Dynamic Electrophoretic Mobility in Concentrated Dispersed Systems. Cell Model

Electroacoustic characterization of concentrated dispersed systems requires an adequate theory of dynamic electrophoretic mobility which takes into account particle−particle interaction. The concept of the “cell model” provides convenient and comprehensive means for creating this theory. There are two different versions of the electrokinetic cell model. The first one was introduced by Levine and Neale, the second one by Shilov and Zharkikh. The Levine−Neale cell model gives a large discrepancy with experimental data as it was shown by O'Brien and Hunter. We suggest several reasons indicating that the Shilov−Zharkikh cell model is more adequate than the Levine−Neale one. First of all, it gives transition to the Smolichowski law for electroosmosis which is valid for concentrated systems. The Shilov−Zharkikh cell model yields a symmetrical Onsager relationship between kinetic coefficients as well as the Maxwell−Vagner law for electric conductivity. In addition, the Shilov−Zharkikh cell model predicts much stronger volume fraction dependence of dynamic electrophoretic mobility. Such strong dependence corresponds to O'Brien−Hunter experimental data which could not be explained by the Levine−Neale cell model. We developed two versions of the theory using different constrains. The first version is valid only at low frequency, but it takes into account surface conductivity. The second version neglects surface conductivity. At the same time this second version takes into account inertia effects which makes it valid at high frequencies. We do not address a question of the appropriate frame of references for the dynamic electrophoretic mobility. All calculations are performed in the frame of references which is associated with the liquid.