Oscillatory Flow Through a Channel With Stick-Slip Walls: Complex Navier’s Slip Length

Abstract

Effective slip lengths for pressure-driven oscillatory flow through a parallel-plate channel with boundary slip are deduced using a semi-analytic method of eigenfunction expansions and point matching. The channel walls are each a superhydrophobic surface micropatterned with no-shear alternating with no-slip stripes, which are aligned either parallel or normal to the flow. The slip lengths are complex quantities that are functions of the oscillation frequency, the channel height, and the no-shear area fraction of the wall. The dependence of the complex nature of the slip length on the oscillation frequency is investigated in particular.