Electrokinetic Lift of a Sphere Moving in Slow Shear Flow Parallel to a Wall

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.

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“…Note that for identical zeta potentials on the particle and the wall ϕ 0 need not be explicitly calculated since (2.8) yields [7] …”

Section: Problem Formulationmentioning

confidence: 99%

Shear-induced Electrokinetic Lift at Large Péclet Numbers

Schnitzer

Frankel

Yariv

2012

Math. Model. Nat. Phenom.

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“…This implies that L * =−L, from which it follows that the lift force must be zero by symmetry. Some nonlinear mechanisms that break the symmetry of the Stokes equations have been proposed and tested experimentally, such as fluid inertia, 6 electrokinetics, 7 and non-Newtonian effects. 8 As pointed out previously for cylindrical journal bearings, 9 elastic deformations of the boundaries also represent a source of irreversibility and nonlinearity of the flow.…”

Section: Introductionmentioning

confidence: 99%

The elastohydrodynamic force on a sphere near a soft wall

2007

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The influence of soft boundaries on the forces experienced by a small sphere undergoing slow translation and rotation near a wall is investigated using asymptotic and numerical methods. The clearance between the sphere and the wall is assumed to be small, so that the lubrication approximation holds in the gap. The forces induced by boundary deformation break the symmetry of the Stokes equations, leading to irreversibility of the motion of the sphere and yielding a nonzero lift force. A general formulation, applicable to any constitutive equation of the wall, is presented, and an asymptotic analysis for slightly soft boundaries is developed and applied to a thin compressible elastic layer coating a rigid surface. Expressions are derived for the elastohydrodynamic lift exerted on a sphere moving parallel to the wall, which include the influence of the sphere rotation in the direction of its motion. The results extend and correct previous work, and are different from those for the elastohydrodynamic motion of a cylinder near a wall, in that the geometry eliminates the occurrence of maximum lift and optimum choice of the material properties of the boundary.

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“…These models show that apparently small nonlinear mechanisms can nevertheless generate Stokes-flow irreversibility, and hence their consequences may be important. For example, in the shear-induced lift experiments of Alexander & Prieve (1987) and Bike, Lazarro & Prieve (1995), electroviscous forces give rise to an otherwise impossible motion in a direction perpendicular to the driving motion.…”

Section: Discussionmentioning

confidence: 99%

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

Schnitzer

Yariv

2015

J. Fluid Mech.

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We employ the moderate-Péclet-number macroscale model developed in part 2 of this sequence (Schnitzer, Frankel & Yariv, J. Fluid Mech., vol. 704, 2012, pp. 109-136) towards the calculation of electroviscous forces on charged solid particles, engendered by an imposed relative motion between these particles and the electrolyte solution in which they are suspended. In particular, we are interested in the kinematic irreversibility of these forces, stemming from the diffusio-osmotic slip which accompanies the salt-concentration polarisation induced by that imposed motion. We illustrate the electroviscous irreversibility using two prototypic problems, one involving side-by-side sedimentation of two spherical particles, and the other involving a force-free spherical particle suspended in the vicinity of a planar wall and exposed to a simple shear flow. We focus upon the pertinent limit of near-contact configurations, where use of lubrication approximations provides closedform expressions for the leading-order lateral repulsion. In this approximation scheme the need to solve the advection-diffusion equation governing the salt-concentration polarisation is circumvented.

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Electrokinetic Lift of a Sphere Moving in Slow Shear Flow Parallel to a Wall

Cited by 37 publications

References 0 publications

Shear-induced Electrokinetic Lift at Large Péclet Numbers

Shear-induced Electrokinetic Lift at Large Péclet Numbers

The elastohydrodynamic force on a sphere near a soft wall

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

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