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Liquid Collection on Welwitschia-Inspired Wavy Surfaces

Hydrophobic (HPo) surfaces for atmospheric water harvesting applications require sophisticated wettability and microstructure patterns, which suffer from high cost and low durability against severe mechanical and environmental degradations. Inspired by the leaves of Welwitschia mirabilis, a long lifespan desert-living plant, we present a robust superhydrophilic (SHPi) surface design which is capable of enhancing both dew condensation and fog capture. The surface consists of a parallel-aligned millimetric wavy topography on top of which random nanostructures are grown. By studying the liquid dynamics, we have shown a unique mechanism of water transport on the SHPi wavy surface by droplet splitting and Laplace pressure gradient. It has been revealed that the efficient water transport on the SHPi wavy surface synergistically interacts with the enhanced diffusion flux of water vapor on the convex regions and significantly improves the efficiency of filmwise condensation. We have further demonstrated that wavy features enhance the probability of fog droplet collisions by disturbing the air flow and increasing the mean free path of fog droplets.


Introduction
Dew condensation and fog capture are the two main mechanisms of atmospheric water harvesting. 1-3 As a phase change heat transfer phenomena by nature, dew condensation on a supercooled surface consists of nucleation, droplet growth, and condensate removal. 4,5 Although nucleation is energetically preferred, superhydrophilic (SHPi) surfaces, on which condensation occurs in a filmwise manner, are believed to be inferior to hydrophobic (HPo) and superhydrophobic (SHPo) surfaces due to the thermal insulating effect of the condensate film. [6][7][8][9] However, dropwise condensation can fail on SHPo surfaces under a large subcooling and a high condensation rate, because droplets inevitably nucleate within the nanoscale surface textures, which impales the Cassie-Baxter wetting state and causes the surface flooding problem. 10,11 Condensate on the flooded surfaces is subject to significant retention force due to the surface roughness, and the condensation efficiency can be largely deteriorated because of the immobile droplets. 12,13 On the other hand, water harvesting by capturing fog droplets is not only an interfacial process, but also a problem of fluid dynamics. Fog droplets (1-40 μm in diameter) in the air flow collide with the solid surfaces at first, and are then transported and collected. 14,15 In the first step, the macroscopic geometry of the fog collectors influences the air flow field near the surface and hence the probability of fog droplets colliding with the surface. 16,17 Microscopically, it has been shown that the surface wettability needs to be carefully chosen, since the SHPi mesh suffers from the clogging problem which reduces the permeability of the collector, whereas the deposited fog droplets on the SHPo mesh can reenter the air flow without being effectively captured. 18,19 However, for the water transport step, studies on the fog capturing behavior of single wire systems revealed that the onset time needed for collecting fog drops in the reservoir is minimized on the SHPi surfaces because of the spontaneous water spreading. 20,21 Therefore, a surface design with proper macroscopic geometry and surface wettability to optimize both fluid dynamics and liquid transport is yet to be fully developed. 22,23 Here, we report the surface design with millimetric wavy patterns inspired by the leaves of Welwitschia mirabilis, a long life-spanned desert-living plant, for both efficient dew condensation and fog capturing. For condensation, we employ the diffusion-enhanced droplet growth mechanism on the convex surface features discovered in our previous studies. 24, 25 We further study the droplet transport mechanism on the convex surfaces with various wettabilities. We demonstrate that, different than on the extensively-studied flat surfaces, the SHPi convex surfaces benefit from a unique droplet splitting mechanism which keeps the thickness of condensate to be effectively zero. The water mobility is further enhanced by introducing the curvature gradient to the surface geometry so the condensate is spontaneously transported away from the convex regions driven by the Laplace pressure. For fog capturing, we show that the wavy features disturb the air flow so the probability of droplet collision with the surface increases. The SHPi wettability effectively retains the captured fog droplets, and transports them to the reservoir. or IPA/water mixture) at an infusion rate of 1 μL/sec. To minimize the kinetic energy of the drops, the wedge surface was horizontally placed close to the needle so the distance that the drops fell before touching the surface was small (about 1 mm). A high-speed camera (Photron Mini AX) with a macro lens (Nikon AF-S NIKKOR 85mm f/1.8G) was used to record the cross-sectional view of the deposited droplets at a frame rate of 5000 fps.
Visualization of the Water Meniscus. The profile of the water meniscus on the superhydrophilic wavy surface was visualized under a reversed confocal laser scanning microscopy (Leica SP5, 5× objective lens). Rhodamine 6G (99%, Sigma-Aldrich), a typical dye for fluorescence probes, was dissolved in DI water at a concentration of 1 mg/L. The solution was then dispensed on the horizontally-placed superhydrophilic wavy surface to ensure the sample is uniformly wetted. The sample was then gradually tilted until the waves are vertically oriented, and the excessive liquid was removed from the surface by gravity. The sample was placed upside-down on the stage, and was scanned by a 520 nm laser beam which has a shorter wavelength than the absorption maximum of Rhodamine 6G at 530 nm, and fluorescence emission within 550-590 nm was collected to form the image. To obtain the cross-sectional profile of the meniscus, the scanning was conducted under the z-stack mode with a total z-volume of 2.5 cm and a step size of 1 μm to cover the entire range from the valley to the peak of the sample. The bias applied to the top plate was then switched to positive, at which t = 0 is defined, and the surface temperature reached 2.5˚C within 5 min. The condensation processes were recorded by a DSLR camera (Nikon D5500) and a macro lens (Nikon AF-S NIKKOR 85 mm f/1.8G). A schematic of the condensation setup is shown in Fig. 1A.

Droplet Stability on a Wedge-Shape Convex Surface
Due to the constraint of minimum surface energy, the equilibrium shape of a droplet resting on a flat surface is a spherical cap when the capillary force dominates. 26 As shown in Fig. 2A, the maximum thickness of the liquid cap (ℎ "#$ ), and the water-solid interface area ( ) is given by: where is the volume of the droplet, the apparent contact angle, the radius of the contact area. Since the enhancement of water vapor diffusion is the most pronounced at the apex of the convex  features, the maximum thickness of the droplet coverage at the apex is of significant implications to the overall condensation efficiency. Fig. 3 marks the ℎ "#$ for various CA and combinations after the kinetic energy of the droplets has fully dissipated (t = 75 μs). It is clear that, for the same CA, decreasing effectively results in a smaller ℎ "#$ . When is large for droplet to statically sit on the apex, decreasing CA leads to smaller ℎ "#$ , while when is small, increasing and decreasing CA can both leads to ℎ "#$ close to zero, by the droplet splitting and repelling mechanism, respectively.
To quantitatively understand the correlation between the fate of the droplet and CA/ combinations, we simplify the problem to 2-dimensional, as shown in Fig. 4. The equilibrium profile of a sessile microdroplet in 2D is part of a circle, since such geometry minimizes the circumference with a constant enclosed area. Two critical relations can be found by this analysis.
When CA < 90°− C 0 , i.e. low CA and low , the surface tension is unable to support the droplet to stably sit on the apex, and splitting will occur. When CA > 90°+

Condensation on the Wedge-Shaped Convex Surfaces
The droplet instability on the convex surface is verified in condensation. As shown in

Liquid Transport by Continuous Curvature Gradient
An obvious shortcoming for the SHPi wedge surface for condensation is that, due to the infinite curvature at the apex, the droplets are pinned on the two half-planes where the curvature is zero as shown by the dashed circles in Fig. 6. The splitting mechanism for the wedge geometry does not apply to transport the condensate further away from the apex so the condensate can be  Welwitshcia mirabilis, a desert-living plant which has a long lifespan of over 1000 years, shows unusual hierarchical structure of its leaves. 27 As shown in Fig. 7A, the leaves show a continuous wavy pattern on the scale of ~1 mm instead of a flat geometry as the first tier, on which the second-tier nanoscale roughness is present. Inspired by this wavy geometry, we modify the wedge shape apex into a wavy pattern with continuous surface curvature. By using the SHPi wettability, the liquid spreads on the surface and well conforms the geometry of the solid substrate.
We hypothesize that spontaneous liquid transport will occur because of the Laplace pressure gradient caused by the curvature gradient. We design our surface geometry as a periodic pattern, where the curvature linearly decreases from positive (at the peaks) to negative (at the valleys), as illustrated in Fig. 7B. Fig. 7C shows the equilibrium profile of water on the SHPi wavy surface. Even though the entire surface is wetted by water, the water then preferentially resides in the valley where the curvature is negative, while the peak region shows a zero thickness of water film. Note that the direction of gravity points upwards, meaning the capillary force outweighs the gravitational force in such length scale. The transport mechanism was also studied by liquid infusion experiments. As shown in Fig. 7D, a needle was in contact with the peaks. By expelling water at a rate of 0.5 μL/s, the liquid spontaneously transports into the valley on the SHPi surface, and the thickness of water at the peak regions where the liquid was infused is negligible. In comparison, on a SHPi flat surface, the liquid accumulates in size, resulting in a substantial thickness which is similar to what is observed in filmwise condensation on a flat surface. On a superhydrophobic surface, however, the droplet grows in size without any lateral motion relative to the peak. The peak was covered by the drop, similar to the pinned droplets shown in Fig. 6.

Condensation on the Wavy Surface
The synergy between the diffusion-based droplet growth and the curvature-driven liquid transport was studied by the condensation experiments. To better visualize the motion of condensed liquid, the peak of the wavy surface was dyed by a particle of Rhodamine 6G. As shown in Fig. 8, the solid dye particle was dissolved in the condensed liquid, and shows the path along which the liquid moves. On the SHPi sample, condensation preferentially happens on the peaks, the same as we observed on the wedge-shaped surfaces. Droplets grow and the transport initiates when they are large enough (t = 10 min). The droplets stop their motions when they reach the valleys, where the condensate is collected. It is worth noting that the first the liquid thickness at the peaks is not negligible before the droplets depart from the peaks (t < 15 min). This is because droplet pinning occurs at the water front, where the non-wetted region becomes wetted due to the droplet motion. However, such pinning is significantly reduced as condensation proceeds. As shown when t = 60 min, most of the peak areas are refreshed without significant condensate thickness. Such enhancement of liquid mobility suggests that water infused in the nanoscale roughness of the SHPi surface, and the condensate is effectively 'self-lubricated'.
However, on the hydrophobic and superhydrophobic wavy surfaces, the condensation mode is very different. Because the condensate does not move in a filmwise manner, the liquid collection relies on the motion of each individual droplet. The droplets are therefore pinned on the peaks without moving into the valleys. As the number density and size of the droplets increase, the overall condensation rate slows down, which further inhibits the droplet growth. The Laplace pressure gradient does not apply to such droplets which show very different profile shape than the underlying substrate. The condensed droplets were then detached and rolled down along the peaks because of gravity. As the number of condensation cycles increase, the dropwise condensation mode gradually fails and because of the Cassie-Baxter to Wenzel transition. Different than the high droplet mobility on the SHPi surfaces, the condensate transport did not benefit from the filmwise mode, because the hydrophobic nature of the underlying substrate significantly pins the condensate at the contact line by exhibiting a high energy barrier to be wetted.

Fog Collection on the Wavy Surface
The quantitative results are shown in Fig. 9. As shown, the fog collection rates for all four wettabilities of the wavy surfaces were higher than that of the flat HPi surface. Furthermore, the SHPi wavy surfaces possessed the highest fog collection rate at 2 and 3 m/s. Simulation results of flow streamlines interacting with the wavy surfaces are shown in Fig. 9A. As shown, the separation occurs almost immediately after contacting the surface, resulting in low velocity vortices located in the channels of the waves, while bulk flow is found farther away. The free path of fog droplets Droplets initially deposit on the peaks of the waves, then transport into the valleys as they grow. Once a droplet reaches a critical volume, the droplet sheds from the surface and is collected.
Wind speed: 1m/s A B C near the wavy surface features is significantly elongated by the vortices, and hence the probability for the droplets to collide with the surface and get captured is enhanced. A qualitative assessment of experimental data in Figs. 9B and C shows that droplets in the bulk flow initially deposit on the peaks of waves, coalesce, and are transported into the valleys using the Laplace pressure gradient.
There, the droplets continue to grow in a low velocity regime, thus reducing evaporative losses as well as losses due to re-entrainment. The droplets continue to grow until a critical volume is achieved where gravitational forces exceed the retention force dictated by the surface chemistry and morphology. At this point, droplets are shed downwards to the collection apparatus.

Conclusion
In all, we studied the optimized combination of macroscopic and micro/nanoscale surface texture as well as the surface chemistry for efficient water condensation from the air. We discovered the distinct modes of water droplet when it sits on the apex of a wedge-shape convex surface. The droplet splitting mechanism, especially, gives an opportunity to the development of efficient filmwise condenser which does not rely on the degradable hydrophobic coatings.
However, by combining the enhanced diffusion on the convex surface features, it was found that the droplets were pinned on the two half-planes without being transported further away from the apex, and the condensation efficiency could be potentially compromised. Inspired by the hierarchical surface texture of the leaves of Welwitschia mirabilis, we rationally designed a surface profile with continuous curvature gradient. We found that liquid can be spontaneously transported from the peaks to the valleys, following the curvature gradient. By combing the wavy geometry and the superhydrophilic surface wettability, we were able to achieve an efficient condensation of water vapor which outperforms the dropwise condensation on the hydrophobic and superhydrophobic surfaces, which were believed to be superior to the filmwise mode. We envision this study provides physical insights on the phase change and transport phenomenon for a wide range of applications including condensation heat exchangers, desalination, and microfluidics.