Abstract
Charged porous media are pervasive, and modeling such systems is 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 microscale, fundamental microscopic concepts and corresponding mass and momentum balance equations for charged porous media are presented. Given the highly coupled nonlinear physiochemical processes in charged porous media as well as the huge discrepancy in length scales of these physiochemical 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 is discussed.
Highlights
Chemical transport, and deformation in charged porous media are important topics studied in many engineering applications and natural phenomena, where the electrostatic or electrokinetic forces due to the charged solid surfaces become important
All fundamental phenomena in porous media such as singlephase and two-phase flow hydrodynamics, solute transport, and deformation can be highly influenced by charged surfaces, which are not included in the classical Darcy-scale flow and deformation theory
Clayey soils are a notable example of porous media, where flow, transport, and deformation are strongly influenced by the charged surfaces due to a small pore size distribution and large surface area-to-volume ratio
Summary
Many natural and synthetic materials have charged surfaces (e.g., clay, charged nanoparticles, polymers) due to the electron imbalance of their molecular structures. The charged surface produces an electric field, which attracts counterions (dissolved ions from a salt compound, e.g., NaCl, in water, that have the opposite charge of the surface) in an ionic solution or electrolyte. The electrical potential measured at the shear plane ( called the slipping plane), roughly at the interface between the Stern layer and diffuse layer, is referred to as the zeta potential (ζ ). Note that the anions and cations will appear together in the bulk phase because, by definition, it has zero electric potential and zero net charge density ( zi cbi = 0). The concentrations of the co-ions (with respect to the sign of the surface charge) in the diffuse layer will always be smaller than (or equal to) the bulk concentration (cbi ) and the concentration of the counterions in the diffuse layer will be larger than cbi. I where is permittivity (Farad m−1 or CV−1 m−1), a property of a material representing its ability to store electrical energy
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