Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces

Abstract

A series of experiments are presented which study the flow kinematics of water past drag-reducing superhydrophobic surfaces. The ultrahydrophobic surfaces are fabricated from silicon wafers using photolithography and are designed to incorporate precise patterns of micrometer-sized ridges aligned in the flow direction. The ridges are made hydrophobic through a chemical reaction with an organosilane. An experimental flow cell is used to measure the velocity profile and the pressure drop as a function of the flow rate for a series of rectangular cross-section microchannel geometries and ultrahydrophobic surface designs. The velocity profile across the microchannel is determined through microparticle image velocimetry ($\mu$ -PIV) measurements capable of resolving the flow down to lengthscales well below the size of the surface features. Through these detailed velocity measurements, it is demonstrated that slip along the shear-free air-water interface supported between the hydrophobic micrometer-sized ridges is the primary mechanism responsible for the drag reduction observed for flows over ultrahydrophobic surfaces. A maximum slip velocity of more than 60% of the average velocity in the microchannel is found at the center of the shear-free air-water interface whereas the no-slip boundary condition is found to hold along the surface of the hydrophobic ridges. The experimental velocity and pressure drop measurements are compared to the predictions of numerical simulations and an analytical theory based on a simple model of an ultrahydrophobic surface composed of alternating shear-free and no-slip bands with good agreement.