An ion diffusion model in semi-permeable clay materials

Ion diffusion in semi-impermeable clay materials dynamically interacts with electrostatic fields (or diffuse double layers) associated with clay particles. Current theory of ion transport in porous media containing fixed charges on solid materials, however, cannot explicitly account for the dynamic interactions. Here we proposed a model by coupling electrodynamics and nonequilibrium thermodynamics to describe ion diffusion in the clay materials. The developed model was validated by comparing the calculated and measured apparent ion diffusion coefficients in clay materials as a function of ionic strength, which affects the overlap extent of the electrostatic double layers associated with adjacent clay particles. The model shows that ion diffusion in clay materials is a complex function of factors including surface charge density, tortuosity, porosity, chemico-osmotic coefficient, and ion self-diffusivity. At transitional states, ion diffusive fluxes are dynamically related to the electrostatic fields, which shrink or expand as ion diffusion. 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 expressed by the ion diffusivity in bulk electrolytes corrected by a tortuosity factor and concentration gradient variations at the interfaces between clay materials and bulk solutions.