Shear-induced Electrokinetic Lift at Large Péclet Numbers

O. Schnitzer; I. Frankel; E. Yariv

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 4, page 64-81
  • ISSN: 0973-5348

Abstract

top
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.

How to cite

top

Schnitzer, O., Frankel, I., and Yariv, E.. "Shear-induced Electrokinetic Lift at Large Péclet Numbers." Mathematical Modelling of Natural Phenomena 7.4 (2012): 64-81. <http://eudml.org/doc/222425>.

@article{Schnitzer2012,
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. },
author = {Schnitzer, O., Frankel, I., Yariv, E.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {electro-viscous forces; Stokes flows; singular perturbations},
language = {eng},
month = {7},
number = {4},
pages = {64-81},
publisher = {EDP Sciences},
title = {Shear-induced Electrokinetic Lift at Large Péclet Numbers},
url = {http://eudml.org/doc/222425},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Schnitzer, O.
AU - Frankel, I.
AU - Yariv, E.
TI - Shear-induced Electrokinetic Lift at Large Péclet Numbers
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/7//
PB - EDP Sciences
VL - 7
IS - 4
SP - 64
EP - 81
AB - 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.
LA - eng
KW - electro-viscous forces; Stokes flows; singular perturbations
UR - http://eudml.org/doc/222425
ER -

References

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

NotesEmbed ?

top

You must be logged in to post comments.