Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media

In this paper, we address the manner in which the continuumscale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations, which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer "compartments." We then apply molecular dynamics (MD) simulations to determine molecularscale diffusion coefficients D_interlayer teriayer of water tracers and representative cations(Na⁺, Cs⁺, Sr²⁺) in Na-smectite interlayers. We find that a remarkably simple expression relates D _interiayer to the pore-scale parameter δ_nanopore ≤ 1, a constrictive factor that accounts for the lower mobility in interlayers as compared to macropores: δ_nanopore = D _interlayer/D₀, where D₀, is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracers H ₂O, Na⁺, Sr²⁺1, and Cs⁺ in compacted Nasmectite-rich materials.