Generalization of Interfacial Electrohydrodynamics in the Presence of Hydrophobic Interactions in Narrow Fluidic Confinements Suman Chakraborty * Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302, India (Received 3 December 2007; published 7 March 2008) We show that the interfacial electromechanics in narrow fluidic confinements exhibits a universal dependence with the intrinsic surface-wettability characteristics, independent of the details of the bulk flow actuating mechanisms. Towards this proposition, we develop a generalized mesoscale model, which is extensively tested for combined electro-osmotic and pressure-driven nanochannel flows. Agreement with the molecular dynamics simulations is found to be quantitative. DOI: 10.1103/PhysRevLett.100.097801 PACS numbers: 68.15.+e, 47.45.Gx, 82.45.h Electrohydrodynamics within the electrical double layer (EDL) is central to the understanding of the transport characteristics of charged colloidal systems [1] in micro- or nanoscale fluidic devices and systems. The concerned applications are truly diverse in nature, encompassing the manipulation of biological macromolecules and cells in lab-on-a-chip based high throughput systems. Significant electrokinetic effects (such as electro-osmosis, electropho- resis, streaming potential) governing the physical behavior of these systems may have far-ranging scientific and tech- nological consequences, since these can provide strin- gently controllable, rapid, and efficient means for manipu- lating flows in narrow fluidic confinements. Traditionally (and perhaps nonphysically), these effects have been postulated to be somewhat uncorrelated with the other fundamental and intrinsic transport characteristics of nar- row confinements, such as the interfacial wettability con- ditions, particularly over the experimentally tractable spatiotemporal regimes. This deficit in fundamental under- standing has evidently stemmed from the complexities in describing the underlying thermofluidic interactions at physical scales that are substantially larger than those addressed in the detailed molecular scale models. In nanochannel flows, hydrophobic interactions are likely to trigger an apparent slip phenomenon, due to a spontaneous transition of the liquid to a less dense phase in the interfacial region [2]. This, in turn, is expected to alter the so-called zeta potential ( ), which is classically defined as the electrical potential in the plane of ‘‘zero slip,‘‘ in a dynamically evolving manner. Despite the recent advance- ments in the analysis of electrohydrodynamics in small scale systems, several fundamental aspects of this interac- tion still remain to be poorly understood, especially within the limits of experimentally resolvable physical scales. Here what is proposed is believed to be the first gener- alized mesoscale description depicting a coupling between the complex hydrophobic interactions and the electrome- chanics within the EDL in narrow fluidic confinements. On the basis of the resultant conjecture, we arrive at a universal expression of an augmented slip parameter, as a combined function of an equivalent interfacial potential and an ap- parent slip length, independent of the details of the flow actuation mechanism, by appealing to a generalized defi- nition of the effective zeta potential. Without sacrificing the requirements of a consistent representation, the present modeling effort further reduces the necessity of executing explicit and expensive molecular dynamics (MD) simula- tions for capturing the underlying physics. Two new features are introduced into the present model for achieving the above-mentioned feat, in an effort to discover a universal interplay between the EDL electro- hydrodynamics and the hydrophobic interactions in micro- or nanochannels. First, the hydrophobicity at the substrate- fluid interface is explicitly represented through an order- parameter description. This is achieved by exploiting a direct relationship between the effective contact angle and the surface value of the order parameter. The model is further sensitized to the rapidly varying small length scale fluctuations of the order parameter about its slowly- varying components, as well as the modifications of the local molecular fields due to the replacement of polar liquids by rigid walls (triggering the possibility of separation-induced phase transition processes). Second, the structuration-induced oscillations in the micro-ion den- sity profiles are accounted for through an electrical poten- tial correction in the classical electromechanical descrip- tion. The coupling between the electrohydrodynamic and hydrophobic interactions is achieved by postulating this correction term as an explicit function of the hydrody- namic order-parameter distribution (mimicking the varia- tions in the fluid phase density profile). With the above physical considerations, it is established that the physics of coupling between hydrophobic interactions in narrow flu- idic confinements and the electromechanics within the EDL can be quantitatively reproduced by the generalized order-parameter model, without explicitly resolving the molecular details. The present model stems its physical description from the free energy (F) of the system, which comprises two major components (F  F 1  F 2 ). The first component, F 1 , is the so-called Ginzburg-Landau free energy for a binary mixture. Physical origin of the existence of such a PRL 100, 097801 (2008) PHYSICAL REVIEW LETTERS week ending 7 MARCH 2008 0031-9007= 08=100(9)=097801(4) 097801-1  2008 The American Physical Society