(a) Schematic of a superhydrophobic surface with ridges and grooves. (b) Schematic of the air–water meniscus on one of the grooves. The shape of the meniscus is calculated by applying balance of forces between hydrostatic and trapped air pressures, and capillarity.
Schematics of the transient behavior of the air–water meniscus at (a) regime I and (b) regime II. Note that t cr is the critical time at which the interface is separated from the sharp edges of the groove, and that t f is the failure time at which the interface touches the bottom of the groove.
(a) Contour plot presenting normalized critical pressure P cr /P ∞ vs. groove width w and groove depth h. Hydrostatic pressures smaller (greater) than this pressure correspond to regime I (regime II). Note that higher critical pressures are obtained when w is large and h is small (larger contributions from the entrapped air at h/w ≪ 1). Conditions at which the air–water interface touches the groove's bottom before reaching the critical time (h = h min ) are omitted from the contour plot. (b) Minimum depth h min of grooves with different widths and Young–Laplace contact-angles.
The curve in the h–w plane corresponds to the groove widths and depths at which the derivative of the critical pressure with respect to the w, , vanishes. In the region below the curve ( ), compression of the trapped air is the dominant effect, while in the region above the curve ( ), capillarity is dominant.
The effects of groove width depth on failure time (in minutes) subjected to hydrostatic pressures of 0.4 m ((a) and (b)), and 2.5 m ((c) and (d)) of water.
Comparison between performance of two grooves with different widths of 20 and 100 μm but otherwise identical under two different hydrostatic pressures of 14.7 kPa (the critical pressure for the narrower groove) and 100.1 kPa (critical pressure for the wider groove) in (a) and (b), respectively.
(a) Air–water interface at different times, for a groove with w = 100 μm, h = 30 μm, and θ = 115°, subject to a hydrostatic pressure of 10 cm. (b) Location of the deepest point of the interface (x = 0) vs. time. (c) Surface transitioning from the Cassie state to the Wenzel state is shown with contour plots.
Failure and critical times for a groove with w = 100 μm, h = 30 μm, and θ = 115°, subject to a wide range of hydrostatic pressures from 10 cm to 5 m. The critical pressure for the groove is 3.5 m of water.
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