Multi-scale periodic homogenization of ionic transfer in cementitious materials

A multi-scale periodic homogenization procedure of the ionic transfers in saturated porous media is proposed. An application on a multi-scale porous material was achieved for establishing models describing a ionic transfer from Nernst-Planck-Poisson-Boltzmann system. The first one is obtained by homogenization from the scale of Debye length to the capillary porosity scale, by taking into account the electrical double layer phenomenon. The second one results from another homogenization procedure from the capillary porosity scale to the scale of the material, where the electrical double layer effects are naturally negligible. A numerical parametric study is conducted on three dimensional elementary cells in order to highlight the effects of the electrical double layer on the ionic transfer parameters. Comparisons with existing experimental data are also presented and discussed. The double homogenization procedure gives homogenized diffusion coefficients very close to those obtained experimentally for chlorides ions from electrodiffusion tests carried out in laboratory.