Dispersion of charged tracers in charged porous media

We report a lattice-Boltzmann scheme to compute the dispersion of charged tracers in charged porous media under the combined effect of advection, diffusion and electro-migration. To this end, we extend the moment propagation approach, introduced to study the dispersion of neutral tracers (Lowe C. and Frenkel D., Phys. Rev. Lett., 77 (1996) 4552), to include the effect of electrostatic forces. This method allows us to compute the velocity autocorrelation function of the charged tracers with high accuracy. The algorithm is validated studying the dispersion coefficient in the case of electro-osmotic flow in a slit without added salt. We find excellent agreement between the numerical and analytical results. This method also provides the full time dependence of the diffusion coefficient, including for charged tracers. We illustrate on the slit case how D(t), which is measured by NMR to probe the geometry of porous media, reflects how the porosity explored by tracers depends on their charge.