Geometry-dependent reduced-order models for the computation of homogenized transfer properties in porous media, part II: electrical double layer effects

A reduced-order model (ROM) based on proper orthogonal decomposition (POD) is proposed to solve fastly the strongly nonlinear elementary cell problem derived from the periodic homogenization of the Nernst-Planck-Poisson-Boltzmann equations. In previous works, multiscale models have been developed, in order to take separately into account the macro- and microscopical aspects of ionic diffusion, under the assumption that the porous medium consists of the periodic repetition of a single microscopic representative elementary volume (REV). More recently, a numerical method based on POD-ROM has been developed in order to take into account the variability of the REV at the macroscopical scale, which involves the numerical resolution of a large amount of instances of the cell problem. Presently, this method is extended to the case where the REV's size is of the order of the Debye length and where the adsorption during the transfer of ions by the solid-fluid interface is considered.