Evaluation of Tortuosity Models for Predicting Solute Diffusion in Unsaturated Soils.

Diffusion is an important mechanism of solute transport, and it is often described by Fick’s Law. In unsaturated porous media, the rate of solute diffusion decreases with decreasing soil water content due to the reduced cross-sectional area of the liquid phase and the longer diffusive pathway. This reduction is accounted by the ‘tortuosity’ factor, the fraction of diffusion coefficients of solute in soil and liquid phase. Direct measurement of effective diffusion coefficient to obtain tortuosity is time and labor consuming, thus many models have been proposed to predict the tortuosity for unsaturated porous media. These models can be categorized into four groups: (1) water content based, (2) water content-porosity-bulk density based, (3) water content-bulk density-soil water characteristic based, and (4) conceptual models. In this study, effective diffusion coefficients of packed soil cores of a sand, a sandy clay loam, and a clay were measured by equilibrating the core samples with 0.01M KBr solution to a range of desired water contents. Ion exchange membrane method was used to measure the effective diffusion coefficients of bromide in the core samples. The measured effective diffusion coefficients were used to evaluate the aforementioned tortuosity models. Results show that the water content based and water content-porosity-bulk density based models have very limited prediction capability, as they require individual empirical constants to model soils in different textures and bulk densities. Water content-bulk density-soil water characteristic based models give better prediction if the measured effective diffusion coefficient at saturation and the soil water characteristic data are available. The conceptual models have limited prediction capability, but they serve to explain the dynamics of the diffusion process and can predict the trend of the effective diffusion coefficient changes as water content changes.