Shear-Driven Failure of Liquid-Infused Surfaces

Rough or patterned surfaces infused with a lubricating liquid display many of the same useful properties as conventional gas-cushioned superhydrophobic surfaces. However, liquid-infused surfaces exhibit a new failure mode: the infused liquid film may drain due to an external shear flow, causing the surface to lose its advantageous properties. We examine shear-driven drainage of liquid-infused surfaces with the goal of understanding and thereby mitigating this failure mode. On patterned surfaces exposed to a known shear stress, we find that a finite length of the surface remains wetted indefinitely, despite the fact that no physical barriers prevent drainage. We develop an analytical model to explain our experimental results, and find that the steady-state retention results from the ability of patterned surfaces to wick wetting liquids, and is thus analogous to capillary rise. We establish the geometric surface parameters governing fluid retention and show how these parameters can describe even random substrate patterns.

Figure 1

(a) Cross section of the microfluidic flow cell, showing the configuration at the beginning of an experiment. Distances in the $y$ direction are exaggerated. The aqueous solution (blue) flows in the left inlet and out the first (slot-shaped) outlet. The grooves are filled with oil (green), and connect to the reservoir of oil at the flow cell terminus. (b) This planform view shows the entire device before drainage commences. Low viscosity oil fills the 50 longitudinal grooves at the center of the device and fluoresces green. (c) Snapshots of a sample shear-driven drainage experiment subject to an aqueous flow of $Q=2\mathrm{mL}/\min$ (${\tau }_{yx}=5.2\mathrm{Pa}$). (d) Micrograph of the silicon wafer micropattern that is used to mold the grooves, including the surface profile (purple). Grooves appear dark gray and walls appear light gray.

Figure 2

(a) Representative groove cross sections from the steady-state configuration of an experiment conducted at $Q=2\mathrm{mL}/\min$ with low viscosity oil, taken at the outlet slot ($x=0\mathrm{mm}$) and the far upstream end of the wetted groove ($x=-5.5\mathrm{mm}$). (b) The steady-state deflection at the center of the groove $\delta (x)$ with theoretical predictions (Supplemental Material [35]) plotted as dashed lines. Gray is low viscosity oil at $Q=2\mathrm{mL}/\min$, red is high viscosity oil at the same flow rate, and blue is low viscosity oil at $Q=1\mathrm{mL}/\min$. (c) Schematic of one groove, showing geometric parameters and the shape of the interface deduced from (b).

Figure 3

Drainage curves for grooves, plotted as length versus time, with dimensional results in (a) and (c) and nondimensional results in (b) and (d). Gray is low viscosity oil at $Q=2\mathrm{mL}/\min$, red is high viscosity oil at the same flow rate, and blue is low viscosity oil at $Q=1\mathrm{mL}/\min$. The theoretical prediction from the Supplemental Material [35] is plotted in dashed black. Top row [panels (a) and (b)] shows the effect of varying flow rate and bottom row [panels (c) and (d)] shows the effect of varying the oil viscosity. Each line represents the average wetted length of all of the defect-free grooves from one experiment. Most experiments contain surface defects that cause multiple grooves to drain with a different behavior ($\approx 5–10$ of the 50 grooves in each experiment); these grooves are excluded from the averaging. The plot includes multiple experiments conducted with low viscosity oil at the higher flow rate in order to indicate the degree of natural variability in the data.

Figure 4

(a) Steady-state length $L_{\infty }$, normalized by $\gamma /{\tau }_{yx}$, for varying groove aspect ratio, with low viscosity oil; $Q=2\mathrm{mL}/\min$ (red), $Q=1\mathrm{mL}/\min$ (blue), and $Q=0.5\mathrm{mL}/\min$ (orange). Squares are for grooves with $h\approx 10\mu \mathrm{m}$, and circles are for grooves with $h\approx 20\mu \mathrm{m}$. The theoretical prediction from Eq. (2), $L_{\infty }{\tau }_{yx}/\gamma =2c_{p}h/c_s{r}_{\min }$, is given by the dashed line. (b) Groove resistance coefficients $c_p$ (green), $c_s$ (purple), and the ratio $c_p/c_s$ (black) as a function of aspect ratio $w/h$. Each curve asymptotes to the dashed line of the same color.

Figure 5

(a) Snapshots of a shear-driven drainage experiment on a substrate consisting of randomly placed posts. A script was written in MATLAB to define the uniformly random locations of the cubes on a $1\text{−}\mu \mathrm{m}$ grid subject to two conditions: (1) that the area density of the posts is 25%, and (2) that the minimum space between posts is $3\mu \mathrm{m}$ (to aid with photolithography). The pattern is initially filled completely with low viscosity oil (green). The oil drains due to an external aqueous flow of $Q=0.5\mathrm{mL}/\min$. (b) Micrograph of the silicon wafer micropattern that is used to mold the posts (light gray), including a surface profile (purple).