Microgroove geometry dictates slippery hydrodynamics on superhydrophobic substrates

Abstract

We report the detailed hydrodynamics over micro-grooved substrates in a confined hydrophobic microfluidic environment. In sharp contrast to the traditional premises, the liquid-air interface shape or interfacial slip velocity is not presumed a priori. We compare our results with the reported analytical solutions of the low Reynolds number flow with the Navier slip boundary condition considering a predefined flat interface. Discrepancies between such simplified solutions and the comprehensive solutions reported here clearly suggest the critical implications of the microgroove geometry and Reynolds number toward altering the flow physics. Our results reveal that the slip velocity at the interface and the slip length is directly proportional to the microgroove width, whereas the slip length increases with the increasing width and decreases with the increase in the Reynolds number. These results may open up new possibilities of tuning the micro-grooved geometry toward obtaining desired flow characteristics in superhydrophobic microchannels, for which simplified models based on pre-defined interfacial topology may not reliably work.