Laminar flow in a microchannel with superhydrophobic walls exhibiting transverse ribs

One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of microribs 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 microribs and cavities that are aligned normal to the channel axis (principal flow direction), these micropatterns form a repeating, periodic structure. This paper presents results of a study exploring the momentum transport in a parallel-plate microchannel with such microengineered walls. The investigation explored the entire laminar flow Reynolds number range and characterized the influence of the vapor cavity depth on the overall flow field. The liquid-vapor interface (meniscus) in the cavity regions is treated as flat in the numerical analysis and 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 by matching the velocity and shear stress at the interface. Regions of slip and no-slip behavior exist and the velocity field shows distinct variations from classical laminar flow in a parallel-plate channel. The local streamwise velocity profiles, interfacial velocity distributions, and maximum interfacial velocities are presented for a number of scenarios and provide a sound understanding of the local flow physics. The predictions and accompanying measurements reveal that significant reductions in the frictional pressure drop (enhancement in effective fluid slip at the channel walls) can be achieved relative to the classical smooth-channel Stokes flow. Reductions in the friction factor and enhancements in the fluid slip 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 slip length and average friction factor–Reynolds number product exhibit a flow Reynolds dependence. Furthermore, the predictions reveal the global impact of the vapor cavity depth on the overall frictional resistance.