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Surface morphology of the lotus leaf and schematic diagram of dual-level structure: (a,b) Micron-sized mastoid and nano-sized branching structures (Reproduced with permission from [40]. Copyright Wiley-VCH, 2002); (c) designed plane surface with dual-level structure; (d) designed convex surface with dual-level structure.

Surface morphology of the lotus leaf and schematic diagram of dual-level structure: (a,b) Micron-sized mastoid and nano-sized branching structures (Reproduced with permission from [40]. Copyright Wiley-VCH, 2002); (c) designed plane surface with dual-level structure; (d) designed convex surface with dual-level structure.

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Reducing the contact time of a water droplet on non-wetting surfaces has great potential in the areas of self-cleaning and anti-icing, and gradually develops into a hot issue in the field of wettability surfaces. However, the existing literature on dynamic behavior of water drops impacting on superhydrophobic surfaces with various structural shapes...

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... It also enables efficient mist collection, with a collection rate of up to 12.0 L/(m 2 ·h), which is 830% higher than that of smooth copper plates. Lian et al. [28] drawing inspiration from the microstructure of natural superhydrophobic surfaces, like lotus and rice leaves, two and three-layer structures were created on planar and convex surfaces of a 7075 aluminum alloy substrate using WEDM, and after spraying hydrophobic nanoparticles on the surface, they exhibited good superhydrophobic properties with static contact angles up to 156.9±0.7°. From the above studies, while the technology of producing superhydrophobic surfaces on metal substrates via WEDM is relatively mature, further research is needed in the simulation of wetting performance. ...
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... Because the sag mechanism is irrelevant if the designed structures prevent the sagging liquid−air interface from touching the bottom of the substrate, a number of studies have concerned the effect of roughness structures on the energy barrier of the depinning mechanism. Inspired by the lotus leaf, textured surfaces with a hierarchical roughness exhibit a metastable Cassie state of droplets owing to the multi-level energy barrier for the Cassie-to-Wenzel transition (Nosonovsky, 2007;Koch et al., 2009;Bell et al., 2015;Lian et al., 2019;Pan et al., 2019). Nosonovsky (2007) theoretically illustrated that multiscale roughness can help resist the destabilization, thus preventing the liquid penetration even in the case with hydrophilic materials. ...
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Decorating the hydrophobic surfaces with submillimeter patterns has been proved effective in both amplifying the hydrophobic effect and maintaining the wettability robustness. However, the non-robust Cassie wetting state still remains the main reason constraining the practical applications. In the present study, the droplet wetting behavior on a novel surface decorated by primary and secondary structures is investigated by means of three-dimensional direct numerical simulation (DNS). The result shows that compared with that on surfaces with only primary patterns, the new surfaces prohibit the liquid in filtering into the pattern spacing, enhancing the stability of the Cassie wetting state even for an impinging droplet. 1.Introduction Hydrophobic surfaces have gained increasing interest owing to their numerous applications such as self-cleaning on solar panels, anti-icing on airplane wings, and dropwise condensation in heat exchangers. As for the artificial fabrication strategies, chemical coating and topographic structures are commonly employed to enhance water repellence of the substrate. Indeed, studies have demonstrated that the hydrophobicity of water-repel surfaces with submillimetric/millimetric-scale features can be elaborately manipulated via proper design of the surface roughness (1). In addition, the still facing challenges of artificial hydrophobic surfaces such as robustness and durability can be avoided by this fabrication method (2). However, those surfaces may lose the hydrophobicity when liquid penetrates into the pattern spacing forming Wenzel state (3) , thus decreasing the stability of Cassie wetting (4) , which is generally characterized as high contact angles and low contact angle hysteresis. Several articles proposed that surfaces with re-entrant microstructures showed the ability to maintain a metastable Cassie state. Anish (5) developed surfaces possessing re-entrant texture that could support strongly metastable composite solid-liquid-air interfaces, even with very low surface tension liquids such as pentane. By taking into account the tension of the triple line, Edward (6) found the potential barrier separating the Cassie and the Wenzel wetting states increased when liquid penetrated into a hydrophilic relief with reentrant topography, thus leading to stable Cassie wetting. Rishav (7) studied the mushroom-shaped re-entrant microstructures, and a metastable Cassie state was obtained. Other approaches, such as masking surfaces with non-communicating holes (8) or dual-scale and triple-scale micro-nano structures (9) were also proved effectively, but the use of secondary structures for resisting the Cassie-to-Wenzel transition for impinging water droplets has not been explored, to the best of our knowledge. Because the mechanism of droplet impingement on a surface, which is a highly transient process, is difficult to probe by experimental observations alone, the present work is therefore to investigate the dynamics of impinging droplets on surfaces with primary and secondary decorations using three-dimensional direct numerical simulation (DNS), which is based on the coupled level set and volume of fluid (CLSVOF) method for the interface tracking. In addition, the contact angle model is implemented in the boundary condition to consider the effect of surface property on droplets deformation. 2.Methods and modeling Both fluids of air and liquid are treated as isothermal, incompressible, and immiscible Newtonian fluids and no phase change. The governing equations utilized in the present study are the conservation equations of mass and momentum applied to DNS using the in-house code, FK 3 (10,11) , described as follows: ∇ • = 0 (1) (+ • ∇) = −∇ + ∇ • [∇ + (∇) ] + + (2) where denotes the velocity field, the density, the pressure, the mean viscosity, the gravitational acceleration, and the momentum source item concerned with the surface tension and wall adhesion force, which is calculated based on continuum surface force (CSF) model. = () (3) where , and are the surface tension coefficient, curvature and the normal vector of the interface, respectively. Given that the CLSVOF method is utilized in our numerical framework, the free air-liquid interface is captured by a VOF function for satisfying mass conservation, and the Level set function constructed based on VOF function is utilized to compute the interface curvature and vector. More details can be found in the papers (10,11). Near the solid surface, where liquid meets the solid and air, the movement of three-phase contact line (TPCL) critically determines the shape and behavior of a droplet and thus the contact angle should be implemented in the simulations. Sussman's method (12) , considering the contact angle model directly while solving the Level-set functions, is employed in this work. The model validation was performed in our previous work (11). The schematic of the computational domain with uniform staggered grid of 320×300×320 is shown in Fig.1. The grid size is ∆ = 32 µm in all three directions. A spherical water droplet with 0 = 2mm is located above the center of the substrate. A textured surface with primary and secondary submillimeter ridges is placed on the bottom, in which the primary and secondary ridge width, groove width, ridge height are 1 and 2 , 1 and 2 , and 1 and 2 , respectively. According to our previous results (11) , the perfect Wenzel state were obtained when the groove width ratio was larger than 2.0, and the initial was not smaller than 10. Here, the is redefined as = 1 1 ⁄ fixed at 2.1, whereas secondary ridges with varying height 2 are placed in the middle of the primary ridges to investigate the influence of the secondary ridge height on the stability of Cassie wetting state. The detailed simulation parameters are shown in Tab.1. The liquid and air phase properties are same as that in our previous work (11). Additionally, the boundary condition of the substrate is set as wall, while the surroundings are considered as shear free surfaces. In all cases, the gravitational acceleration =9.8m/s 2 is imposed.
... Therefore, it can be seen that groove spacing is one of the main factors affecting the value of the contact angle of the water droplet. As the contact angle of the solid surface is related to the length of the three-phase contact line (TPCL), the contact angle can be expressed as [45] ...
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In order to study the anisotropic behavior of surface contact angle of fluorine rubber (FKM) with rectangular convex structure, firstly, FKM materials with rectangular convex structure were prepared by template method. Secondly, the contact angle of the FKM surface in the direction of 0-90 ° (the direction parallel to the pit is 0 °) was tested. The contact angle data of different surface anisotropy of FKM and the contact diameter of water droplets are summarized. Finally, by using the theory of contact line density and the law of line roughness of FKM surface in different directions, the anisotropic contact angle mechanism of FKM surface structure was explained. The results show that the contact angle and contact diameter of FKM surface are in the observation range of 0 ~ 90 °, and the maximum differences are 9 ° and 162 μm, respectively. The contact angle has an extreme point in the 45 ° observation direction. The contact angle is inversely proportional to the contact diameter. Contact line density and line roughness are the main causes of anisotropic contact angle. In order to reduce the measurement differences caused by anisotropic contact angle, this paper puts forward a new test standard of anisotropic contact angle, which provides a certain theoretical basis and practical value for the future measurement of anisotropic contact angle.
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Bionic superhydrophobic ice-proof surfaces inspired by natural biology show great potential in daily life. They have attracted wide research interest due to their promising and wide applications in offshore equipment, transportation, power transmission, communication, energy, etc. The flourishing development of superhydrophobic ice-proof surfaces has been witnessed due to the availability of various fabrication methods. These surfaces can effectively inhibit the accumulation of ice, thereby ensuring the safety of human life and property. This review highlights the latest advances in bio-inspired superhydrophobic ice-proof materials. Firstly, several familiar cold-resistant creatures with well-organized texture structures are listed briefly, which provide an excellent template for the design of bioinspired ice-proof surfaces. Next, the advantages and disadvantages of the current techniques for the preparation of superhydrophobic ice-proof surfaces are also analyzed in depth. Subsequently, the theoretical knowledge on icing formation and three passive ice-proof strategies are introduced in detail. Afterward, the recent progress in improving the durability of ice-proof surfaces is emphasized. Finally, the remaining challenges and promising breakthroughs in this field are briefly discussed.
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The hydrophobicity of low-energy surfaces is frequently enhanced by masking with micro-structures. However, wetting transition from the Cassie state (total non-wetting state) to the Wenzel state (total wetting state), which often occurs under external factors, such as impingement and vibration, is known to weaken the water repellency, namely, the hydrophobicity of these textured surfaces. The present work numerically examines the stability of the total non-wetting state on the multi-hole surface (MHS) and multi-pillar surface (MPS). The results show that the multi-hole structures not only enhance the hydrophobicity of a surface but also suppress the so-called Cassie-to-Wenzel wetting transition seen on the MPS. On the MHS, the stable air pocket in the holes prevents the three-phase contact line (TPCL) from depinning, thereby stabilizing the total non-wetting state for an impinging droplet. Furthermore, transition to the total wetting state is not found, even under a large We condition due to the corresponding pressure increase in the air pocket. A theoretical model for predicting the maximum spreading factor of an impinging droplet is constructed, which considers the air cavity in the center of the droplet and the energy loss of the TPCL depinning on structures.