Numerical Modeling of Ion Transport and Adsorption in Porous Media: A Two-scale Study for Capacitive Deionization Desalination

A two-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). At the pore scale, the Stokes equation governing water flow in porous CDI electrodes is solved using the lattice Boltzmann method and Nernst-Planck equations describing ion transport is solved using the finite volume method. The ion adsorption process is considered at the surface of carbon electrodes. At the continuum scale, Darcy equation and advection-diffusion equation governing water flow and solute transport through CDI cells are solved using OpenFOAM. After validation against analytical solutions and previously published results, the model is used to study the coupled water flow, ion transport and adsorption at the pore and continuum scales. In the pore-scale modeling, the effect of electrode microstructure, electrical potential and flow velocity on the adsorption processes is quantitatively investigated, and the relative importance of various parameters is determined. In addition, the average adsorption rate derived from the pore-scale simulations is used in the continuum model to simulate water desalination in a flow-through CDI cell. The evolution of salt concentration during desalination has been quantified. It is found that the electrode adsorption capability has a direct influence on overall ion adsorption. Results also demonstrate that a narrower spacer between the two electrodes allows for faster ion adsorption. The presented model provides a numerical tool to quantitatively analyze the ion transport and adsorption in porous electrodes. It can help improve the fundamental understanding of the adsorption processes in porous electrodes for capacitive deionization.