On the hydrodynamic slip of pressure-driven stokes flow cross over parallel grooves of Cassie state accounting for meniscus curvature

This study employs the boundary perturbation method to analyze the hydrodynamic slip of Stokes flows across parallel grooves, taking into account the meniscus curvature. This method, developed for longitudinal flow as reported by Sbragaglia and Prosperetti [“A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces,” Phys. Fluids 19(4), 043603 (2007)] and Kirk et al. [“Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature,” J. Fluid Mech. 811, 315–349 (2017)], is adapted for the transverse flow case. The composite boundary conditions for the first-order correction are obtained by coupling the no-shear stress and impermeability conditions at the liquid–gas interface. Quad-series equations are used to numerically solve the coupling coefficients. The results indicated that the first-order slip length correction for the asymptotic solution of transverse flow is identical to that for the longitudinal problem in the same geometry when the channel depth h → ∞, which is supported absolutely by the shear flow analysis. The results showed that meniscus protrusion into the gas decreases the slip length for arbitrary channel depths in the case of transverse flow. Thus, the first-order slip length may play a decisive role in the pressure-driven Stokes flow in an extremely narrow channel.