Consideration of polydispersity in the evaluation of the dynamic mobility of concentrated suspensions

Many practical uses of electroacoustic methods for the characterization of disperse systems involve concentrated and/or polydisperse suspensions. While the effects of particle concentration have been well described experimentally and theoretically, similar studies considering a wide size distribution of the dispersed particles are lacking. This is not a minor point, as these methods are based on the action of alternating fields (either electric or acoustic) on the systems and the characteristic frequencies and amplitudes are largely determined by the particle geometry. In this work, we first evaluate the effect, on the dynamic (or ac) mobility, of changing the size distribution in the suspension. It is found that the inertia (also called hydrodynamic) relaxation of the mobility is shifted toward lower frequencies, and that the overall mobility spectrum is smoothed when the size polydispersity of the suspension increases. The results theoretically obtained are subsequently used for fitting experimental mobility data corresponding to two alumina samples, in a wide range of particle concentrations and ionic strengths. It is demonstrated that a complete model accounting for polydispersity leads to a better description of the results; very significantly, this can be done by using the zeta potential as the only fitting parameter, and forcing this parameter to be determined only by the ionic strength, and not by the volume fraction.