Dynamic mobility of concentrated suspensions. Comparison between different calculations

One of the fields where electroacoustic techniques (electrokinetic sonic amplitude, ESA, and colloid vibration current, CVI, are presently available) are expected to be most useful is concentrated suspensions. Here, other electrokinetic techniques, linked to the observation of individual particles, show great limitations. In spite of this, the problem of electroacoustics in concentrated suspensions is far from being fully resolved. In this work, the method considered is ESA, where the quantity of interest is the dynamic or ac mobility of the particles, ud*. Our aim is to compare in a systematic way two procedures for the calculation of ud* in concentrated suspensions: One is based upon the use of a cell model, often used in electrokinetics of concentrated systems, and the other is an analytical formula elaborated by O'Brien and coworkers taking explicitly into account particle–particle interactions. On the average both methods seem to describe properly the frequency dependence of ud*, at least up to volume fractions of solids of the order of 40%. Maxima and minima are sometimes found that can be explained through consideration of electrical double layer relaxations (alpha and, mainly, Maxwell–Wagner–O'Konski) affecting the strength of the dipole moment induced by the external field. As to the effect of κa (a: particle radius; κ: reciprocal double layer thickness) on ud*, it is found that the analytical formula, in spite of being a “large κa” model can be used with confidence down to κa ∼ 10. The two methods can also predict the reduction in |ud*| upon increasing volume fraction, but only the cell model suggests that the phase angle of |ud*| goes to zero when the particle-to-particle distance is very much reduced (highest volume fractions). It appears that the phase angle can be very sensitive to the different ways in which the methods used account for the interactions between neighbouring particles, as no significant differences are found when the effect of the volume fraction (or the zeta potential) on |ud*| are estimated using any of the models.