Driving flow through microfluidic channels: analytical solutions generalizing Philip (1972)

Analytical solutions are presented describing pressure-driven flow in superhydrophobic channels whose top and bottom walls are decorated with periodic arrays of no-shear menisci spanning the interstitial regions between no-slip grooves. The case where the menisci have invaded the grooves is also treated. The solutions are natural extensions to well-known mixed no-shear/no-slip solutions due to Philip [ZAMP, 23, 1972]. From the solutions, useful diagnostic quantities such as the hydrodynamic slip length can be easily extracted.