PHYSICAL REVIEW E 85, 046305 (2012) Consistent description of electrohydrodynamics in narrow fluidic confinements in the presence of hydrophobic interactions Jeevanjyoti Chakraborty, 1 Sukumar Pati, 2 S. K. Som, 2 and Suman Chakraborty 1,2,* 1 Advanced Technology Development Centre, Indian Institute of Technology Kharagpur, Kharagpur-721302, India 2 Mechanical Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur-721302, India (Received 18 January 2012; published 11 April 2012) 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. DOI: 10.1103/PhysRevE.85.046305 PACS number(s): 47.61.−k I. INTRODUCTION Hydrophobic interactions in narrow confinements have attracted serious research attention over the past few decades [1,2], attributable to the inherent scientific challenges involved, as well as to overwhelming technological implications towards inducing phenomenal reductions in resistive forces against fluidic transport [3]. The physical origin of such interfacial interactions has been scientifically argued for a long time, postulated on the basic notion that hydrophobic effects are likely to trigger the formation of wall-adjacent depleted phases, primarily governed by the fact that the structure of water molecules next to a hydrophobic surface is apparently less ordered than that in the bulk [4–16]. Fundamentally, this has been attributed to the fact that hydrophobic units are not thermodynamically favored to form hydrogen bonds [17]. Irrespective of the details of the generating mechanism of this depleted phase formed near the walls, the latter has been perceived to serve as an effective smoothening blanket, by disallowing the bulk liquid to come in proximate contact with the rough walls. In the literature, smooth sailing of bulk liquid over an ultrathin cushion of a depleted phase (typically spanning over a length scale of 10 nm) adhering to rough walls, attributable to hydrophobic interactions as described above, has also been conceptualized to give rise to an “apparent slip” phenomenon [18–26], consistent with the physical notion that the liquid apparently slips over the intervening depleted layer, instead of being explicitly slowed down by interference from the wall [27–29]. Such conditions, probed through numerous theoretical and experimental studies [22–89], have been termed as “apparent slip” in the literature, since the no-slip boundary may still remain to be a valid proposition * suman@mech.iitkgp.ernet.in at the solid boundary (until and unless it falls in the slip flow or rarefied flow regimes of gases). In reality, it is only the apparent inability in resolving the sharp velocity gradients within the ultrathin wall-adjacent depleted layer that prompts an analyzer to extrapolate the velocity profiles obtained in the liquid layer above the low-density blanket, thereby marking an apparent deviation from the no-slip boundary condition at the wall. Despite the underlying simplifications, it has become a common practice to treat hydrodynamics in the presence of hydrophobic interactions through the introduction of a Navier slip coefficient at the confining boundaries in describing the pertinent hydrodynamic boundary condition [90–94]. The implications of hydrophobic interactions and the consequent reductions in fluidic friction, as discussed above, may be far reaching. As an illustration, one may cite the instances of electrohydrodynamic transport in the presence of electrical double layer (EDL) effects. In simple terms, EDL is essentially a charged layer adhering to the solid boundary, typically originated out of involved electrochemical interac- tions [95,96]. Since typical length scales of the EDL (termed as Debye length in the literature) are likely to be commensurate with the typical length scales of the wall-adjacent depleted layers formed out of hydrophobic effects, their interactions often turn out to be intriguing. Acknowledging this aspect, researchers have reported phenomenal augmentations in the effective electrohydrodynamic transport (characterized by an effective interfacial potential; more formally known as the zeta potential [95]) in the presence of hydrophobic interactions. This has been attributed to an enhanced pumping effect on the solvent molecules in the EDL due to hydrophobic interactions [49,58,66,73,87,97–106]. Consistent with the above conjecture, electrohydrodynam- ics in the presence of hydrophobic interactions has often been represented as an equivalent electrokinetic transport over slipping surfaces. In an effort towards doing so, however, it needs to be emphasized that it is essential to introduce a slip 046305-1 1539-3755/2012/85(4)/046305(14) ©2012 American Physical Society