Dynamic electrophoretic mobility of spherical colloidal particles with thin electrical double layers in concentrated suspensions

Abstract

An expression for the dynamic electrophoretic mobility μ of spherical colloidal particles with infinitesimally thin double layers ( κa→∞ where κ is the Debye–Hückel parameter and a is the particle radius) in concentrated suspensions in an oscillating electric field is derived on the basis of Kuwabara's cell model [J. Phys. Soc. Jpn. 14 (1959) 527] and the method of Lowenberg and O'Brien [J. Colloid Interface Sci. 150 (1992) 158]. The result agrees with the large κa limiting form of the dynamic mobility obtained previously by solving the full electrokinetic equations [J. Colloid Interface Sci. 195 (1997) 137]. 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 a and the zeta potential ζ, in contrast to the static case ( ω→0), in which case the mobility in the limit of κa→∞ is given by Smoluchowski's formula independent of φ and a. It is also found that the ω dependence of the mobility magnitude becomes less as φ increases, that is, the dynamic mobility at any ω approaches Smoluchowski's static mobility as φ increases.