Predictive-descriptive models for gas and solute diffusion coefficients in variably saturated porous media coupled to pore-size distribution: iv. solute diffusivity and the liquid phase impedance factor

The solute diffusion coefficient in soil (DP) and its dependency on volumetric soil-water content (θ) and matric potential (−ψ) governs release of dissolved chemicals from low-permeable zones of contaminated soils. Further inspired by the intriguing early history of research findings on mineral nutrition of plants and the key role of ion diffusion played in this, we present a model directly linking the ion (solute) diffusion coefficient in variably saturated soil with both θ and ψ. In literature, a linear relationship between the liquid phase impedance factor fl (ratio of relative solute diffusion coefficient, DP/D0, to θ) and θ is typically observed. Assuming a linear impedance factor equation (LIFE), we couple the LIFE with the Campbell soil-water retention model to relate fl and DP/D0 to soil-water matric potential. For loamy and clayey soils, the LIFE-Campbell model in agreement with measured data shows an almost linear relationship between fl and pF [= log(−ψ)] between pF 1.7 and 4.2 (from near field capacity to plant wilting point moisture contents), while the relation between DP/D0 and pF is more nonlinear. We also evaluate links between LIFE threshold water content θth (where solute diffusion ceases because of disconnected or thin water films), LIFE slope H (related to pore network tortuosity), and basic soil physical parameters. Linking θth to a newly defined soil physical characteristic (FCvol; the volumetric content of clay plus organic matter) showed to be highly promising. For 21 soils, the value of θth (m H2O m soil) is close to FCvol (m fines m soil), with θth typically > FCvol for compacted or aggregated soils, and θth = 0.8 FCvol for seven nonaggregated and noncompacted soils with between 5 and 40% clay. Furthermore, θth exhibits a nonlinear relationship with the Philips soil-water sorptivity (S). The LIFE slope H is typically close to unity but is also affected by soil aggregation and compaction. The LIFE-Campbell type model is useful to illustrate effects of pore-size distribution and soil type on solute diffusivity and the impedance factor of the soil liquid phase.