Confluence of channel dimensions and groove width dictates slippery hydrodynamics in grooved hydrophobic confinements

Slippery hydrodynamics in grooved hydrophobic microchannels is known to be primarily dictated by the area of the gas-liquid contact surface. Here, we augment this classical notion by bringing out the critical role played by the channel dimensions on the underlying slip mechanisms and the consequent drag reduction. Our analysis, towards this, reveals the non-trivial implication of gas-liquid interface topology and its position inside the groove towards dictating the underlying frictional characteristics, which in turn is largely dependent on the confluence of the channel hydraulic diameter and the groove width. These results may turn out to be of immense consequence towards arriving at preferred frictional drag characteristics of hydrophobic microchannels and nanochannels by judicious choices of the pertinent geometric parameters.