Axisymmetric electrophoresis of coaxial spheroids

Abstract

The axisymmetric electrophoretic motion of a finite string of colloidal spheroids along their line of centers is considered. The spheroids may differ in size, in aspect ratio, and in zeta potential, and they are allowed to be unequally spaced. The assumption of thin electrical double layers at the particle surfaces is employed. The electrostatic and hydrodynamic governing equations are solved using a boundary collocation method and the interaction effects among the spheroids are calculated for various cases. For the electrophoresis of two spheroids with aspect ratio approaching unity, our results for the particle interactions agree very well with the exact solutions for the corresponding motion of two spheres. An approximate solution for the electrophoretic motion of two arbitrary ellipsoids is also obtained by using a method of reflections and is compared with the collocation solutions in some axially symmetric cases. A calculation of the particle interaction effect on chains of three spheroids reveals that existence of the third particle can significantly affect the electrophoretic mobilities of the other two particles. In general, the effect of particle interactions is much stronger for the situation of oblate spheroids than for the case of prolate spheroids. All of our data demonstrate that the electrophoretic velocity of each spheroid is unaffected by the presence of the others if all of the spheroids have the same zeta potential.