Coupled processes in charged porous media - from theory to applications

Charged porous media are pervasive, and modeling such systems
are mathematically and computationally challenging due to the highly coupled hydrodynamic and electrochemical interactions caused by the presence of
charged solid surfaces, ions in the fluid, and chemical reactions between the
ions in the fluid and the solid surface. In addition to the microscopic physics,
applied external potentials such as hydrodynamic, electrical, and chemical potential gradients, control the macroscopic dynamics of the system. This paper
aims to give fresh overview of modeling pore-scale and Darcy-scale coupled
processes for different applications. At the micro scale, fundamental microscopic concepts and corresponding mass and momentum balance equations
for charged porous media are presented. Given the highly-coupled non-linear
physio-chemical processes in charged porous media as well as the huge discrepancy in length scales of the these physio-chemical phenomena versus the
application, numerical simulation of these processes at the Darcy-scale is even
more challenging than the direct pore-scale simulation of multiphase
flow in porous media. Thus, upscaling the microscopic processes up to the Darcy scale is essential and highly required for large-scale applications. Hence, we provide and discuss Darcy-scale porous medium theories obtained using the hybrid mixture theory and homogenization along with their corresponding assumptions. Then, application of these theoretical developments in clays, batteries, enhanced oil recovery, and biological systems are discussed.