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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.

It is shown that the fundamental expression for the complex permittivity epsilons* of a dilute suspension of monodispersed, spherical particles, epsilons*=epsilone*(1+3phid*), where epsilone* is the complex permittivity of the suspending medium and d* the dipolar coefficient, is strictly valid for any value of the volume fraction phi of particles in the suspension, provided that d* is interpreted as the ensemble average value of the dipolar coefficient of the particles and is defined in terms of the macroscopic electric field in the suspension.

A correction of a recent work on the dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of dispersed particles (C. Grosse, S. Pedrosa, V.N. Shilov, J. Colloid Interface Sci. 251 (2002) 304) is presented. It is shown that the procedure used in that work to calculate the contribution of the particles to the conductivity of the suspension leads to a result that includes the variation of the conductivity of the dispersion medium. Revised analytical and numerical calculations are presented, which strongly reinforce the conclusions reached in the original work: The expression for the conductivity increment based on the value of the dipolar coefficient of the suspended particles (calculated taking into account their electrophoretic motion) appears to be valid over the whole range of particle sizes.

The influence of applied electric field on the field-induced variation of the electrolyte concentration (concentration polarization) disturbs the electro-neutrality of the system, represented by a dispersed particle and its electric double layer in electrolyte solution. The manifestation of this electro-neutrality disturbance in the non-linear electrophoresis was considered in the framework of a procedure of successive approximations in powers of the applied field strength. Analytic expressions describing the component of the electrophoretic velocity proportional to the cubic power of the applied field strength (cubic electrophoresis) were obtained for arbitrary values of the surface conductivity (of Dukhin number). The model restrictions are spherical non-conducting particle with homogeneous surface and thin double layer.

A numerical calculation of the electrophoretic mobility of colloidal particles in weak electrolyte solution is presented. It is based on a previous work (C. Grosse, V.N. Shilov, J. Colloid Interface Sci. 211 (1999) 160-170), where the analytical theory of the thin double layer concentration polarization is generalized to the case of weak electrolytes, i.e., when the dissociation-recombination equilibrium and rate constants both have finite values. The analytical results are first completed by including terms corresponding to co-ions that were neglected in the original presentation. It is shown that these terms that have little bearing in the case of strong electrolytes, become quite important in the case when the electrolyte is weak. The problem is then solved using the network method, leading to numerical results for the electric potential and the concentrations of counterions, co-ions, and neutral ion pairs. Finally, the electrophoretic mobility is calculated both analytically and numerically. It is shown that the hypothesis of a weak electrolyte leads to changes of mobility with respect to the classical results that are even stronger than predicted analytically.

The dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of the dispersed particles is analyzed both theoretically and numerically. It is shown that the simple formula that represents the conductivity as a sum of products: charge times mobility, taken over all the carriers present in the suspension, is only valid for exceedingly low values of the product kappaa. In contrast, the formulation based on the value of the dipolar coefficient of the suspended particles seems to be valid for all the range of particle sizes. This assertion is only true if the dipolar coefficient is calculated taking into account the electrophoretic motion of the particles. For very low values of the product kappaa, the dipolar coefficient of particles free to move can be several orders of magnitude larger than that of immobile particles.

The analytical theory of the thin double-layer concentration polarization in dilute suspensions of colloidal particles, generalized by the authors to the case of weak electrolyte solutions [C. Grosse and V. N. Shilov, J. Colloid Interface Sci. 211, 160 (1999)], was used to determine the conductivity dispersion amplitude, the dielectric increment, and the characteristic time of the low-frequency dielectric dispersion (LFDD). It is shown that at constant ionic strength, the conductivity dispersion amplitude always diminishes for weak electrolytes. This is due to the increment in the zero-frequency dipolar coefficient, which occurs because the field-induced ion concentration change around the particle is lowered. On the contrary, while the dielectric increment and the characteristic time of the LFDD usually decrease, they can actually increase when the diffusion coefficient of co-ions is larger than that of counterions. The origin of this behavior is in the appearance of volume charge distributions outside the double layer, which do not vanish for weak electrolytes in the low-frequency limit. Copyright 2000 Academic Press.