Implications of hydrophobic interactions and consequent apparent slip phenomenon on the entrance region transport of liquids through microchannels

Abstract

The implications of entrance region transport in hydrophobic microchannels are theoretically and experimentally investigated in this work. Detailed analytical solutions are derived, depicting the dependences of the liquid phase velocity profiles, entrance lengths, and friction factor variations on the relative thickness of a nanobubble-dispersed layer formed in the vicinity of the microchannel wall as a consequence of localized hydrophobic interactions. It is revealed that even for a layer of nanobubbles formed with a typical thickness in the tune of three orders of magnitude lower than the characteristic microchannel dimensions, the entrance length can be enhanced to the limit of about 1.5 times than that for the cases devoid of any hydrophobic interactions. The pressure drop characteristics in the entrance region, as obtained for such cases, can turn out to be of significant consequence with regard to the design of typical pressure-driven microflow systems involving hydrophobic substrates. Closed-form expressions for the effective friction factor are also derived so that more accurate and scientific guidelines can be provided for design of hydrophobic microchannels, rather than trivially overruling the consequences of entrance region transport that is commonly exercised on a routine basis.