Electrokinetic slip flow

Yang, J., Kwok, D.Y., Electrokinetic slip flow in microfluidic-based heat exchangers with rectangular microchannels, Int. J. Heat Exchangers, Vol. 5, pp. 201 - 220, (2004). 

Yang and Kwok [8] presented the analytical solution of fully developed electrokinetic flow subjected to sinusoidal pressure gradient or sinusoidal external electric field. The combined effect of slip flow and electrokinetics was demonstrated on the velocity profile in confined geometries. The velocity profile was observed to be a function of both slip coefficient and external electric field. They observed that both these effects play important roles for flow inside microchannels. 

How close are and A reply to this question involves the comparison of results from disparate measurements and models. Electrokinetlc potentials can be obtained from electrokinetics after making some assumption on the slip process, i.e. about the hydrodynamics of tangential flow, whereas requires information on double layers and/or stability and some model about the double layer under static conditions. There is no a priori reason to expect identity between the results. However, for practical purposes the outcome might be that the two are close enough to consider them as the same. Let us therefore now consider the slip process and the charge distribution in a double layer in more detail than in sec. 4.1b. 

The treatment given above of the diffuse double layer is based on the assumption that the ions in the electrolyte are treated as point charges. The ions are, however, of finite size, and this limits the inner boundary of the diffuse part of the double layer, since the center of an ion can only approach the surface to within its hydrated radius without becoming specifically adsorbed (Fig. 6.4.2). To take this effect into account, we introduce an inner part of the double layer next to the surface, the outer boundary of which is approximately a hydrated ion radius from the surface. This inner layer is called the Stern layer, and the plane separating the inner layer and outer diffuse layer is called the Stern plane (Fig. 6.4.2). As indicated in Fig. 6.4.2, the potential at this plane is close to the electrokinetic potential or zeta ( ) potential, which is defined as the potential at the shear surface between the charge surface and the electrolyte solution. The shear surface itself is somewhat arbitrary but characterized as the plane at which the mobile portion of the diffuse layer can slip or flow past the charged surface. 

Yang J, Kwok DY (2003) Effect of liquid slip in electrokinetic parallel-plate microchannel flow. J Colloid Interface Sci 260 225-233... 

Evanescent wave microscopy has already yielded a number of contributions to the fields of micro-and nanoscale fluid and mass transport, including investigation of the no-slip boundary condition, applications to electrokinetic flows, and verification of hindered Brownian motion. With more experimental data and improvements to TIRE techniques, the accuracy and resolution of these techniques are certain to improve. Areas of potential improvements include development of rmiform-sized and bright tracer particles, creation of high-NA imaging optics and high-sensitivity camera systems, and further development of variable index materials for better control of the penetration-depth characteristics. 

In microfluidics, control and manipulation of fluid flow can be accomplished by pressure-driven, electrokinetic, magnetohydrod3mamic, centrifugal, and capillary forces. When forces such as electrokinetic and magnetohydrodynamic forces act on the walls of a microcharmel, a slip in the fluid flow occurs at the walls. On the other hand, when forces such as pressure-driven forces act on the inlet or outlet, a laminar flow of fluid experiences no slip at the walls. Thus, the middle of the charmel flows at a higher velocity than near the... 

Stokes second problem and is specifically referred to as the slip velocity approach in electroosmotic flows. More general discussions of the applicability of such slip velocity approach in electrokinetic flows were provided elsewhere [6]. Using the slip velocity approach, the steady velocity field of a fully developed flow driven by an applied electric field, E, and a pressure gradient, dp/dz, is governed by the Stokes equation, expressed as... 

Once the electrochemical problem is solved, the ICEO flow is obtained by solving Stokes equations, Vp = rjV u and V M = 0, with electro-osmotic slip given by Eq. (1) with the induced zeta potential, = ir. Although this set of approximations can only be justified at low voltages in a dilute solution [3], it has had many successes in predicting induced-charge electrokinetic phenomena in experiments outside this regime. 

This represents the so-called "gas cushion model" of hydrophobic slippage, which got a clear microscopic foundation in terms of a prewetting transition. Being a schematic representation of a depletion close to a wall, this model provides a useful insight into the sensitivity of the interfacial transport to the structure of the interface. Similarly, electrokinetic flow displays the apparent slip. Note that recent molecular slip studies - also suggested a kind of the "vapor cushion model," where b a e, but apparently in a one-component S5 em the value of e is too small to describe most of experimental data, suggesting that a two-component system - is required. Whether or not the addition of a hydrophobic solute will lead to nonlinear dependence of h on e remains an open question and has to be investigated. 

Of course, the area of research connected with interface transport phenomena is still at its infancy. Thus, the role of surface conductance just started to be probed. Besides that, many assumptions exploited above should obviously be relaxed. For example, in the future, we suggest as a fruitful direction to consider electro-osmotic flow in a thin gap and to assume a partial slip at the gas sectors. It will be very important to investigate transverse electrokinetic phenomena, which could be greatly amplified by using striped superhydrophobic surfaces. Note that if the charge is varied along the direction of the electric field, the fluid close to a superhydrophobic wall is pulled periodically in opposite directions. As a result, the recirculation rolls should develop on a scale proportional to the texture size, L. This should provide an additional opportunity for mixing, similar to that described in but hopefully much faster. 

T. M. Squires, Electrokinetic flows over inhomogeneously slipping surfaces, Phys. Fiuids, 20, 092105 [2008],... 

It appears that, in all modes of calculation, the electrical potential in the slipping-plane between the fixed and the flowing liquid is determinative for the electrokinetic phenomena. This potential is usually called the zeta-potential (C). 

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