Drag Measurements in Laminar Flows over Superhydrophobic Porous Membranes

An anomalous hydrodynamic response has recently been observed in oscillating flows on mesh-like porous superhydrophobic membranes.\footnote{S. Rajauria, O. Ozsun, J. Lawall, V. Yakhot, and K. L. Ekinci, Phys. Rev. Lett. 107, 174501 (2011)} This effect was attributed to a stable Knudsen layer of gas at the solid-liquid interface. In this study, we investigate laminar channel flow over these porous superhydrophobic membranes. We have fabricated surfaces with solid area fraction $\phi_{s}$, which can maintain intimate contact with both air and water reservoirs on either side. Typical structures have linear dimensions of 1.5~mm $\times$ 15~mm $\times$ 1~$\mu$m and pore area of 10~$\mu$m $\times$ 10~$\mu$m. The surfaces are enclosed with precisely machined plastic microchannels, where pressure driven flow of DI water is generated. Pressure drop across the microchannels is measured as a function of flow rate. Slip lengths are inferred from the Poiseuille relation as a function of $\phi_{s}$ and compared to that of similar standard superhydrophobic surfaces, which lack intimate contact with an air reservoir.