Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media Page: 3 of 31
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How do continuum-scale transport properties arise from the molecular- and pore-scale features
of porous media? In the present paper, we address this abiding question for the particular case of
the "apparent" diffusion coefficient Da [defined by the continuum-scale relation N, = Da, aC*/ax~,
if N, is the mass flux density of the species of interest along the x, direction and C* is its total
concentration per volume of porous medium] of water tracers and dissolved solutes in smectite-
rich porous media. These diffusion coefficients are widely used in reconstructing the
geochemistry of sedimentary formations (1, 2) and in predicting the performance of natural or
engineered contaminant barrier systems (3, 4), radioactive waste repositories (5, 6), and CO2
repositories (7, 8).
We have previously investigated the relationship between Da and the pore-scale features of
water-saturated smectite-rich porous media (9-11), finding that Da values of water and cations
can be modeled rather simply as a sum of two terms describing diffusion in macropore and
smectite interlayer nanopore "compartments":
Da, IDO = 1/G, (amacropore + nanoporekanopore) (1)
In Eq. 1, Do is the diffusion coefficient of the species of interest in bulk liquid water, G, is a
"geometry factor" that accounts for tortuosity, pore connectivity and pore-size variability (12),
amacropore and anaopore are the mole fractions of the species of interest located in macropores and
smectite interlayer nanopores, respectively (amacropore + anaopore = 1 if adsorption on smectite edge
surfaces or on non-smectitic minerals is negligible), and Snanopore is a "constrictivity factor" that
accounts for the lower mobility of species in interlayers as compared to macropores (13).
Equation 1 shares a conceptual basis (the treatment of interlayer nanopores as a well-defined
compartment of the overall pore space) with models of surface geochemistry (14) and chemo-
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Bourg, I.C. & Sposito, G. Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media, article, December 1, 2009; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1012739/m1/3/: accessed March 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.