Porous Superhydrophobic Membranes: Hydrodynamic Anomaly in Oscillating Flows

We have fabricated and characterized a novel superhydrophobic system, a mesh-like porous superhydrophobic membrane with solid area fraction ${\mathrm{\Phi }}_s$, which can maintain intimate contact with outside air and water reservoirs simultaneously. Oscillatory hydrodynamic measurements on porous superhydrophobic membranes as a function of ${\mathrm{\Phi }}_s$ reveal surprising effects. The hydrodynamic mass oscillating in-phase with the membranes stays constant for $0.9\le {\mathrm{\Phi }}_s\le 1$, but drops precipitously for ${\mathrm{\Phi }}_s<0.9$. The viscous friction shows a similar drop after a slow initial decrease proportional to ${\mathrm{\Phi }}_s$. We attribute these effects to the percolation of a stable Knudsen layer of air at the interface.