Laminar Channel Flow With Hydrodynamic Slip

Abstract

A theoretical and experimental investigation of slip flow over an ultrahydrophobic surface in a rectangular cross-sectional channel was conducted. The experiments consisted of the flow of water over a LOTUS-paint coated surface in a rectangular channel. The tests included flows at three different Reynolds numbers, Re = 129.6, Re = 103.6, Re = 69.1. Velocity measurements were made using a Laser Doppler Velocimeter (LDV). Velocity measurements for the no-slip conditions were also made for a flow rate of Re = 129.6 and compared with the slip profile. An uncoated surface was used for these measurements. The velocity profile and the flow rate for fully-developed channel flow were derived as a function of the slip length and slip velocity. The experimental data was used to determine the slip velocities and slip lengths for different Reynolds numbers from the theoretical equation. These quantities, used in the theoretical equation generated the necessary theoretical profiles for comparison with experiments. The slip velocities and slip lengths were evaluated by considering two locations, y = h and y = h/3. The profiles drawn from the theoretical equation evaluated from the slip velocities and lengths using the locations y = h and y = h/3 compared reasonably well with the experimental measurements. The volumetric flow rates computed theoretically using the slip lengths and slip velocities also compared well with the experimental values. The measurements highlight the effects of slip on one surface of the channel.