Morphology of gas cavities on patterned hydrophobic surfaces under reduced pressure

Gas cavities trapped on structured hydrophobic surfaces play important roles in realizing functionalities such as superhydrophobicity, drag reduction, and surface cleaning. The morphology of the cavities exhibits strong dependence on system parameters which impact the performance of these surfaces. In this work, a complete theoretical analysis is presented to predict cavity morphological change under reduced liquid pressure, on a submerged hydrophobic surface patterned with cylindrical pores. Equilibrium solutions are derived for five different phases, namely, (I) pinned recession, (II) depinned recession, (III) Cassie-Baxter, (IV) expansion, and (V) coalescence; their stabilities are also analyzed. A phase map is developed outlining the different regimes with respect to the gas amount and liquid pressure. Importantly, phase (IV) exhibits a complex stability behavior that leads to two possible routes to coalescence, which lends two different mechanisms of cavitation. Accordingly, the threshold pressure for cavitation can be calculated. The theoretical model is supported by direct experimental measurements via confocal microscopy and demonstrates good quantitative accuracy. This work provides a predictive tool for the design of functional structured hydrophobic surfaces.