Effects of hierarchical features on longevity of submerged superhydrophobic surfaces with parallel grooves

While the air–water interface over superhydrophobic surfaces decorated with hierarchical micro- or nanosized geometrical features have shown improved stability under elevated pressures, their underwater longevity—-the time that it takes for the surface to transition to the Wenzel state—-has not been studied. The current work is devised to study the effects of such hierarchical features on the longevity of superhydrophobic surfaces. For the sake of simplicity, our study is limited to superhydrophobic surfaces composed of parallel grooves with side fins. The effects of fins on the critical pressure—-the pressure at which the surface starts transitioning to the Wenzel state—-and longevity are predicted using a mathematical approach based on the balance of forces across the air–water interface. Our results quantitatively demonstrate that the addition of hierarchical fins significantly improves the mechanical stability of the air–water interface, due to the high advancing contact angles that can be achieved when an interface comes in contact with the fins sharp corners. For longevity on the contrary, the hierarchical fins were only effective at hydrostatic pressures below the critical pressure of the original smooth-walled groove. Our results indicate that increasing the length of the fins decreases the critical pressure of a submerged superhydrophobic groove but increases its longevity. Increasing the thickness of the fins can improve both the critical pressure and longevity of a submerged groove. The mathematical framework presented in this paper can be used to custom-design superhydrophobic surfaces for different applications.