Superhydrophobic surfaces for extreme environmental conditions

Abstract

Superhydrophobic surfaces for repelling impacting water droplets are typically created by designing structures with capillary (antiwetting) pressures greater than those of the incoming droplet (dynamic, water hammer). Recent work has focused on the evolution of the intervening air layer between droplet and substrate during impact, a balance of air compression and drainage within the surface texture, and its role in affecting impalement under ambient conditions through local changes in the droplet curvature. However, little consideration has been given to the influence of the intervening air-layer thermodynamic state and composition, in particular when departing from standard atmospheric conditions, on the antiwetting behavior of superhydrophobic surfaces. Here, we explore the related physics and determine the working envelope for maintaining robust superhydrophobicity, in terms of the ambient pressure and water vapor content. With single-tier and multitier superhydrophobic surfaces and high-resolution dynamic imaging of the droplet meniscus and its penetration behavior into the surface texture, we expose a trend of increasing impalement severity with decreasing ambient pressure and elucidate a previously unexplored condensation-based impalement mechanism within the texture resulting from the compression, and subsequent supersaturation, of the intervening gas layer in low-pressure, humid conditions. Using fluid dynamical considerations and nucleation thermodynamics, we provide mechanistic understanding of impalement and further employ this knowledge to rationally construct multitier surfaces with robust superhydrophobicity, extending water repellency behavior well beyond typical atmospheric conditions. Such a property is expected to find multifaceted use exemplified by transportation and infrastructure applications where exceptional repellency to water and ice is desired.

Keywords: droplet impact; superhydrophobic; wetting.

Fig. 1.

Droplet impact on superhydrophobic surfaces with multitier surface texture in varying atmospheric conditions $\left(We=39\right)$. Side-view impact sequences for different environmental conditions: (A) high pressure, moderately humid $\left(\left[p,p_{\text{v}}\right]=\left[\mathrm{95,1.3}\right]\hspace{0.17em}\text{kPa}\right)$; (B) medium vacuum, dry $\left(\left[p,p_{\text{v}}\right]=\left[0.1,\approx 0\right]\hspace{0.17em}\text{kPa}\right)$; (C) low vacuum, dry $\left(\left[p,p_{\text{v}}\right]=\left[9,\approx 0\right]\hspace{0.17em}\text{kPa}\right)$; and (D) low vacuum, humid $\left(\left[p,p_{\text{v}}\right]=\left[\mathrm{9,2.3}\right]\hspace{0.17em}\text{kPa}\right)$. Impalement in B and D is defined by the presence of a daughter droplet on the surface after rebound and is indicated by red arrows. (D, Inset) Micrograph of the multitier superhydrophobic surface. (E) Plot of p_v vs. p vs. impalement (red asterisks) or rebound (blue circles). A transition zone exists within which both outcomes are possible (white region). The black line of $p_{\text{v}}=p$ bounds the impossible to access gray region in which $p_{\text{v}}>p$. Individual data points have $n\ge 5$; the red, white, and blue domains have a total of $N\left(\text{red,white,blue}\right)=\left(\mathrm{80,100,60}\right)$, respectively. (Scale bars: A–D, 2 mm; D, Inset, 20 µm.)

Fig. 2.

Properties of impalement. (A) Side-view impact sequence of a typical impalement case $\left(We=39\right)$ defining initial droplet diameter area, D₀, and daughter droplet impaled diameter, D_d. (Scale bar: 2 mm.) (B) Plot of the probability of impalement, Φ, vs. p for $p_{\text{v}}\approx 0\hspace{0.17em}\text{kPa}$ (red line) and $p_{\text{v}}=2.3\hspace{0.17em}\text{kPa}$ (blue line). Individual data points have $n\ge 10$. (C) Box plot of normalized impaled area, ${\left(D_{\text{d}}/D_0\right)}^2$, vs. p for $p_{\text{v}}\approx 0\hspace{0.17em}\text{kPa}$ (red; n = 15) and $p_{\text{v}}=2.3\hspace{0.17em}\text{kPa}$ (blue; $n\ge 10$). The dotted line corresponds to the resolution limit of our measurements.

Fig. 3.

Bottom-view impact sequences at low speed (We = 48): $\left[p,p_{\text{v}}\right]=\left[\mathrm{95,1.3}\right]\hspace{0.17em}\text{kPa}$ (A), $\left[p,p_{\text{v}}\right]=\left[2.5,\approx 0\right]\hspace{0.17em}\text{kPa}$ (B), and $\left[p,p_{\text{v}}\right]=\left[2.5,2.3\right]\hspace{0.17em}\text{kPa}$ (C). (C, Inset) Scanning electron microscopy micrograph of iCVD-coated PUA micropillars $\left[d,s,h\right]=\left[2.5,5.0,5.8\right]\hspace{0.17em}\text{μm}$. (A) Partial impalement with entrained bubble; full rebound observed ($\mathrm{\Phi }=0$, $n=6$). (B) Partial impalement with smaller entrained bubble; full rebound observed ($\mathrm{\Phi }=0$, $n=14$). (C) Full impalement with small entrained bubble; daughter droplet visible on surface after contraction ($\mathrm{\Phi }=0.85$, $n=13$). Columns 6 and 7 show magnified bottom views of red-framed regions and based on this, extrapolated side-view schematics of meniscus penetration at maximum droplet spreading: $\sim 2.2\hspace{0.17em}\text{ms}$ after impact. Sequences are synchronized to the first moment that the droplet appears in focus (white dot in center of frame). (Scale bars: A–C, 1 mm; column 6 in A–C, 0.5 mm; C, Inset, 10 µm.)

Fig. 4.

Condensation-based impalement model. (A) Schematic of the droplet with dimple (not to scale) immediately before impact. The increases in gas pressure and temperature, ∆p_g and ∆T_g, respectively, are calculated immediately beneath the droplet in the region denoted by the ×. (B) ∆p_g*/p of gas entrained by the droplet at impact for fixed $R=1.03\hspace{0.17em}\text{mm}$, $\sigma =0.072\hspace{0.17em}\text{N}\hspace{0.17em}{\text{m}}^{-1}$, ${\rho }_{\text{l}}=998\hspace{0.17em}\text{kg}\hspace{0.17em}{\text{m}}^{-3}$, and ${\mu }_{\text{g}}=1.83\times {10}^{-5}\hspace{0.17em}\text{Pa}\hspace{0.17em}\text{s}$. The relative pressure increase can be seen to be very small for all but low p and high We. The dashed line corresponds to the compressible limit above which $\epsilon >1$ and is treated as $\epsilon =1$ for the calculation of $\mathrm{\Delta }{p}_{\text{g}}^{\ast }$ in Eq. 2. (C) Plot of the supersaturation in the intervening gas layer, ${\varphi }_{\text{g}}$, across a range of ϕ and $\mathrm{\Delta }{p}_{\text{g}}^{\ast }/p$. The × symbol in B and C corresponds to the experimental conditions in Fig. 3C, yielding $\mathrm{\Delta }{p}_{\text{g}}^{\ast }/p\approx 7$ and ${\varphi }_{\text{g}}\approx 7.2$. (D) Plot of $J$ vs. ${\varphi }_{\text{g}}$ for a flat area of sample. $J\ge 1\hspace{0.17em}{\text{μm}}^{-2}\hspace{0.17em}{\text{μs}}^{-1}$ corresponds to a high likelihood of a nucleus growing on the surface. For one nucleus per micropillar unit cell, $J\ge 1\times {10}^{-2}\hspace{0.17em}{\text{μm}}^{-2}\hspace{0.17em}{\text{μs}}^{-1}$ is required corresponding to ${\varphi }_{\text{g}}\approx 5$.

Fig. 5.

Pressure-based impalement mechanism analysis $\left(We=63\right)$. (A) Plot of H_d/h vs. p at impact (solid line) predicting decreased dimple size at lower p as we enter a more compressible regime (decrease in ε; dashed line). (B) Bottom-view images and schematics for impalement at We = 63 for p = 95 kPa (Upper) and p = 2.5 kPa (Lower). L_d decreases for lower p ($L_{\text{d}}=\left[0.32\pm 0.04,0.16\pm 0.02\right]\hspace{0.17em}\text{mm}$, respectively). (Scale bar: 0.5 mm.) (C) Plot of L_d vs. p for impalement at $We=63$. Bottom-view measurements (squares, n = 3; error bars represent one SD of uncertainty, hidden by marker for p = 1 kPa) can be fitted to the scaling $L_{\text{d}}=a{\left(R{H}_{\text{d}}\right)}^{1/2}$ with $a=8$ (solid line) and H_d, a function of p, calculated from Eq. 1. (D) Plot of the gas cushion thickness coefficient, $\delta =H_{\text{d}}/\lambda$, across a range of p and We. The dashed line represents $\delta =1$, below which the likelihood of impalement is increased by the absence of a significant air cushion beneath the droplet on impact.

Fig. 6.

Bottom-view impact sequences for hierarchical micropillars $\left(We=63\right)$: $\left[p,p_{\text{v}}\right]=\left[2.5,\approx 0\right]\hspace{0.17em}\text{kPa}$ (A) and $\left[2.5,2.3\right]\hspace{0.17em}\text{kPa}$ (B; $\mathrm{\Phi }=0$, $n=5$ for both cases). (A, Insets) Micrograph of hierarchical micropillars $\left[d,s,h\right]=\left[2.5,5.0,5.8\right]\hspace{0.17em}\text{μm}$ and added nanotexture. (Scale bars: A and B, 1 mm; A, Upper Inset, 5 µm; A, Lower Inset, 500 nm.)