Consistent description of electrohydrodynamics in narrow fluidic confinements in the presence of hydrophobic interactions

Electrohydrodynamics in the presence of hydrophobic interactions in narrow confinements is traditionally represented from a continuum viewpoint by a Navier slip-based conceptual paradigm, in which the slip length carries the sole burden of incorporating the effects of substrate wettability on interfacial electromechanics, precluding any explicit dependence of the interfacial potential distribution on the substrate wettability. Here we show that this traditional way of treating electrokinetics-wettability coupling may lead to serious discrepancies in predicting the resultant transport characteristics as manifested through an effective zeta potential. We suggest that an alternative consistent description of the underlying physics through a free-energy-based formalism, in conjunction with considerations of hydrodynamic and electrical property variations consistent with the pertinent phase-field description, may represent the underlying consequences in a more rational manner, as compared to the traditional slip-based model coupled with a two-layer description. Our studies further reveal that the above discrepancies may not occur solely due to the slip-based route of representing the interfacial wettability, but may be additionally attributed to the act of discretizing the interfacial phase fraction distribution through an artificial two-layer route.