THE VISCOUS-FLOW OF CHARGED-PARTICLES THROUGH A CHARGED CYLINDRICAL TUBE

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 vis cous 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 and Derj aguin 1974; O'Brien 1983), valid for sufficiently high electrolyte con centration and where the polarization of the electrical double layer i s included. Using a multipole expansion an infinite set of linear equa tions for the multipoles will be derived from which the electro-kineti c 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 rad ius kappa(-1), the zeta-potentials of the spheres zeta(p), and of the wall of the tube zeta(w) and the valency Z of the electrolyte. From th ese coefficients a relation is found between the pressure drop Delta(p ) 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 appl ied electrical field E(0) on the other side. For some values for the s ystem 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 o f these streamlines show that depending on the conditions on the syste m vortices may appear.