Infinite Lifetime of Underwater Superhydrophobic States

Submerged superhydrophobic (SHPo) surfaces are well known to transition from the dewetted to wetted state over time. Here, a theoretical model is applied to describe the depletion of trapped air in a simple trench and rearranged to prescribe the conditions for infinite lifetime. By fabricating a microscale trench in a transparent hydrophobic material, we directly observe the air depletion process and verify the model. The study leads to the demonstration of infinite lifetime ($>50$ days) of air pockets on engineered microstructured surfaces under water for the first time. Environmental fluctuations are identified as the main factor behind the lack of a long-term underwater SHPo state to date.

Figure 1

The sample and testing setup. (a) SEM images of a single-trench sample with the microscale trench characterized by length $l$, width $w$, and depth $h$. (b) Schematic illustration of the experimental setup to visualize the air-water meniscus inside the trench throughout the depletion process. One sample was immersed in water of height $H$ in a clear tube and observed from the side, as indicated by the arrow A in (a).

Figure 2

Observed air depletion and trench wetting. (a) Air-water meniscus visualized by the setup shown in Fig. 1 with the viewing direction A shown in Fig. 1. Images from top to bottom show the meniscus starting to bend, depinning, sliding down, touching the trench bottom and fully wetting the trench. Shown on the right are the corresponding cross-sectional schematics with viewing direction B. For a complete movie, see Video S1 [24]. (b) Experimental and theoretical data of the meniscus position over time reveal two distinctive stability conditions, determined by the immersion depth $H$. The meniscus position is defined as the distance from the top edge of the trench to the lowest position of meniscus. Experimental data were obtained from continuous microscopy images of the air-water meniscus, as shown in Fig. 2, using samples with $w=147\mu \mathrm{m}$, $h=85\mu \mathrm{m}$, and $l=1\mathrm{mm}$. Uncertainty of the position measurement ($\sim 3\mu \mathrm{m}$) is shown in the Figure. Calculated for the same trench geometry and immersion depth, the solid line fit the data best with $k_p=2.5\times {10}^{-12}\mathrm{cm}/(\sec ·\mathrm{Pa})$, while the dotted lines show the influence of $k_p$ with $2\times {10}^{-12}\mathrm{m}/(\sec ·\mathrm{Pa})$ and $3\times {10}^{-12}\mathrm{m}/(\sec ·\mathrm{Pa})$, respectively. The dot-dash line denotes the maximum deflection of the meniscus while the meniscus remained pinned at the top edge.

Figure 3

Observed lifetime of trapped air. (a) Air-water meniscus seen from above the sample with low-magnification camera. The meniscus appears black. The black strip at $t=0\mathrm{hr}$, the broken strip at $t=8.5\mathrm{hr}$, and the disappearance of the strip at $t=16\mathrm{hr}$ indicate the beginning, touching bottom, and full wetting, respectively, corroborating the observation in Fig. 2. (b) Lifetime of trapped air as a function of immersion depth with trench width of $147\mu \mathrm{m}$ (closed square), $96\mu \mathrm{m}$ (closed circle), and $46\mu \mathrm{m}$ (closed triangle) as the parameter. The measurement errors of immersion depth (i.e., $\pm 2.5\mathrm{mm}$ due to evaporation, as explained in the Supplemental Material [24]) and lifetime (i.e., the interval between snapshots) are too small to appear in the given scales. The symbols with an arrow indicate at least 1200 hours, considered infinite in this study. Each of the three colored shades indicates the uncertainty range of critical depth $H_c$ for a given trench width. (c) Critical immersion depth $H_c$ as a function of trench width $w$. The experimental results are from the uncertainty ranges (i.e., the colored shades) in (b). The solid line is the theoretical prediction of Eq. (4) with 130° as the advancing contact angle measured on the trench sidewall (obtained in the Supplemental Material [24]).