinched off, and the front part of the cavity was attached to the interface of the sphere, showing a water-drop outline shape. When the length and shape of the air-entrained cavity tended to be stable, the tail cavity and splashing liquid film gradually disappeared with the action of gravity and surface tension. Therefore, there were three stages in the formation of a cavity, including flow formation, cavity opening, and cavity closing (Supporting Information Movies S3 and S4). The sphere with the nanostructure coverage ratio www.advmatinterfaces.de of +1/3 and an attached cavity after pinching off exhibited a total volume of 5.40 ± 0.23 cm 3 , nearly five times that of the sphere with a volume of 1.07 cm 3 .
Therefore, the nanostructure was significantly important for the formation of a cavity. When a sphere entered the water with the nanostructural region facing down, no matter how tiny the area of the nanostructural region was (for example, even r = +1/8), a cavity could be trapped. However, when a sphere entered the water with the nanostructural region facing up, the nanostructural region ratio had to reach 1/3 to form a cavity.
As shown in Figure 3a, when the spheres impacted the water surface with the nanostructures facing upward, almost no cavity trapped was on the sphere with small nanostructural coverage ratios (−1/8 and −1/6) or when released just above the water surface (i.e., a release height of approximately 0 cm). The increase of the nanostructural coverage ratios and the release heights of the spheres could both induce cavity formation. Specifically, an air-entrained cavity was only generated when the nanostructural coverage ratios reached or were larger than 1/3. That is to say, 1/3 was the smallest value to trap a cavity on the spheres when the nanostructures faced upwards. The pinchingoff depth of a sphere increased with the release height. As a result, the cavity was stretched in the vertical direction, and the length of the cavity increased. Spheres with a fixed release height exhibited a similar pinching-off point with a depth at larger nanostructural coverage ratios (r ≥ 1/2), thereby resulting in similar cavity lengths and perfectly streamlined water-drop shapes.
However, when spheres were released with the nanostructures downwards, an air-entrained cavity was observed with the nanostructural coverage ratio ranging from +1/8 to 1 when the release height was larger than 0 mm (Figure 3b). The depth of the pinching point and the volume of the cavity increased with the increase of the release height for the same nanostructural coverage ratio. The shape of the cavity that formed at the same release height exhibited little difference with various nanostructural coverage ratios. Therefore, we could conclude that when the sphere impacted the water surface with the nanostructural region downward, only a very tiny region area (for example, r = 1/8) effectively worked to make the water splash and then trap a cavity.
We further traced the falling spheres with different nanostructural coverage ratios, release heights, and directions at depths ranging from 60.0 cm to 80.0 cm underwater, as shown in Figure 3c,d. Within such a region of depth, the same sphere (i.e., the sphere with the same nanostructural coverage ratio, release height, and direction) moved at a uniform velocity. The shear stress of the surrounding water and the increase in the hydrostatic pressure changed the shapes and states of the underwater cavities.
As shown in Figure 3c, no cavity was observed underwater with the nanostructural coverage ratio of −1/8 and −1/6 if the nanostructural region faced upwards. When the nanostructural coverage ratio increased to −1/3 and above, partial cavities were observed underwater at the release heights of 10 and 20 cm. The tail of the partial cavities was changed from a sharppointed shape to a blunt shape. Some wrinkles were observed on the cavity surface, and a small number of gas bubbles were shed from the rear part of the cavity. An increase in the release height increased the volume of the cavity, and the cavity tended to be more stable and achieved streamlined shapes. When the release height increased to 50.0 cm, the cavity appeared to have a streamlined water drop shape, and the further increase of the release height made the cavity shape change very slightly. Additionally, the shape and volume of the cavity formed by the same release height and different nanostructural ratios differed slightly.
When the nanostructure region faced downward, the shapes and states of the underwater cavities on the spheres with various nanostructural coverage ratios were similar at the same release height. For example, when the sphere with a nanostructural coverage ratio of +1/8 was released from a height of 10.0 cm, a great number of gas bubbles were shed from the rear part of the cavity. The underwater cavity shape gradually developed into a streamlined body with the increase of the release height. If the cavity shape reached the streamlined body, the cavity length did not further increase after the release height was raised. This trend of cavity shape development could be also observed in the spheres with other nanostructural coverage ratios.
After investigating the stability of the cavity on the superhydrophobic sphere, we found that there were two factors that caused the instability of the underwater cavity. One factor was the flow separation behind the sphere. The cavity with a large volume and a perfectly streamlined body shape could diminish this instability factor. The other factor was the increasing hydrostatic pressure of the surrounding water. The instability could be transferred upward to the tail of the cavity, resulting in a decrease in the cavity volume. The cavity could recover to a stable state because of the air-entrained capability of the spheres.

Drag Reduction Effect of the Janus Microstructural Spheres with a Cavity in Aqueous Media
The total volume of the attached cavity and sphere (V C ) was stabilized at the depth of 60-80 cm below the water surface. V C was calculated by fitting the image of the underwater cavity with the algebraic curve and then integrating the fitting curve (Supporting Information S7). When the microstructure regions faced upward, the volume of the cavity was 0 cm 3 for the spheres with the microstructural coverage ratios of −1/8 and −1/6 (Figure 4a). For the spheres with the microstructural coverage ratio of −1/3, −1/2, −2/3, and 1, the volume of the cavity increased with the increase of the release height. Taking the microstructural coverage ratio of −2/3 as an example, the  When the microstructure regions faced downward, the Vc values of the spheres with the various microstructural coverage ratios of 1/8, 1/6, 1/3, 1/2, 2/3, and 1 were larger than zero if the release height was greater than 0 cm. The V c values increased with the increase of the release height. At the same release height, the Vc values varied little with the different microstructural coverage ratios. For example, the V C values of the spheres with the microstructural coverage ratio of 2/3 were 2.58, 4.38, 5.40, 7.37 and 7.75 cm 3 at the release heights of 10, 20, 30, 50, and 70 cm, respectively. At the release height of 30 cm, the volumes of the cavities trapped on the spheres with the microstructural ratios of 1/8, 1/6, 1/3, 1/2, 2/3, and 1 were 6.17, 6.06, 5.68, 6.81, 5.40, and 6.66 cm 3 , respectively.
To investigate the drag reduction effect of the Janus microstructural spheres, we introduced the dimensionless hydro dynamic parameter drag coefficient C D to quantify the hydrodynamic drag of the moving spheres with different microstructural coverage ratios, release heights, and directions (Supporting Information S8). For the spheres without any cavities, i.e., the spheres with the microstructural coverage ratios of −1/8 and −1/6, the C D values were relatively large, ranging from 0.47 to 0.53, as shown in Figure 4c (Figure 4d). The larger the release height was, the smaller the C D values were. At the same release height, there was a tiny difference in the C D values on the spheres with different microstructural coverage ratios.
Thus, the C D values were determined based on the shape and volume of the cavity. For example, on the spheres with the microstructural coverage ratio of 1, the volumes of the cavities were 3.15, 4.41, 6.66, 7.09, and 7.84 cm 3 at the release heights of 10 cm, 20 cm, 30 cm, 50 cm, and 70 cm, respectively, corresponding to the C D values of 0.323, 0.257, 0.101, 0.084, and 0.033, respectively; the drag reduction efficiencies were 37.88%, 49.80%, 78.51%, 83.46%, and 93.36%, respectively. Therefore, a fully developed cavity had a better drag reduction effect than a partially developed cavity.

Cavity Formation Mechanisms
To explain the underlying mechanism of the influence of the position, the distribution, and direction of the nanostructures on the cavity formation, we focused on the detailed dynamics www.advmatinterfaces.de of the impacting processes of the Janus interfaces with different nanostructural coverage ratios when the nanostructure faced upward and downward. At the exceedingly early stage of impact, a thin liquid film developed and tended to wet the spherical surface. On the smooth spherical surface, the thin water film climbed up along with its leading-edge splashing. Correspondingly, no cavity was formed. Instead, a vertical jet was observed (Figure 5a, Figure S20a, Movies S5 and S6, Supporting Information). As known, the remaining open aperture only aided in increasing the subsequent air entrainment if the thin film was detached. The film detachment could always be induced by increasing the impact velocity or the CA (θ): [13,15,16,49] where g 0 , l, and ζ are the numerical prefactors, γ LV is the liquidgas surface tension, µL is the viscosity of the liquid, and U* is the critical or transition velocity with the assumption that the thin film will detach. In our experiment, the parameters g 0 , l, ζ, γ LV , and µL were all the same during the free water impact.
Only U* was dependent on the CA (θ). Generally, for a hydrophobic sphere, U* is significantly reduced with an increase in θ. Thus, it is widely believed that a superhydrophobic sphere was the best solution for inducing film detachment at a low impacting velocity to form the splash crown, which results in air entrainment. [3] The cooperation of the nanostructure and low surface energy on the superhydrophobic sphere in this research hindered the water penetrating the topography, resulting in air layers being trapped among the topography to form the Cassie-Baxter state.
When the nanostructure was introduced on the top part of the sphere, a thin liquid film developed first and tended to wet the smooth part of the spherical surface. The thin water film climbed up along until the splashing leading edge met the nanostructure, and then the thin film was detached (Figure 5a, Figure S20b, Supporting Information). When the nanostructural coverage ratios were small (−1/8 and −1/6), the detached water film met above the spheres, leaving a vertical jet of water. The detached thin film only developed to a splash crown if nanostructural coverage ratios increased to −1/3 or even above (Figure 5a, Supporting Information S10, and Movies S7 and S8, Supporting Information). Correspondingly, the remaining open aperture aided in increasing the subsequent air entrainment, and the air-entrainment cavity was trapped on the sphere surface. Interestingly, as long as the nanostructural coverage ratio reached −1/3, a tiny impacting velocity (larger than 0) cloud caused the detached water film to form a splash crown (Supporting Information S11). If the nanostructure was introduced on the bottom part of the sphere, only a tiny region of the nanostructures (for example, the nanostructural coverage ratio of +1/8) could help a thin liquid film to detach and then directly develop to a splash crown (Figure 5b, Supporting Information S12, Movies S9 and S10, Supporting Information).
We explain the physics using the Reynolds, Bond, Weber, and Froude numbers, which we defined as / , / , / , and / e 0 , respectively, where η and ρ are the dynamic viscosity and the density of the liquid, g is the acceleration of gravity, and σ is the surface tension. We used the diameter d instead of the sphere radius as the appropriate length scale in defining the above dimensionless numbers because it resulted in transitional behaviors around a value of one. In our investigation, R e was in the range of 1.992 × 10 5 -5.269 × 10 5 , Bo was 0.0219, We was in the range of 0.345-2.413, and Fr was in the range of 15.748-110.233.
The high static CAs and the similar advancing and receding CAs illustrated that there was perfect superhydrophocisity of the etched regions. When the spheres were immersed into Plastrons are defined as the thin air-pockets locked within the surface porosity of a solid when wetted. They play a fundamental role in materials which display high contact angles. Visually, the plastron can be identified by its inherent slivery mirror-like complex during immersion in water, owing to the total internal reflectance (TIR) of light. After the immersion of 48 h underwater, The silver-mirror sheen still existed on the nanostructural region. These results demonstrated that the fabricated superhydrophobic nanostructural region can maintain the Cassie state underwater for a longevity more than 48 h. In addition, in the process of cavity formation (pinching off timescale = 100 ms), the superhydrophobic nanostructural region can maintain the Cassie state and stabilize the gas-liquid interface (Supporting Information S13).
The presence or absence of an air film trapped between the water and the impacting sphere determined whether the surface was in a Cassie-Baxter, Wenzel-Cassie composite or even Wenzel state, respectively. If water partly or completely penetrates the microstructures of the spheres, Wenzel-Cassie composite or even Wenzel state was developed. Pockets of air remained trapped between the posts if the characteristic curvature pressure P c exceeded the impregnation pressure P I , which had both dynamic and hydrostatic components. [50] The characteristic curvature pressure was determined by the rough microstructures, while the impregnation pressure depended on the depth Z and the speed U of the sphere, i.e., P I = (ρU 2 cos 2 β + ρgZ) ( Figure S36, Supporting Information). The rough microstructures could be represented by a periodic array of posts with separation w and height h. . The latter condition depends on β. However, since the porous nanostructures were grown above the clusters of nanoneedles, it was difficult to impregnate into the nanopores and nanoclusters at the same time. Thus, Wenzel-Cassie composite state developed at the nose so the sphere, and Cassie-Baxter generated at the equator. When the sphere impacted the water surface, the Cassie-Baxter state was achieved as soon as water film met the nanostructures. Therefore, when the nanostructures faced upward, the water film first wetted the smooth sphere surface with a Wenzel state. The Cassie-Baxter state was only achieved if the climbing water film met the nanostructures. Thus, the Z values were about 1.79 and 2.42 cm on the spheres with nanostructural coverage ratios of −1/8 and −1/6, respectively. Both the vertical and radial extents of the cavity were close to the order of the capillary length ( /( ) 0.27 cm c σ ρ = = l g ), and the sphere sank and was completely immersed in water with a small cavity trapped at low W e and B o .

Conclusions
Form drag force, as a crucial form of hydrodynamic drag resistance, occurs with the pressure difference due to the physical dimensions of a blunt object obstructing and altering the flow of a fluid (i.e., flow-separation phenomena). An innovative approach to form drag reduction has been achieved by changing the shape of a blunt body to a streamlined body by introducing a cavity. It is widely believed that the construction of a superhydrophobic sphere is the best solution for introducing a cavity because the nonwetting state of water film on a superhydrophobic surface induces the film detachment at low impacting velocity to form a splash crown, and then air entrainment is achieved. We found that nanostructures, especially the position, coverage ratios, and impacting directions of nanostructures, manipulated the performance of the water film on the sphere surface. Water could not impregnate the nanostructures and the Cassie-Baxter state was achieved. Thus, when the climbing water film met the nanostructures, the water film detached. When the nanostructure faced upward, the detached thin film only developed to a splash crown on the spheres if the nanostructural coverage ratios increased to −1/3 or even above. Correspondingly, the remaining open aperture aided in increasing the subsequent air entrainment, and the air-entrainment cavity was trapped on the sphere surface. However, if the nanostructure faced downward, only a tiny region of the nanostructures (for example, a nanostructural coverage ratio of +1/8) could help a thin liquid film to detach and then directly develop into a splash crown and air entrainment cavity.

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Air-Entraining Cavity Formation Experiment: The experiments used a rectangular tank with a length of 20.0 cm, a width of 15.0 cm, and a depth of 80.0 cm made of poly (methyl methacrylate) (PMMA) to contain the water. Different asymmetric spheres were individually held by the electromagnet at a height H 0 above the water surface. Each sphere was then carefully released from rest and fell toward the water at a speed of U g H = 2 0 0 . The impact process was recorded using a highspeed video camera (i-SPEED 713, IX, UK) with a typical filming frame rate of 2000 fps.

Measurement of The Underwater Spheres and their Velocities:
The experiments used a rectangular tank with a length of 20.0 cm, a width of 15.0 cm, and a depth of 80.0 cm made of PMMA to contain the water. Different asymmetric spheres were individually held by the electromagnet and released carefully. A high-speed video camera (i-SPEED 513, IX, UK) with a typical filming frame rate of 2000 fps was used to record the underwater motion. Several representative frames from the high-speed video captured the movement of the sphere to a typical distance of 10 cm underwater. These representative frames were able to catch the falling time t, based on which the average velocity could be calculated as U = 0.1/t.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.