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The electrophoretic mobility of rod-like particles

Published online by Cambridge University Press:  26 February 2013

Ehud Yariv  and
Ory Schnitzer
Ehud Yariv*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Ory Schnitzer
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: [email protected]
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Abstract

At finite Dukhin numbers, where Smoluchowski’s formula is inapplicable to thin-double-layer electrophoresis, the mobility of non-spherical particles is generally anisotropic. We consider bodies of revolution of otherwise arbitrary shape, where a uniformly applied electric field results in a rectilinear motion in the plane spanned by the field direction and the particle symmetry axis, as well as (for particles lacking fore–aft symmetry) rigid-body rotation about an axis perpendicular to that plane. Focusing upon slender particles, where the ratio $\epsilon $ of cross-sectional and longitudinal scales is asymptotically small, the translational and rotational mobilities are obtained as quadratures which depend upon the lengthwise distribution of the scaled cross-sectional width and the force densities associated with rigid-body motion. These mobility expressions approach finite limits as $\epsilon \rightarrow 0$, yielding closed-form expressions for specific particle geometries.

JFM classification

Complex Fluids: Colloids Complex Fluids: Complex Fluids Low-Reynolds-number flows: Slender-body theory
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , R3
Copyright
©2013 Cambridge University Press

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