Electrophoresis of nonuniformly charged ellipsoidal particles

Abstract A theory is developed for the motion of a charged ellipsoidal particle in a uniform electric field. The Helmholtz limit of a thin double layer is assumed but the zeta potential is allowed to be an arbitrary function of position on the surface of the particle. The resulting formulas for translation and rotation of the particle are applied to spheroids with an axisymmetric distribution of zeta potential. The translational velocity depends on the monopole and quadrupole moments of the zeta potential as well as on the orientation of the particle with respect to the applied electric field, while the angular velocity is proportional to the cross-product between the dipole moment and the field. Sample calculations are used to demonstrate possible effects of the dipole and quadrupole moments on the mean electrophoretic velocity of a dilute suspension of identical particles. A particularly interesting result is that spheroids that are electrically neutral (zero net charge) can have a significant electrophoretic mobility. Application of our theory to literature data for the electrophoretic mobility of kaolinite particles shows that the classical Smoluchowski equation can lead to erroneous estimates of the zeta potential for the faces of these disk-like particles.