Shear-induced Electrokinetic Lift at Large Péclet Numbers

Abstract

Abstract. We analyze the problem of shear-induced electrokinetic lift on a particle freely suspended near a solid wall, subject to a homogeneous (simple) shear. To this end, we apply the large-Péclet-number generic scheme recently developed by Yariv et al. (J. Fluid Mech., Vol. 685, 2011, p. 306). For a force-and torque-free particle, the driving flow comprises three components, respectively describing (i) a particle translating parallel to the wall; (ii) a particle rotating with an angular velocity vector normal to the plane of shear; and (iiii) a stationary particle in a shear flow. Symmetry arguments reveal that the electro-viscous lift, normal to the wall, is contributed by Maxwell stresses accompanying the induced electric field, while electro-viscous drag and torque corrections, parallel to the wall, are contributed by the Newtonian stresses accompanying the induced flow. We focus upon the near-contact limit, where all electro-viscous contributions are dominated by the intense electric field in the narrow gap between the particle and the wall. This field is determined by the gap-region pressure distributions associated with the translational and rotational components of the driving Stokes flow, with the shear-component contribution directly affecting only higher-order terms. Owing to the similarity of the corresponding pressure distributions, the induced electric field for equal particle-wall zeta potentials is proportional to the sum of translation and rotation speeds. The electro-viscous loads result in induced particle velocities, normal and tangential to the wall, inversely proportional to the second power of particle-wall separation.

Transport of Multivalent Electrolyte Mixtures in Micro- and Nanochannels

“…Dr. Yoda's group has also shown that smaller a  0.2 m0.5 m particles convected by a uniform flow in the presence of an electric field parallel to the wall, as is the case for EO flow driven by a voltage gradient, also experience a repulsive force, with a magnitude that appears, admittedly over a limited range of parameters, to be proportional to E 2 and a 2 , in agreement with theoretical predictions of a"dielectrophoretic-like" repulsive force due to nonuniformities in the local electric field in gap between the particle and wall [11]. However, the discrepancy between theoretical predictions and experimental estimates of the magnitudes of both the dielectrophoretic-like repulsion and shear-induced electrokinetic lift [12] are at least an order of magnitude, suggesting that we lack a theoretical understanding of both types of wall-normal forces.…”

The lift force on a charged sphere that translates and rotates in an electrolyte

“…where ⍀ is a unit vector along the axis of rotation. Substituting (20), (21), and (26) into (17)- (19) returns the boundaryvalue problem The force on the particle is evaluated by inserting (20) and (21) into (12), yielding…”

“… have observed dielectrophoretic focusing of particles to the center of a channel, in the absence of a pressure driven flow. Further, the lift force is not due to so‐called “electrokinetic lift,” originating from motion of the particle relative to the wall under the imposed shear, since this effect is also always repulsive .…”

Streaming-potential phenomena in the thin-Debye-layer limit. Part 3. Shear-induced electroviscous repulsion

“…An analytic investigation of the above two problems thus appears intractable. Nonetheless, by focusing upon the common situation wherein the gap is narrow, we obtain useful lubrication-type approximations -a route already taken in the context of earlier thin-double-layer models (Bike & Prieve 1990;van de Ven, Warszynski & Dukhin 1993;Tabatabaei, van de Ven & Rey 2006), and in our own demonstrations (Schnitzer et al , 2012a of the large-Péclet-number model of part 1. As will become evident, the resulting approximations predict electroviscous forces that scale inversely with the square of the gap thickness.…”

“…Using the model developed in part 1, we have illustrated large-Péclet-number irreversibility using two prototypical problems: one involving two spheres sedimenting sideby-side, where electroviscous forces result in a repulsion force along the line of centres (Schnitzer, Khair & Yariv 2011), and one involving a particle in a shear flow (Schnitzer, Frankel & Yariv 2012a). In the large-Péclet-number scheme, extracting the irreversible part of the electroviscous force is relatively straightforwardly since this part is solely associated with the induced electric field (the 'streaming potential').…”