The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can predict the phenomena like a heavy decrease in relative permittivity of the suspension and counterion stratification near highly charged colloidal particles. In this work we numerically obtain the electric potential, the counterion concentration and the relative permittivity around a charged particle in a concentrated salt-free suspension corrected by non-uniform size effects and orientational ordering of water dipoles. The results show the worth of such corrections for medium to high particle charges at every particle volume fraction. We conclude that non-uniform size effects and orientational ordering of water dipoles are necessary for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions.

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For binary solvent mixtures composed of ions and two kinds of polar solvents, the electric double layer near a charged object is strongly affected by not only the binary solvent composition but also the nature of the solvents, such as the volume and dipole moment of the solvent molecule. Accounting for the difference in sizes of solvents and the orientational ordering of solvent dipoles, we theoretically obtain general expressions for the spatial distribution functions of solvents and ions, in planar geometry and within the mean-field approach. While focusing on long-range electrostatic interaction and neglecting short-range interactions such as preferential solvation, our approach predicts an asymmetric depletion of the two solvents from the charged surface and a behavior of decreased permittivity of the binary solvent mixture. Furthermore, we suggest that the key factor for the depletion is the ratio of the solvent dipole moment to the solvent volume. The influence of the binary solvent composition, the volume of solvent and the dipole moment of the solvent on the number density of solvents, the permittivity and the differential capacitance is presented and discussed. We conclude that accounting for the difference in the volume and dipole moment between polar solvents is necessary for a new approach to represent more realistic situations such as preferential solvation.