Abstract Understanding the time‐dependent scaling of chemical weathering has been a significant research goal for over a decade. A percolation theoretical treatment of nonreactive solute transport that was previously shown compatible with the scaling of chemical weathering rates is here shown to be compatible with soil formation rates, and with C and N sequestration rates in the soil as well. In this theoretical framework, the percolation backbone fractal dimensionality, which generates the long‐time tail of the solute arrival time distribution, also predicts the scaling of the reaction rates, while laboratory proportionality to the fluid flow velocity translates to an analogous relevance of the vertical infiltration rate in the field. The predicted proportionality of solute transport to net infiltration generates simultaneously the variability in soil formation rates across 4 orders of magnitude of precipitation and 12 orders of magnitude of time scales.
Abstract Understanding and accurate prediction of gas or liquid phase (solute) diffusion are essential to accurate prediction of contaminant transport in partially saturated porous media. In this study, we propose analytical equations, using concepts from percolation theory and the Effective Medium Approximation (EMA) to model the saturation dependence of both gas and solute diffusion in porous media. The predictions of our theoretical approach agree well with the results of nine lattice Boltzmann simulations. We find that the universal quadratic scaling predicted by percolation theory, combined with the universal linear scaling predicted by the EMA, describes diffusion in porous media with both relatively broad and extremely narrow pore size distributions.
A previous work investigated the dry-end deviation from fractal scaling of water retention characteristics of a suite of 43 U.S. Department of Energy (USDOE) Hanford site soils in relationship with the vanishing of solute diffusion at a moisture content θt It was found that the deviation from fractal scaling of the water retention set on at a moisture content typically about 0.06 higher than the moisture content at which solute diffusion vanishes. Assuming that the vanishing of solute diffusion resulted from a lack of continuity of the water phase, we interpreted the deviation from fractal scaling in terms of a lack of water-phase continuity rather than as a breakdown of the fractal model. Now the wet-end deviations from fractal scaling of the same suite of soils are investigated. It is shown that the wet-end moisture contents at which the deviation occurs are correlated with the critical volume fraction for percolation and with the dry-end deviations. However, wet-end deviations occur at moisture contents closer to full saturation than do dry-end deviations from zero saturation. This contrast between the wet and dry ends of the water retention curve, h(θ), is suggested to be a result of the role of equilibration in the experimental determination of h(θ), and thus to be traceable to the much lower values of the hydraulic conductivity, K, at the dry end.
