An ion diffusion model in semi-permeable clay materials.

Clay materials typically contain negative surface charges that induce electrostatic fields (or diffuse double layers) in electrolytes. During ion diffusion in a porous medium of clay materials, ions dynamically interact with the electrostatic fields associated with individual clay grains by depressing or expanding the electrostatic double layers, which subsequently affects ionic fluxes. Current theory of ion transport in porous media, however, cannot explicitly account for the dynamic interactions. Here we proposed a model by coupling electrodynamics and nonequilibrium thermodynamics (EDNT) to describe ion diffusion in clay materials as a complex function of factors including clay surface charge density, tortuosity, porosity, chemicoosmotic coefficient, and ion self-diffusivity. The model was validated by comparing the calculated and measured apparent ion diffusion coefficients in clay materials as a function of ionic strength. At transitional states, ion diffusive fluxes are dynamically related to the electrostatic fields, which shrink or expand as ion diffusion occurs. At steady states, the electrostatic fields are time-invariant and ion diffusive fluxes conform to flux and concentration gradient relationships; and apparent diffusivity can be approximated by the ion diffusivity in bulk electrolytes corrected by a tortuosity factor and macroscopic concentration discontinuities at the interfaces between clay materials and bulk solutions.