Effects of interface deformation on flow through microtubes containing superhydrophobic surfaces with longitudinal ribs and grooves

This paper presents analytical and numerical results for Poiseuille flow through microtubes patterned with superhydrophobic surfaces which consist of alternative ribs and grooves aligned longitudinally with the flow direction. The superhydrophobic surface prevents the flowing liquid from penetrating the grooves and the liquid–gas interface experiences deformation as a consequence of a pressure difference across the interface. Employing a domain perturbation technique, the effects of a small interface deformation on the effective slip behavior are analytically quantified. For large interface deformations, numerical studies are performed to predict the effects of interface protrusion on the effective slip behavior of the superhydrophobic microtube. Comparisons are made between the effective slip behavior for tube and channel flows patterned with superhydrophobic surfaces containing alternating longitudinal ribs and grooves.