Electro-diffusive transport in macroscopic porous media: Estimation of effective transport properties using numerical upscaling
In engineering approaches, the electro-diffusive transport behavior of ions through charged porous media is often described by phenomenological theories, formulated on the observation scale of the macroscopic material, without considering the underlying physics on the particle scale. We propose a new approach, by implementing a generalized multiscale framework, based on the classical PoissonNernstPlanck theory, which is valid for both charged and uncharged porous media. A numerical upscaling scheme is employed for evaluation of the transport properties in the governing macroscopic equations. Macroscale estimates of the effective diffusion coefficients and of the effective fixed charge concentration are found based on the electrolyte background concentration and on the surface charge applied on the microscale. To demonstrate this new methodology, we implement the upscaling scheme for three different pore geometries: a linear cylindrical pore, a linear slit, and a spherical inclusion. For the chosen geometries and boundary conditions, we find a significant dependence of the effective macroscale properties on the magnitude of prescribed concentrations, the particle surface charge, and the shape of the pore space. Parametric studies reveal effective diffusion coefficients in charged porous media exceeding the corresponding self-diffusion coefficients by up to 34%. For a constant macroscopic concentration gradient, decreasing background concentrations result in a moderate increase of effective diffusion coefficients. The magnitude of the surface charge turns out to strongly influence the effective diffusion coefficients, that is increasing the magnitude of surface charge leads to significantly increased effective diffusion coefficients. These results suggest that rigorously considering electrochemical couplings will lead to a deeper understanding as to the origins of macroscopic experimental observations, and with future inclusion of effects such as cation exchange, to improved computer simulation-based modeling of ion transport through charged porous materials such as clay soils.
porous media multiscale poissonnernstplanck nonlinear numerical model