Sedimentation velocity and potential in a concentrated colloidal suspension: Effect of a dynamic Stern layer

Abstract

The standard theory of the sedimentation velocity and potential of a concentrated suspension of charged spherical colloidal particles, developed by H. Ohshima on the basis of the Kuwabara cell model (J. Colloid Interf. Sci. 208 (1998) 295), has been numerically solved for the case of non-overlapping double layers and different conditions concerning volume fraction, and ζ-potential of the particles. The Onsager relation between the sedimentation potential and the electrophoretic mobility of spherical colloidal particles in concentrated suspensions, derived by Ohshima for low ζ-potentials, is also analyzed as well as its appropriate range of validity. On the other hand, the above-mentioned Ohshima's theory has also been modified to include the presence of a dynamic Stern layer (DSL) on the particles’ surface. The starting point has been the theory that Mangelsdorf and White (J. Chem. Soc. Faraday Trans. 86 (1990) 2859) developed to calculate the electrophoretic mobility of a colloidal particle, allowing for the lateral motion of ions in the inner region of the double layer (DSL). The role of different Stern layer parameters on the sedimentation velocity and potential are discussed and compared with the case of no Stern layer present. For every volume fraction, the results show that the sedimentation velocity is lower when a Stern layer is present than that of Ohshima's prediction. Likewise, it is worth pointing out that the sedimentation field always decreases when a Stern layer is present, undergoing large changes in magnitude upon varying the different Stern layer parameters. In conclusion, the presence of a DSL causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case, for every volume fraction. Reasons for these behaviors are given in terms of the decrease in the magnitude of the induced electric dipole moment on the particles, and therefore on the relaxation effect, when a DSL is present. Finally, we have modified Ohshima's model of electrophoresis in concentrated suspensions, to fulfill the requirements of Shilov–Zharkhik's cell model. In doing so, the well-known Onsager reciprocal relation between sedimentation and electrophoresis previously obtained for the dilute case is again recovered but now for concentrated suspensions, being valid for every ζ-potential and volume fraction.