Dispersion of charged tracers in charged porous media

¹  FOM Institute for Atomic and Molecular Physics - Kruislaan 407, 1098 SJ Amsterdam, The Netherlands, EU
²  ANDRA - Parc de la Croix Blanche, 1/7 rue Jean Monnet 92298 Châtenay Malabry cedex, France, EU
³  Departament de Fisica Fonamental, Universitat de Barcelona - Carrer Martí i Franqués 1, 08028-Barcelona, Spain, EU
⁴  Department of Chemistry, University of Cambridge - Lensfield Road, Cambridge CB2 1EW, UK, EU

Corresponding author: benjamin.rotenberg@upmc.fr

Received: 17 April 2008
Accepted: 16 June 2008

Abstract

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 , which is measured by NMR to probe the geometry of porous media, reflects how the porosity explored by tracers depends on their charge.