Résumé
Ion concentration profiles and electro-osmosis have been theoretically investigated by complementary methods. The counterion profiles of these charged porous media are obtained from microscopic (molecular dynamics) and mesoscopic (Brownian dynamics and Poisson-Boltzmann equation) models. Thus, the limit of validity of the more macroscopic approaches has been quantified. The electro-osmotic flow is evaluated from a similar multi-scale description. A proper evaluation of the Kubo relations adapted to this dynamical process allowed the value of this transport quantity to be obtained from the microscopic model. The comparison with the classical Smoluchowski theory of this electrokinetic phenomenon shows that the latter cannot be applied unless slip hydrodynamic boundary conditions are taken into account. The corresponding slipping length is roughly equal to 6 Å.