AXISYMMETRICAL ELECTROPHORESIS OF MULTIPLE COLLOIDAL SPHERES

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.