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The viscous flow of charged particles through a charged cylindrical tube

Published online by Cambridge University Press:  26 April 2006

Paul Venema
Paul Venema
Affiliation:
Laboratory of Colloid Chemistry, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Present address: Ingeny B.V., Einsteinweg 5, PO Box 685, 2300 AR Leiden. The Netherlands.
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Abstract

An analysis is given for the electro-kinetic transport properties in a system consisting of a line of identical spheres placed equidistantly with their centres on the axis of a cylindrical tube containing a viscous fluid. Both the spheres and the wall of the tube are charged and a two-species symmetrical electrolyte with valence Z is present in the system. As a result of the charges on the surface of the spheres and on the surface of the tube electrical double layers will develop. When an electrical field is applied to the system an electrokinetic motion is induced. We will use the thin double layer theory (Dukhin & Derjaguin 1974; O'Brien 1983), valid for sufficiently high electrolyte concentration and where the polarization of the electrical double layer is included. Using a multipole expansion an infinite set of linear equations for the multipoles will be derived from which the electro-kinetic transport coefficients may be determined. These coefficients depend on the system parameters, such as the radius of the tube R, the radius of the sphere a, the separation between the spheres d, the Debije radius κ-1, the zeta-potentials of the spheres ζp and of the wall of the tube ζw and the valency Z of the electrolyte. From these coefficients a relation is found between the pressure drop Δp per unit length and the drag force D on the spheres on one side and with the velocity U of the spheres, the total discharge Q and the applied electrical field E0 on the other side. For some values for the system parameters we have numerically solved the infinite set of linear equations by truncation and calculated the transport coefficients. We have also calculated the streamlines for some situations. The plots of these streamlines show that depending on the conditions on the system vortices may appear.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 45 - 73
Copyright
© 1995 Cambridge University Press

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