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Boundary effects on electrophoretic motion of colloidal spheres

Published online by Cambridge University Press:  20 April 2006

H. J. Keh  and
J. L. Anderson
H. J. Keh
Affiliation:
Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213 Present address: Department of Chemical Engineering, National Taiwan University, Taipei 107 Taiwan, R.O.C.
J. L. Anderson
Affiliation:
Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213
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Abstract

An analysis is presented for electrophoretic motion of a charged non-conducting sphere in the proximity of rigid boundaries. An important assumption is that κa → ∞, where a is the particle radius and κ is the Debye screening parameter. Three boundary configurations are considered: single flat wall, two parallel walls (slit), and a long circular tube. The boundary is assumed a perfect electrical insulator except when the applied field is directed perpendicular to a single wall, in which case the wall is assumed to have a uniform potential (perfect conductor). There are three basic effects causing the particle velocity to deviate from the value given by Smoluchowski's classic equation: first, a charge on the boundary causes electro-osmotic flow of the suspending fluid; secondly, the boundary alters the interaction between the particle and applied electric field; and, thirdly, the boundary enhances viscous retardation of the particle as it tries to move in response to the applied field. Using a method of reflections, we determine the particle velocity for a constant applied field in increasing powers of λ up to O(λ6), where λ is the ratio of particle radius to distance from the boundary. Ignoring the O(λ0) electro-osmotic effect, the first effect attributable to proximity of the boundary is O(λ3) for all boundary configurations, and in cases when the applied field is parallel to the boundaries the electrophoretic velocity is proportional to ζp − ζw, the difference in zeta potential between the particle and boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 417 - 439
Copyright
© 1985 Cambridge University Press

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References

Adamson, A. W. 1982 Physical Chemistry of Surfaces. Wiley-Interscience.
Anderson, J. L., Lowell, M. E. & Prieve, D. C. 1982 Motion of a particle generated by chemical gradients, Part 1. Non-electrolytes. J. Fluid Mech. 117, 107.Google Scholar
Anderson, J. L. 1983 Movement of a semipermeable vesicle through an osmotic gradient. Phys. Fluids 26, 2871.Google Scholar
Anderson, J. L. 1985 Effect of nonuniform zeta potential on particle movement in electric fields. J. Coll. Interface Sci. (to appear).Google Scholar
Brenner, J. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242.Google Scholar
Brenner, H. 1964a The Stokes resistance of a slightly deformed sphere. Chem. Engng Sci. 19, 519.Google Scholar
Brenner, H. 1964b The Stokes resistance of an arbitrary particle - IV. Arbitrary fields of flow. Chem. Engng Sci. 19, 703.Google Scholar
Deblois, R. W. & Bean, C. P. 1970 Counting and sizing of submicron particles by the resistive pulse technique. Rev. Sci. Instrum. 41, 909.Google Scholar
Dukhin, S. S. & Derjaguin, B. V. 1974 Electrokinetic phenomena. In Surface and Coll. Science (ed. E. Matijevic), vol. 7. Wiley.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.
Happel, J. & Byrne, B. J. 1954 Motion of a sphere and fluid in a cylindrical tube. Ind. Engng Chem. 46, 1181.Google Scholar
Hunter, R. J. 1981 Zeta Potential in Colloid Science. Academic.
Levine, S., Mingins, J. & Bell, G. M. 1967 The discrete-ion effect in ionic double-layer theory. J. Electroanal. Chem. 13, 280.Google Scholar
Morrison, F. A. 1970 Electrophoresis of a particle of arbitrary shape. J. Coll. Interface Sci. 34, 210.Google Scholar
Morrison, F. A. & Stukel, J. J. 1970 Electrophoresis of an insulating sphere normal to a conducting plane. J. Coll. Interface Sci. 33, 88.Google Scholar
Newman, J. S. 1973 Electrochemical Systems. Prentice-Hall.
O'Brien, R. W.1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Coll. Interface Sci. 92, 204.Google Scholar
O'Brien, R. W. & Hunter, R. J.1981 The electrophoretic mobility of large colloidal particles. Can. J. Chem. 59, 1878.Google Scholar
O'Brien, R. W. & White, L. R.1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday II 74, 1607.Google Scholar
Prieve, D. C., Anderson, J. L., Ebel, J. P. & Lowell, M. E. 1984 Motion of a particle generated by chemical gradients, Part 2. Electrolytes. J. Fluid Mech. 148, 247.Google Scholar
Sonshine, R. M., Cox, R. G. & Brenner, H. 1966 The Stokes translation of a particle of arbitrary shape along the axis of a circular cylinder. Appl. Sci. Res. 16, 273.Google Scholar
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350.Google Scholar