Prediction of laminar flow in a microchannel with transverse ultrahydrophobic ribs

One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of micro-ribs and cavities on the channel walls. When treated with a hydrophobic coating, the liquid flowing in the microchannel wets only the surfaces of the ribs, and does not penetrate the cavities, provided the pressure is not too high. The net result is a reduction in the surface contact area between channel walls and the flowing liquid. For micro-ribs and cavities that are aligned normal to the channel axis (principal flow direction), these micro-patterns form a repeating, periodic structure. This paper presents experimental and numerical results of a study exploring the momentum transport in a parallel plate microchannel with such microengineered walls. The liquid-vapor interface (meniscus) in the cavity regions is treated as ideal in the numerical analysis (flat). Two conditions are explored with regard to the cavity region: 1) The liquid flow at the liquid-vapor interface is treated as shear-free (vanishing viscosity in the vapor region), and 2) the liquid flow in the microchannel core and the vapor flow within the cavity are coupled through the velocity and shear stress matching at the interface. Predictions and measurements reveal that significant reductions in the frictional pressure drop can be achieved relative to the classical smooth channel Stokes flow. Reductions in the friction factor are greater as the cavity-to-rib length ratio is increased (increasing shear-free fraction) and as the channel hydraulic diameter is decreased. The results also show that the average friction factor - Reynolds number product exhibits a flow Reynolds dependence. Furthermore, the predictions reveal the impact of the vapor cavity regions on the overall frictional resistance.