Particle interactions in electrophoresis: IV. Motion of arbitrary three-dimensional clusters of spheres

Abstract

A combined analytical—numerical study of the electrophoretic motion of an arbitrary finite cluster of colloidal spheres is presented. The spheres may each be suspended freely in the fluid, or they may be connected by infinitesimally thin rods to form a rigid aggregate. Also, the spheres are allowed to differ in size and in zeta potential at the surface. The theory developed is the most general solution to the problem of electrophoresis of an assemblage of spheres surrounded by thin electrical double layers in a three-dimensional unbounded medium. Using a boundary-collocation technique, the electrostatic and hydrodynamic governing equations are solved in the quasisteady situation and the interaction effects among the spheres are calculated for various cases. For the electrophoresis of two-sphere systems, our results for the translational and angular velocities of the particles at all orientations and separation distances agree very well with the exact solutions obtained by using spherical bipolar coordinates. For the cases of a rigid cluster composed of two or three spheres, the numerical calculations for the particle mobility parameters show that “neutral” particles (with zero area-averaged zeta potential) can be driven to migrate by the applied electric field. The direction of migration of a linear “neutral” cluster is decided by the zeta potential associated with the sphere (or spheres) whose local electric field at the surface is stronger than that of the other sphere (or spheres). All of our data demonstrate that the electrophoretic velocity of each sphere in an unbounded fluid is unaffected by the presence of the others if all of the spheres have the same zeta potential. Finally, our numerical results for the interaction between two electrophoretic spheres are used to find the effect of volume fractions of particles of each type on the mean particle velocities in a bounded dispersion.