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Axisymmetric electrophoresis of multiple colloidal spheres

Published online by Cambridge University Press:  26 April 2006

Shing B. Chen  and
Huan J. Keh
Shing B. Chen
Affiliation:
Department of Chemical Engineering, National Taiwan University. Taipei, Taiwan, Republic of China
Huan J. Keh
Affiliation:
Department of Chemical Engineering, National Taiwan University. Taipei, Taiwan, Republic of China
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Abstract

A study of the electrophoretic motion of a chain of colloidal spheres along the line through their centres is presented. The spheres may differ in radius and in zeta potential and they are allowed to be unequally spaced. Also, the spheres can be either freely suspended in the fluid or linked by infinitesimally thin rods with arbitrary lengths. The fluid can contain an arbitrary combination of general electrolytes. Although the thin-double-layer assumption is employed, the polarization effect of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of ions at the outer edge of the double layer can be derived and used as the boundary conditions for the fluid domain outside the thin double layer. Using a collocation technique along with these boundary conditions, a set of electrokinetic equations governing this problem is solved in the quasi-steady state and the particle interaction effects are computed for various cases. The most important discovery is that a group of particles with the same zeta potential will interact with one another, unlike the no-interaction results obtained in previous investigations assuming that the double layer is infinitesimally thin. For most situations, the particle interaction among the spheres is a complicated function of the properties of the spheres and ions. Also, it no longer varies monotonically with the extent of separation for some cases. The phenomena cannot be predicted systematically by a simple general rule.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 251 - 276
Copyright
© 1992 Cambridge University Press

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References

Anderson, J. L. & Prieve, D. C. 1991 Diffusiophoresis caused by gradients of strongly adsorbing solutes. Langmuir 7, 403.Google Scholar
Chen, S. B. & Keh, H. J. 1988 Electrophoresis in a dilute dispersion of colloidal spheres. AIChE J. 34, 1075.Google Scholar
Dukhin, S. S. & Derjaguin, B. V. 1974 Electrokinetic phenomena. In Surface and Colloid Science (ed. E. Matijevic), vol. 7. Wiley.
Dukhin, S. S. & Shilov, V. N. 1980 Kinetic aspects of electrochemistry of disperse systems. Part II. Induced dipole moment and the non-equilibrium double layer of a colloid particle. Adv. Colloid Interface Sci. 13, 153.Google Scholar
Fair, M. C. & Anderson, J. L. 1990 Electrophoresis of dumbbell-like colloidal particles. Intl J. Multiphase Flow 16, 663.Google Scholar
Gluckman, M. J., Pfeffer, R. & Weinbaum, S. 1971 A new technique for treating multiparticle slow viscous flow: axisymmetric flow past spheres and spheroids. J. Fluid Mech. 50, 705.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.
Keh, H. J. & Chen, S. B. 1989a Particle interactions in electrophoresis — I. Motion of two spheres along their line of centres. J. Colloid Interface Sci. 130, 542.Google Scholar
Keh, H. J. & Chen, S. B. 1989b Particle interactions in electrophoresis — II. Motion of two spheres normal to their line of centres. J. Colloid Interface Sci. 130, 556.Google Scholar
Keh, H. J. & Yang, F. R. 1990 Particle interactions in electrophoresis — III. Axisymmetric motion of multiple spheres. J. Colloid Interface Sci. 139, 105.Google Scholar
Keh, H. J. & Yang, F. R. 1991 Particle interactions in electrophoresis — IV. Motion of arbitrary three-dimensional clusters of spheres. J. Colloid Interface Sci. 145, 362.Google Scholar
O'Brien, R. W. 1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 92, 204.Google Scholar
O'Brien, R. W. 1986 Electroosmosis in porous materials. J. Colloid Interface Sci. 110, 477.Google Scholar
O'Brien, R. W. & Ward, D. N. 1988 The electrophoresis of a spheroid with a thin double layer. J. Colloid Interface Sci. 121, 402.Google Scholar
O'Brien, R. W. & White, L. R. 1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday Trans. II 74, 1607.Google Scholar
Reed, L. D. & Morrison, F. A. 1976 Hydrodynamic interaction in electrophoresis. J. Colloid Interface Sci. 54, 117.Google Scholar