Skip to main content Accessibility help
×
Home

Strong-field electrophoresis

  • Ory Schnitzer (a1) and Ehud Yariv (a1)

Abstract

We analyse particle electrophoresis in the thin-double-layer limit for asymptotically large applied electric fields. Specifically, we consider fields scaling as , being the dimensionless Debye thickness. The dominant advection associated with the intense flow mandates a uniform salt concentration in the electro-neutral bulk. The large tangential fields in the diffuse part of the double layer give rise to a novel ‘surface conduction’ mechanism at moderate zeta potentials, where the Dukhin number is vanishingly small. The ensuing electric current emerging from the double layer modifies the bulk electric field; the comparable transverse salt flux, on the other hand, is incompatible with the nil diffusive fluxes at the homogeneous bulk. This contradiction is resolved by identifying the emergence of a diffusive boundary layer of thickness, resembling thermal boundary layers at large-Reynolds-number flows. The modified electric field within the bulk gives rise to an irrotational flow, resembling those in moderate-field electrophoresis. At leading order, the particle electrophoretic velocity is provided by Smoluchowski’s formula, describing linear variation with applied field.

Copyright

Corresponding author

Email address for correspondence: udi@technion.ac.il

References

Hide All
1. Bender, C. & Orszag, S. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill Book Company.
2. Dukhin, S. S. 1965 Diffusion-electrical theory of electrophoresis. In Twentieth Intl Cong. on Pure and Applied Chemistry, vol. A72. p. 68.
3. Dukhin, S. & Shilov, V. 1969 Theory of static polarization of diffuse part of thin electric double layer of spherical particles. Colloid J. USSR 31, 564.
4. Dukhin, S. S. & Derjaguin, B. V. 1974 Electrokinetic phenomena. In Surface and Colloid Science (ed. Matijevic, E. ), vol. 7. John Wiley & Sons.
5. Hinch, E. J., Sherwood, J. D., Chew, W. C. & Sen, P. N. 1984 Dielectric response of a dilute suspension of spheres with thin double layers in an asymmetric electrolyte. J. Chem. Soc., Faraday Trans. 2 80 (5), 535551.
6. Kumar, A., Elele, E., Yeksel, M., Khusid, B., Qiu, Z. & Acrivos, A. 2006 Measurements of the fluid and particle mobilities in strong electric fields. Phys. Fluids 18, 123301.
7. Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.
8. Morrison, F. A. 1970 Electrophoresis of a particle of arbitrary shape. J. Colloid Interface Sci. 34, 210214.
9. O’Brien, R. W. & Hunter, R. J. 1981 The electrophoretic mobility of large colloidal particles. Can. J. Chem. 59 (13), 18781887.
10. Prieve, D. C., Ebel, J. P., Anderson, J. L. & Lowell, M. E. 1984 Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 148, 247269.
11. Prieve, D. C., Sides, P. J. & Wirth, C. L. 2010 2-D assembly of colloidal particles on a planar electrode. Curr. Opin. Colloid Interface Sci. 15 (3), 160174.
12. Rivette, N. & Baygents, J. 1996 A note on the electrostatic force and torque acting on an isolated body in an electric field. Chem. Engng Sci. 51 (23), 52055211.
13. Rubinstein, I. & Zaltzman, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Models Meth. Appl. Sci. 11, 263300.
14. Saville, D. A. 1977 Electrokinetic effects with small particles. Annu. Rev. Fluid Mech. 9, 321337.
15. Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.
16. Yariv, E. 2006 “Force-free” electrophoresis? Phys. Fluids 18, 031702.
17. Yariv, E. 2010 An asymptotic derivation of the thin-Debye-layer limit for electrokinetic phenomena. Chem. Engng Commun. 197, 317.
18. Yariv, E., Schnitzer, O. & Frankel, I. 2011 Streaming-potential phenomena in the thin-Debye-layer limit. Part 1. General theory. J. Fluid Mech. 685, 306334.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Strong-field electrophoresis

  • Ory Schnitzer (a1) and Ehud Yariv (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed