Ion Diffusion Within Water Films in Unsaturated Porous Media

Diffusion is important in controlling local solute transport and reactions in unsaturated soils and geologic formations. Although it is commonly assumed that thinning of water films controls solute diffusion at low water contents, transport under these conditions is not well understood. We conducted experiments in quartz sands at low volumetric water contents (θ) to quantify ion diffusion within adsorbed films. At the lowest water contents, we employed fixed relative humidities to control water films at nm thicknesses. Diffusion profiles for Rb⁺ and Br^- in unsaturated sand packs were measured with a synchrotron X-ray microprobe, and inverse modeling was used to determine effective diffusion coefficients, D_e, as low as ∼9 × 10^-15 m² s^-1 at θ = 1.0 × 10^-4 m³ m^-3, where the film thickness = 0.9 nm. Given that the diffusion coefficients (D_o) of Rb⁺ and Br^- in bulk water (30 °C) are both ∼2.4 × 10^-9 m² s^-1, we found the impedance factor f = D_e/(θD_o) is equal to 0.03 ± 0.02 at this very low saturation, in agreement with the predicted influence of interface tortuosity (τ_a) for diffusion along grain surfaces. Thus, reduced cross-sectional area (θ) and tortuosity largely accounted for the more than 5 orders of magnitude decrease in D_e relative to D_o as desaturation progressed down to nanoscale films.