Numerical simulation of liquid-gas interface formation in long superhydrophobic microchannels with transverse ribs and grooves

Superhydrophobic microchannels have evolved recently as an accepted strategy to mitigate the hydrodynamic resistance tendered in micro-constrictions. In this work, hydrodynamics of a hydrophobic microchannel realized by entrapping air in the cavities located between transversely oriented ribs is numerically investigated. An interface formed between the liquid and air/vapor in the confinement facilitates a resistance free slipping surface for the flowing water. The shape of the meniscus is determined by the pressure difference between air and liquid and is classified as convex, flat, and concave depending on the protrusion angle. Several applications require a long hydrophobic channel in which the liquid pressure decreases lengthwise; consequently the interface shape changes as well. In this regard, a mathematical model is proposed to predict the protrusion angle at a specific distance from the inlet of microchannel. This is incorporated in the computational fluid dynamics (CFD) simulations to define the static geometry of the interface which is varying throughout the length of the channel. Moreover, the boundary is treated as a combination of flat no-slip and curved shear-free regions to mimic the ribs and cavities. Further, the evolution of interface morphology is captured using the volume-of-fluid (VOF) scheme by considering a static contact angle at the solid surface to check the validity of the suggested model. Dynamically evolved protrusion angle is measured for various liquid-gas interface pressures and it is observed that the theoretical scaling proposed by Laplace and Young is well obeyed. Though CFD-VOF simulation scheme is an effective tool for predicting the pressure dependent liquid-gas meniscus and concurrent hydrodynamics of the ribbed microchannel, it is resource intensive. The present study demonstrates that the developed model for static boundary may be adopted alternatively to predict the hydrodynamics of a long hydrophobic microchannel by saving computational resources.