Surface transport processes in charged porous media

Abstract

Surface transport processes are very important in chemistry, colloidal sciences, engineering, biology, and geophysics. Natural or externally produced charges on surfaces create electrical double layers (EDLs) at the solid-liquid interface. The existence of the EDLs produces several complex processes including bulk and surface transport of ions. In this work, a model is presented to simulate bulk and transport processes in homogeneous porous media comprising big pores. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A volume averaging technique is used to derive the averaged transport equations in the limit of thin electrical double layers. Description of the EDL between the electrolyte solution and the charged wall is accomplished using the Gouy-Chapman-Stern (GCS) model. The surface transport terms enter into the average equations due to the use of boundary conditions for diffuse interfaces. Two extra surface transports terms appear in the closed average equations. One is a surface diffusion term equivalent to the transport process in non-charged porous media. The second surface transport term is a migration term unique to charged porous media. The effective bulk and transport parameters for isotropic porous media are calculated solving the corresponding closure problems.

One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

“…Starting from the point formulation for the Poisson equation, Gabitto and Tsouris [18] derived the relevant equations corresponding to this case: where zi is the ionic charge, av is the specific surface area (Aαβ/Vm), Vm is the volume of the small scale REV, Aαβ is the interface α-β area, VT is the thermal voltage (R T/F), R is the gas constant, F is the …”

“…Starting from the point formulation for the Poisson equation, Gabitto and Tsouris [18] derived the relevant equations corresponding to this case:…”

“…We again follow the work by Gabitto and Tsouris [18] deriving the following volume averaged equation:…”

“…Gabitto and Tsouris [18] showed that the value of the effective diffusivity (D i,e f f ) is a function of the geometry and the charge at the electrolyte-solid interface, while the effective mobility (U i,e f f ) is only a function of the geometry. Therefore, the effective diffusivity and the effective mobility are not equal as is the case in the point equations.…”

“…Equations (16) and (18) are the starting point for the one-and two-equation model derivations for the electrostatic potential. In order to derive a one-equation model, we assume that the mass and potential equilibrium principle holds.…”