Relevance of diffuse-layer, Stern-layer and interlayers for diffusion in clays: A new model and its application to Na, Sr, and Cs data in bentonite

The diffusive flux of cations is enhanced and that of anions is decreased compared to that of water tracers in bentonite or other clays, as a result of electrostatic interactions between ions and the charged clay surfaces. Clays are often used or foreseen as barriers in waste disposal in order to protect the environment from hazardous materials. A consistent description of diffusion of various ions and uncharged species is important in this context, especially if long-term interactions between clays and other materials shall be predicted by reactive transport simulations. Here, diffusion of a suite of tracers (HTO, Cl, Na, Sr and Cs) in bentonite was investigated. Experimental through-diffusion data at different bentonite dry densities were described with models of increasing complexity. First, ‘standard’ empirical single ion transport models (uncoupled, simple Fickian diffusion) were applied for each density. These models served as reference cases for comparisons. For sorbing tracers (Na, Sr, Cs), surface diffusion models were used in a next step, where average surface mobilities for the cations were determined based on comparisons with transport parameters from HTO diffusion. Finally, a more complex model was developed in order to describe anion and cation diffusion in a coupled way. This model accounts for locally parallel diffusion in different environments, namely in ‘free’ water unaffected by surface charges, in diffuse (Donnan) layer water, within the Stern layer, and within interlayer water (D-S-I model). This coupled model requires additional parameters related to the bentonite microstructure as well as to cation mobilities in the Stern layer and in the interlayer. The latter were taken from literature. Microstructural parameters were constrained in a manner that overall anion exclusion matches anion accessible porosities found by the simple Fickian diffusion model. This was possible with a reasonable choice of microstructure parameters that are consistent with literature values. A good agreement between the experimental data and the simulated cation diffusion coefficients of the D-S-I model was found, using constraints by the HTO and Cl diffusion data. The interlayer pathway was found to be most important for diffusion of Na, Sr and Cs through bentonite. Stern layer diffusion was significant and more important than diffusion through the diffuse layer for Cs and Sr, while for Na the two pathways were of equal importance.