Golden section criterion to achieve droplet trampoline effect on metal-based superhydrophobic surface

Pin effect and adhesion effect limit the consecutive rebound of droplets. Here, authors propose a strategy of balancing pin and adhesion on microstructures with medium spacing to obtain more consecutive rebound times of droplets.
Golden section criterion to achieve droplet trampoline effect on metal-based superhydrophobic surface

In October 2023, the team of Professor Luquan Ren from Jilin University reported a novel “golden section” design criterion to regulate the droplet rebound number on metal-based surface, subverting conventional knowledge. Especially, the droplet can continuously rebound for 17 times on the metal-based surface, exhibiting an amazing phenomenon of “droplet trampoline”. The droplet rebound number has been experimentally revealed to be closely related to Weber number. Novel quantitative formulas were proposed to predict droplet rebound number and clarify the coupling effect of the structure spacing and the Weber number on the rebound mechanisms, which can be utilized to establish the regulation criteria of rebound numbers and develop novel metal-based superhydrophobic materials.

Recently, the applications of superhydrophobic surfaces have become research hotspots, and many strategies have emerged to facilitate the rapid separation of droplets from superhydrophobic surfaces. Previous studies mainly focused on the droplet contact time to evaluate the dynamic water repellency of surfaces. Nonetheless, the consecutive droplet rebound seems to be a potential phenomenon that has been ignored. In particular, the number of consecutive droplet rebounds (NR) can substantially reflect the dynamic wettability of the surface, and exhibit a promisingly practical value. For example, droplet rebounds are expected to be suppressed on hot surfaces (inhibiting the Leidenfrost effect) to obtain high cooling efficiency, and are undesirable on plant surfaces for better pesticide absorption. On the contrary, more droplet rebounds are required to remove more pollutants from surfaces to realize self-cleaning or to prevent droplets from staying on the surface to delay icing. However, the correlation between the consecutive rebound behavior of droplets and surface structure is crucial to regulate the surface dynamic wettability based on structure design. Moreover, the structure parameter and Weber number (We) are key factors that affect droplet dynamic behaviors. Hence, it is necessary to reveal the effect of surface structure spacing (DS) on the NR within a wide range of We.

Considering superhydrophobic laser-ablated surfaces with DS of 50 µm, 500 µm and 1000 µm (referred to as S50, S500 and S1000, respectively). It is difficult to confirm significant differences in the dynamic behavior of droplets on the three surfaces at a relatively lower We of 22.2 except for the values of NR. However, the droplet rebound behaviors on the surfaces were different at a relatively higher We of 61.0. Specifically, the droplet was partially pinned to the microstructure and could not completely detach from the S50 surface with small DS, and there was liquid adhesion on the S1000 surface with large DS. Briefly, both the partial pinning caused by small DS and the liquid adhesion caused by large DS prevented the droplet rebound, thereby limiting the NR. Surprisingly, droplet could rebound for 12 times on S500 surface at high We without any residual liquid, indicating that the S500 surface exhibited robust water repellency. That means the DS can be optimized to obtain more consecutive droplet rebounds, which is expected to be explored.

Fig. 1 Droplet dynamic behavior on laser-ablated microstructures with different DS. a-c Scanning electronic micrographs of laser-ablated aluminum surfaces with DS of 50 µm, 500 µm and 1000 µm, respectively. d-f Similar droplet rebound behaviors on S50, S500 and S1000 surfaces at a relatively lower We of 22.2. g-i Different droplet rebound behaviors at a relatively higher We of 61.0.

We obtained a series of micro-protrusion structures with different DS by adjusting the laser scan spacing ranging from 50 µm to 1000 µm (referred to as S50-S1000), and measured the NR of prepared surfaces in a wide range of We. Specifically, the S300, S400 and S500 surfaces with no liquid residue are approximately at the golden ratio region in the overall DS range, which is named as the gold region. The water repellency of the surface represented by consecutive droplet rebounds first enhances and then deteriorates as the DS increases. In particular, the residual rates of the surfaces of the gold region are all 0, exhibiting an amazing “golden section” effect.

Fig. 2 Consecutive droplet rebound characteristics of laser-ablated structures with different DS. a Average NR of droplets impacting on surfaces of three typical regions at a series of We in a range from 0 to 82. b Total average NR which represents the droplet rebound ability of each surface. c Residual rates of all surfaces.

 The design concept of fabricating fine microstructures and reducing surface energy to achieve better hydrophobicity and facilitate droplet separation is widely acknowledged. Conventionally, droplets can more easily rebound on the surface due to smaller solid-liquid contact area of the denser microstructure corresponding to smaller DS. However, the large dynamic pressure of small solid-liquid contact area may cause the permeation effect and the transition from Cassie-Baxter state to Wenzel state. Here, we analyzed the differences in dynamic behavior of droplets on microstructures with different DS. Both pin effect and adhesion effect caused by small DS and large DS suppressed the consecutive droplet rebound. The discovery is completely different from the design concept of superhydrophobic surface based on minimal microstructure, which subvert traditional cognition and can provide new horizons for superhydrophobic design.

Fig. 3 Contact characteristics of solid-liquid interface and droplet dynamic behaviors on microstructures with different DS. a Permeation effect facilitated by high dynamic pressure due to large transversal resistance and small solid-liquid contact area on the microstructure with small DS. b Complete droplet rebound without residue on the microstructure with medium DS. c Solid-liquid interface adhesion on the hydrophilic large flat caused by large laser scan spacing.

Different dynamics of droplets on microstructures with different DS leads to different NR, relating to different energy dissipations during the bouncing process of droplets. We compared energy dissipation characteristics of surfaces with different DS, indicating that energy dissipation of droplet on microstructures with medium DS was lower. We obtained the coupled distribution of NR corresponding to different We and DS by combining the NR level of different DS and the trend of NR along with We. The highest NR are concentrated in the low We and medium DS region, which suggest that multiple rebounds of droplet can be realized through designing rational DS and small We.

Fig. 4 The effect of DS on NR and the distribution map of NR. a Energy dissipation characteristics of all surfaces. b The analysis of correlation between DS and NR. c Theoretical distribution of NR that combines the trend of NR with We and the droplet rebound abilities of all surfaces on the coupled two dimensions of We and DS. d Experimental distribution of NR on the basis of two dimensions of We and DS.

In this work, we established the correlation between NR and DS, as well as a connection between NR and We. The golden section criterion provide a new horizon for regulating dynamic wettability of surface and developing new bio-inspired materials. The derived theoretical model is expected to inspire new strategies to realize efficient thermal management, anti-icing, self-cleaning and droplet control.

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