FREQUENCY-DEPENDENCE OF ELECTROACOUSTIC (ELECTROPHORETIC) MOBILITIES

The direct characterization of electrokinetic mobilities in concentrated (> 1% (v/v)) dispersions is now feasible by using electrokinetic sonic amplitude (ESA) measurements of the acoustic pressure amplitude response to an applied radio frequency (rf) field. The calibration of such measurements in terms that can be related to static electrophoretic mobilities rests on the theoretical ratio of dynamic and static mobilities, \mu(omega)/mu(0)\, where omega is the angular frequency of the applied rf field. We report here dynamic and static electrophoretic measurements for colloidal polystyrene and poly(methyl methacrylate) latexes, alumina, and silica, and we examine the self-consistency of these measurements for three theories of the frequency dependence of the mobility ratio, \mu(omega)/mu(0)\. The motion of particles in an oscillating electric field results from the applied electrical force and the opposing drag (velocity) and inertial forces. A theory due to O'Brien gives good self-consistency. Another theory, due to Babchin, Chow, and Sawatzky, differs significantly from the O'Brien theory in the treatment of particle drag. Scaling for these drag effects shows that both theories give nearly the same account of inertial or particle density effects. A more recent theory of Sawatzky and Babchin numerically matches the O'Brien theory over a considerable range in frequency, particle size, and particle density and provides an analytical rationalization for the scaling observed between the O'Brien and the Babchin, Chow, and Sawatzky theories.