Two-Dimensional Analysis of Air-Water Interface on Superhydrophobic Grooves under Fluctuating Water Pressure

We theoretically investigate the collapse (i.e., wetting) transition of the air-water interface on fully submerged superhydrophobic surfaces with micro-sized grooves under the fluctuating water pressure and the diffusion of the trapped air pockets. For the analysis, a nonlinear oscillator equation to describe the dynamics of the two-dimensional air-water interface on a single groove is derived, which is solved for a range of parameters of groove geometry and harmonically fluctuating water pressure. The results show that the pressure fluctuation across the interface encourages the early collapse of a plastron before reaching the critical hydrostatic pressure (i.e., maximum immersion depth) predetermined by the geometry. The dependence of plastron longevity on the surface geometry is found such that the plastron on a narrow groove (≤∼5 μm) (collapses mostly due to gas diffusion) lasts days while the ones on wider grooves (>∼35-45 μm, for example), more susceptible to the oscillating pressure, last a much shorter duration. The interplay between the air compression due to water impalement and the change of the volume of impaled water due to gas diffusion determines the response of plastron to fluctuating water pressure, which is analyzed in detail through the introduction of nondimensional parameters, and the critical groove width (most vulnerable to the external perturbations) is explained further. Finally, as a countermeasure to the fluctuating water pressure, it is suggested that the enhanced advancing contact angle of the groove sidewall (e.g., hierarchical structure) mitigates the negative effects.