Laminar flow in a microchannel with hydrophobic surface patterned microribs oriented parallel to the flow direction

Abstract

This paper reports results of an analytical and experimental investigation of the laminar flow in a parallel-plate microchannel with ultrahydrophobic top and bottom walls. The walls are fabricated with microribs and cavities that are oriented parallel to the flow direction. The channel walls are modeled in an idealized fashion, with the shape of the liquid-vapor meniscus approximated as flat. An analytical model of the vapor cavity flow is employed and coupled with a numerical model of the liquid flow by matching the local liquid and vapor phase velocity and shear stress at the interface. The numerical predictions show that the effective slip length and the reduction in the classical friction factor-Reynolds number product increase with increasing relative cavity width, increasing relative cavity depth, and decreasing relative microrib/cavity module length. Comparisons were also made between the zero shear interface model and the liquid-vapor cavity coupled model. The results illustrate that the zero shear interface model underpredicts the overall flow resistance. Further, the deviation between the two models was found to be significantly larger for increasing values of both the relative rib/cavity module width and the cavity fraction. The trends in the frictional pressure drop predictions are in good agreement with experimental measurements made at similar conditions, with greater deviation observed at increasing size of the cavity fraction. Based on the numerical predictions, an expression is proposed in which the friction factor-Reynolds number product may be estimated in terms of the important variables.