Electrophoresis of spheroidal particles having a random distribution of zeta potential

Charge nonuniformity on colloidal particles can be a dominant factor in determining the bulk stability of a dispersion. However, experimental measurements of such nonuniformity are lacking. One straightforward technique for measuring the charge nonuniformity on particles is `electrophoretic rotation', and the calculations in this paper enable the interpretation of electrophoretic rotation experiments for spheroids. For systems with infinitesimal double layers, it is shown that if the charge (or ζ potential) is randomly distributed over the individual particles in a dispersion, where each particle is covered with N equal-area patches, then the spheroids will on average rotate with an angular velocity proportional to σ<sub>ζ</sub>/√N, where σ<sub>ζ</sub> is the standard deviation of zeta potential on the patches. This is true for any random distribution of ζ potential, which emphasizes that `random' implies `nonuniform'. Whereas standard translational electrophoretic mobility gives the average zeta potential (〈ζ〉) on particles, the rotational electrophoretic mobility gives the standard deviation of ζ potential (σ_ζ).