A simple model of the high-frequency dynamic mobility in concentrated suspensions

Because electroacoustic techniques are gaining interest in many fields of colloid science, a number of theories dealing with the phenomenon of electrophoresis in high-frequency (on the order of the MHz) electric fields have been developed. In the present work we propose a straightforward derivation of a simple formula for the dynamic mobility of colloidal particles in mildly concentrated systems. Starting with a simple expression for the electrophoretic mobility in dilute suspensions, given as a function of the zeta potential and of the dipole coefficient, we introduce successive corrections related to: (i) the back flow of fluid induced by the electrophoretic motion of the particles; (ii) the electrostatic interactions among particles; (iii) the difference between the macroscopic and the external electric fields; (iv) the difference between the zero-momentum and the laboratory reference frames. Considering furthermore that the frequency dependence of the dipole coefficient is due to the Maxwell–Wagner–O'Konski double-layer relaxation, we obtain a mobility expression that compares well with other (semi)analytical models and (in proper conditions) with numerical cell-model calculations. However, its main merit is that it allows to understand, to a large extent, the physical origin of the frequency and volume fraction dependences of the dynamic mobility.

Graphical abstractA simple model is derived to explain the frequency and volume fraction dependence of the dynamic electrophoretic mobility of concentrated suspensions. The evaluation compares favorably with existing more elaborate methods in a wide range of conditions.Figure optionsDownload full-size imageDownload as PowerPoint slide