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 continuum-scale 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 molecular-scale diffusion coefficients D{sub interlayer} of water tracers and representative cations (Na{sup +}, Cs{sup +}, Sr{sup 2+}) in Na-smectite interlayers. We find that a remarkably simple expression relates D{sub interlayer} to the pore-scale parameter {delta}{sub nanopore} {<=} 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: {delta}{sub nanopore} = D{sub interlayer}/D{sub 0}, where D{sub 0} is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracer H{sub 2}O, Na{sup +}, Sr{sup 2+} and Cs{sup +}+ in compacted Na-smectite-rich materials