Dynamic Electrophoretic Mobility of Spherical Colloidal Particles in Concentrated Suspensions

Abstract

A theory for the dynamic electrophoretic mobility μ of spherical colloidal particles in concentrated suspensions in an oscillating electric field is proposed on the basis of Kuwabara's cell model. The dynamic mobility depends on the frequency ω of the applied electric field and the particle volume fraction φ as well as on the reduced particle radius κa(where κ is the Debye–Hückel parameter andais the particle radius) and the zeta potential ζ. A mobility formula which involves numerical integration is obtained for particles with zero permittivity and low ζ. It is found that the mobility magnitude decreases with decreasing κaas in the static case (ω = 0) and as in the single particle case (φ → 0) and that it decreases with increasing ω as in the single particle case. However, the φ dependence of the mobility magnitude is much more complicated. Namely, for small κathe mobility magnitude decreases with increasing φ as in the static case. For large κait increases with increasing φ. For moderate κaand not very low ω the mobility magnitude may exhibit a maximum. In all cases the ω dependence of the mobility magnitude becomes less as φ increases, that is, the dynamic mobility at any ω approaches the static mobility as φ increases. An accurate mobility formula without involving numerical integration applicable for all κaat zero particle permittivity and low ζ is also derived. This formula is applicable even for high ζ at κa→ ∞ unless the dynamic relaxation effect becomes appreciable.