Electrokinetic phenomena in concentrated disperse systems: General problem formulation and spherical cell approach

Electrokinetic Phenomena in concentrated disperse and colloid systems have been studied employing Spherical Cell Approach for over three decades. The critical review of the advances in this area, which is conducted in the present paper, demonstrates a number of contradictions between the results reported by different authors. These contradictions are largely associated with imposition of boundary conditions at the outer boundary of the representative Spherical Cell. In order to establish a correct version of the Spherical Cell Approach, in the present paper, the theory of Electrokinetic Phenomena in concentrated suspensions is revisited by primarily focusing on the boundary conditions employed at the Spherical Cell outer boundary. To this end, a general mathematical problem is formulated for addressing the behavior of a planar layer of a macroscopically homogeneous disperse system under simultaneous influence of the pressure difference, gravitation and applied electric fields. On the basis of the general problem formulation, we present strict definitions of the kinetic coefficients which describe the system behavior. Making use of such definitions, some general relationships are rederived for the kinetic coefficients, namely, the Smoluchowski asymptotic expressions and the Onsager irreversible thermodynamic relationships. The general problem is reformulated for describing the electric, hydrodynamic and ion concentration fields inside the representative Spherical Cell. Using an original approach, a complete set of the boundary conditions is derived by employing the only assumption: the average over the disperse system volume is equal to the average over a representative Spherical Cell volume. A general method for predicting the kinetic coefficients is developed by employing the solution of the formulated problem. The developed method is combined with the method of small perturbation parameter using the normalized zeta potential. Final expressions for the kinetic coefficients are obtained while accounting for the terms proportional to zeta potential. The predictions are compared with results of other publications. On this basis, conclusions are made about the validity of different models proposed in the literature. (c) 2007 Elsevier B.V. All rights reserved.