Directional transport of droplets impacting on superhydrophobic opening triangular groove surfaces

Directional droplet transport is of great importance to various processes including heat transfer, water harvesting and microfluidics. Here, a facile superhydrophobic opening triangular groove surface was proposed, and the directional transport behavior of droplets impacting on the surface was observed. The results show that the essence of the directional transport on the opening triangular groove surface can be attributed to the interaction between the impinging droplet and the groove sidewall, and the directional transport distance is regulated by the contact area during the interaction. Further, by controlling the depth of triangular groove, the triangular opening angle, the impacting point position and the Weber number, the contact area between the droplet and the groove sidewall during the interaction can be changed, leading to the variation of directional transport distance. This study provides a new method for directional droplet transport on superhydrophobic surfaces and offers more options for the manipulation of droplet behavior.


Introduction
Directional transport of droplets impacting on solid surfaces has been extensively investigated and is crucial to many applications, such as water harvesting [1,2], droplet-based electricity generators [3][4][5], and spray cooling [6,7]. Many solid surfaces have been adopted to achieve directional transport of impinging droplets, such as superhydrophobic surfaces with hybrid wettability and patterned superhydrophobic surfaces. Chu et al. [8] reported that when the droplet impacted on the boundary between the superhydrophobic part and hydrophilic part, the directional transport distance of the droplet can be controlled by changing the proportion of the impinging droplet in the hydrophilic part. Zhao et al. [9] investigated the droplet impacting on a heterogenous superhydrophobic surface with hydrophilic strips, and quantitatively manipulated the directional transport distance of the droplet and suppressed the Plateau-Rayleigh instability successfully [10]. However, these surfaces exist many defects such as droplet loss, mixing, and contamination due to the hydrophilic regions. In another research line, on homogeneous superhydrophobic surfaces, an impinging droplet usually manifests a typical elastic rebound because of the negligible viscous dissipation caused by the hydrophobic roughness trapped underlying the impinging droplet. In addition, due to the short contact time [11,12], the bouncing direction of the impinging droplet is hard to be accurately controlled, so special structures are necessary for directional transport of impinging droplets on homogeneous superhydrophobic surfaces. Wang et al. [13] [14,15] proposed an array of equidistant circular grooves, and realized the directional transport of impinging droplets towards the center of the curvature. Nevertheless, the structures mentioned above are difficult to process and costly.
In this study, a facile homogeneous superhydrophobic opening triangular groove surface (SOTGS) is reported. The interaction between the impinging droplet and the groove sidewall causes directional transport of the droplet in the direction away from the top of the triangular groove. The effects of the groove depth H, the triangular opening angle α, the distance between the impacting point and the top of groove (e. g., the impacting point position L), and the Weber number We on the directional transport distance ΔL were explored. The findings may yield more insights into directional droplet transport on superhydrophobic surfaces.

Preparation and characterization of the SOTGS
The substrates, consisting of a superhydrophobic sheet with an opening triangular groove in the upper part and a flat superhydrophobic sheet in the lower part, were made of 6061 aluminum alloys. In the experiment, the grooves with depth H = 1.0 -3.0 mm and opening angel α = 3 -7° were fabricated by wire electrical discharge machining (WEDM). The schematic of the surface topography is depicted in Fig.1 (a). The aluminum substrates were firstly polished by #500, #800 and #1000 abrasive papers, after that, ultrasonically cleaned in acetone, ethanol and deionized water. Next, the acid etching process was conducted to attain step-like microstructures [ Fig.1 (b)] by putting cleaned substrates into 3.0 M HCl. After etching for ~ 7.5 min, substrates were immediately rinsed with deionized water. Then, boiling treatment process was proceeded to achieve needle-like boehmite and alumina nanostructures [ Fig.1 (d)] by putting etched substrates into boiling water for ~ 15.0 min. Finally, to render the surfaces superhydrophobic, low surface energy modification was implemented by immersing the aluminum substrates into 0.5 mM n-hexane solution of trichloro(1H,1H,2H,2Hperfluorooctyl)silane for ~1 h, followed by heat treatment at 150 °C in air for ~1 h. The surface exhibits a superhydrophobic property with an apparent contact angle of over 170°, as shown in Fig.1 (c).
It is worth mentioning that the top of the groove after WEDM is not a strict tip, but the same molybdenum wire with a diameter of 0.18 mm was used to manufacture the groove with different α, which can ensure that the top radii of different grooves keep the same (R~150 μm), as demonstrated in the inset in Fig.1 (a).

Droplet impact experiments
Deionized water droplets with diameter D 0 = 2.6 mm were released from a syringe pump equipped with a fine needle. The distance between the needle and the surface was adjusted to change the impacting velocity v 0 from 0.38 ms -1 to 0.73 ms -1 , corresponding to 5.16 ≤ We ≤ 19.10, where We = ρv 0 2 D 0 /γ is defined as the Weber number, with ρ = 998 kg/m 3 is the liquid density and γ ≈ 73 mN/m is the interface tension of water. The droplet impacting dynamics were recorded synchronously from both the side and top views by two high-speed cameras (Photron SA4) at a frame rate of 3000 fps. The dynamic behaviors of impinging droplets were analysed using ImageJ software. Fig.2 (a) shows the side and top views of a water droplet impacting on the flat superhydrophobic surface at We = 15.61. The impinging droplet holds a circular symmetry in all directions during the whole spreading and retracting processes.

Dynamic behaviors of droplets impacting on the SOTGS
However, on the SOTGS, as shown in Fig.2    From above analysis, the dynamic behaviors of the droplet impacting on the SOTGS are significantly different from that on the flat superhydrophobic surface in the horizontal direction. The possible reason is that the special triangular groove structure results in the interaction between the droplet and the groove sidewall in the horizontal direction, which further causes the lateral offset of the droplet.

Effect of H on the lateral offset distance
To explore the effect of the groove depth H on the lateral offset distance ΔL of the droplet, the opening angle α was fixed at 5°, H was selected as 1.0 mm, 2.0 mm and 3.0 mm. Fig.3 (a) shows that there is no significant difference in ΔL of the droplets for H = 1.0 mm and H = 2.0 mm at L = 4.50 mm. The possible reason is that the impinging droplet is difficult to penetrate into the groove at the small L corresponding to a small gap. For H = 3.0 mm, the droplet has already broken up at a small We, e.g., We = 8.64 [ Fig.3 (a), inset], and ΔL decreases.
When L increases to 7.50 mm, it can be clearly seen that ΔL of the droplet on the SOTGS with H = 2.0 mm is significantly larger than that with H = 1.0 mm, as shown in Fig.3 (b). The possible reason is that the larger gap at the impacting point facilitates the penetration of droplets into the groove, and a larger groove depth can provide larger contact area during the interaction between the droplet and the groove sidewall, resulting in a larger lateral offset distance.

Effect of α on the lateral offset distance
According to above analysis, when the groove depth is H = 1.0 mm, the contact area between the droplet and the groove sidewall is small, leading to a small lateral offset distance. When H = 3.0 mm, the droplet has broken up at small L [ Fig.3 (a), inset], so H = 2.0 mm was selected here. To investigate the effect of the opening angle α on the lateral offset distance ΔL of the droplet, α was selected as 3°, 5° and 7°. When the impacting point is close to the top of the groove (L = 4.50 mm), the droplet can hardly penetrate into the groove at We = 5.16, 8.64 and 12.12. Therefore, the interaction between the droplet and the groove sidewall is similar under different α, leading to inconspicuous difference in ΔL. However, when We increases to 15.61 and 19.10, ΔL increases sharply for the groove with α = 7°, while changes slightly for α = 3° and α = 5°, as shown in Fig.4 (a). The possible reason is that the droplet is more easily to penetrate into the groove with α = 7° at larger We, and the interaction with the groove sidewall is significantly enhanced, leading to a larger ΔL.
As shown in Fig.4 (b), when L = 5.25 mm, the lateral offset distance of the groove with α = 7° is prominently larger than that of the grooves with α = 3° and α = 5°. ΔL of α = 5° is generally larger than that of α = 3°. The possible reason is that when L increases to 5.25 mm, the larger α, the greater the gap at the impacting point, and the easier it is for the droplet to penetrate into the groove, leading to a larger ΔL. Note that, at α = 7°, the droplet has broken up at We = 19.10 [ Fig.4 (b), inset].

Effect of L on the lateral offset distance
Based on the above discussion, L has a slight influence on the lateral offset distance when α = 3° [ Fig.4 (a) and (b)], and the droplet breaks easily on the groove with α = 7° even though L is small [ Fig.4 (b), inset]. Therefore, the groove with α = 5° and H = 2 mm was chosen to explore the effect of the impacting point position L on the lateral offset distance ΔL of the droplet. Fig.5 (a) shows the variation of the lateral offset distance ΔL as a function of the impacting point position L under various We. The lateral offset distance changes with similar tendency at We = 8.64, 12.12 and 15.61. The distinction is that the L values corresponding to the transition points of ΔL (hollow dots) are different for different We. The L values of the transition points for the increasing stage (hollow square dots) of small We (We = 8.69 and 12.12) are greater than that of large We (We = 15.61), which also applies to the decreasing stage (hollow circle dots). The possible reason is that the droplet is more easily to penetrate into the groove and interact with the groove sidewall for large We, leading to a smaller L at the transition point of increasing stage (the green hollow square dot) for large We. Furthermore, the droplet is more easily to spread excessively in the horizontal direction for large We (We = 15.61), which is similar to the Kelvin-Helmholtz instability [16], resulting in energy dissipation (that is, the decrease of ΔL) and a smaller L at the transition point of decreasing stage (the green hollow circle dot) for large We.
In current researches of directional droplet transport, the lateral offset distance ΔL generally increases with We [14,15]. In this work, ΔL does not monotonically increase with We, and is also related to L. As shown in Fig.5 (b), when L = 5.25 mm and 6.75 mm, ΔL increases with We and the maximum ΔL appears at We = 19.10. However, ΔL shows a downward trend with increasing We at other L. When L = 7.50 mm, the droplet breaks at We = 19.10 [ Fig.5 (b), inset].

Conclusion
In this work, a superhydrophobic surface composed of an opening triangular groove was designed and realized the directional transport of impinging droplets. The effects of the groove depth H, the opening angle α, the impacting point position L, and the Weber number We on the lateral offset distance ΔL were experimentally studied. The results are as follows: (1) When L is smaller, the droplet is difficult to penetrate into the groove, so H can hardly cause differences in ΔL. At larger L, increasing H can provide larger contact area during the interaction between the droplet and the groove sidewall, leading to a larger ΔL. However, the droplet breaks easily at a too large H.
(2) When L and We are small, α has a slight effect on ΔL because the droplet is difficult to interact with the groove sidewall. Properly increasing We or L can promote the interaction between the droplet and the groove sidewall to differentiate the effect of α on ΔL, that is, a larger α leads to a larger ΔL.
(3) For the groove with H = 2.0 mm and α = 5°, ΔL changes with L under different We show similar tendency, and the distinction is that the L values of the transition points are different for different We. Besides, ΔL is not only related to We, but also affected by L, so it does not monotonically increase with We.
This work deepens the understanding of impinging droplets behavior on patterned superhydrophobic surfaces and facilitates the application of superhydrophobic surfaces in the field of the manipulation of impinging droplets.