Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T06:53:42.070Z Has data issue: false hasContentIssue false
  • English
  • Français

Shear-induced Electrokinetic Lift at Large Péclet Numbers

Published online by Cambridge University Press:  09 July 2012

O. Schnitzer ,
I. Frankel  and
E. Yariv
O. Schnitzer
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology Technion City, 32000, Israel
I. Frankel
Affiliation:
Department of Aerospace Engineering, Technion – Israel Institute of Technology Technion City, 32000, Israel
E. Yariv*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology Technion City, 32000, Israel
*
∗ Corresponding author. E-mail: [email protected]
Get access

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.

Keywords

electro-viscous forcesStokes flowssingular perturbations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 64 - 81
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

D. J. Jeffrey. Some basic principles in interaction calculations. In E. M. Torry, editor, Sedimentation of small particles in a viscous fluid, chapter 4, pages 97–124. Computational Mechanics, 1996.
L. G. Leal. Advanced Transport Phenomena : Fluid Mechanics and Convective Transport Processes. Cambridge University Press, New York, 2007.
Alexander, B. M., Prieve, D. C.. A hydrodynamic technique for measurement of colloidal forces. Langmuir, 3 (1987) No. 5, 788–795. CrossRefGoogle Scholar
Bike, S. G., L., Lazarro, Prieve, D. C.. Electrokinetic lift of a sphere moving in slow shear flow parallel to a wall I. Experiment. J. Colloid Interface Sci., 175 (1995) No. 2, 411–421. CrossRefGoogle Scholar
Bike, S. G., Prieve, D. C.. Electrohydrodynamic lubrication with thin double layers. J. Colloid Interface Sci., 136 (1990), No. 1, 95–112. CrossRefGoogle Scholar
Bike, S. G., Prieve, D. C.. Electrohydrodynamics of thin double layers : a model for the streaming potential profile. J. Colloid Interface Sci., 154 (1992), 87–96. CrossRefGoogle Scholar
Bike, S. G., Prieve, D. C.. Electrokinetic lift of a sphere moving in slow shear flow parallel to a wall II. Theory. J. Colloid Interface Sci., 175 (1995), No. 2, 422–434. CrossRefGoogle Scholar
van de Ven, T. G. M., P., Warszynski, Dukhin, S. S.. Attractive electroviscous forces. Colloid Surface A, 79 (1993), No. 1, 33–41. CrossRefGoogle Scholar
van de Ven, T. G. M., P., Warszynski, Dukhin, S. S.. Electrokinetic lift of small particles. J. Colloid Interface Sci., 157 (1993), No. 2, 328–331. CrossRefGoogle Scholar
Cox, R. G.. Electroviscous forces on a charged particle suspended in a flowing liquid. J. Fluid Mech., 338 (1997), 1–34. CrossRefGoogle Scholar
Tabatabaei, S. M., T. G. M., van de Ven, Rey, A. D.. Electroviscous sphere-wall interactions. J. Colloid Interface Sci., 301 (2006), No. 1, 291–301. CrossRef
Yariv, E., Schnitzer, O., Frankel, I.. Streaming-potential phenomena in the thin-Debye-layer limit. Part 1. General theory. J. Fluid Mech., 685 (2011), 306–334. CrossRefGoogle Scholar
Schnitzer, O., Khair, A., Yariv, E.. Irreversible Electrokinetic Repulsion in Zero-Reynolds-Number Sedimentation. Phys. Rev. Lett., 107 (2011), 2783014. CrossRefGoogle ScholarPubMed
Keller, J. B.. Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. J. Appl. Phys., 34 (1963), 991–993. CrossRefGoogle Scholar
O’Neill, M. E., Stewartson, K.. On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech., 27 (1967), 705–724. CrossRefGoogle Scholar
Cooley, M. D. A., O’Neill, M. E.. On the slow rotation of a sphere about a diameter parallel to a nearby plane wall. J. Inst. Math. Applics., 4 (1968), 163–173. CrossRefGoogle Scholar
Goldman, A. J., Cox, R.G., Brenner, H.. Slow viscous motion of a sphere parallel to a plane wall – I. Motion through a quiescent fluid. Chem. Engng Sci., 22 (1967), 637–651. CrossRefGoogle Scholar
M. Van Dyke. Perturbation methods in fluid mechanics. Academic press, New York, 1964.
Goldman, A. J., R.G., Cox, Brenner, H.. Slow viscous motion of a sphere parallel to a plane wall — II. Couette flow. Chem. Engng Sci., 22 (1967), No. 4, 653–660. CrossRefGoogle Scholar
O’Neill, M. E.. A sphere in contact with a plane wall in a slow linear shear flow. Chem. Engrg Sci., 23 (1968), No. 11, 1293–1298. CrossRefGoogle Scholar
Cooley, M. D. A., O’Neill, M. E.. On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere. Mathematika, 16 (1969), 37–49. CrossRefGoogle Scholar
O. Schnitzer, I. Frankel, E. Yariv. Streaming-potential phenomena in the thin-Debye-layer limit. Part 2. Moderate Péclet numbers. J. Fluid Mech., (2012), In press.