Evaluation of solute diffusion tortuosity factor models for variously saturated soils

Solute diffusion flux in soil is described by Fick's law along with a tortuosity factor to account for the tortuous and reduced diffusive pathway blocked by soil particles. Predictive models based on empirical or conceptual relationships with other more commonly measured soil attributes have been proposed to replace the time-consuming and multifarious laboratory measurements. However, these models have not been systematically tested and evaluated with soils of different textures under comparable conditions. This study determined solute diffusion coefficients and calculated tortuosity factors of a sand, a sandy clay loam, and a clay at various degrees of water saturation, and used the experimental data to test the predictive capabilities of these models. All the test models can fit the experimental data reasonably well as evidenced by low root mean square errors (RMSEs). When the proposed (fixed) parameter values were used, the widely accepted Millington and Quirk tortuosity model resulted in highest RMSEs for all three test soils. In terms of model efficiency as described by Akaike weight, however, the tortuosity factors of the sand and sandy clay loam soils are best represented by a quadratic function of volumetric soil water content (with the largest Akaike weights), while the combined parallel-series conceptual model assuming different configurations of film and pore water is the best for the clay soil. The Olesen power function tortuosity model has the second largest Akaike weights for the sand and sandy clay loam soils, while the So and Nye linear model has the second largest Akaike weight for the clay soil. The two-region linear model of log (tortuosity factor) versus soil water content uses a similar framework to the conceptual model, and it can satisfactorily fit to the experimental data well (low RMSEs), but with low Akaike weights due to the large number of parameters in the model. Adaption of the findings from this study may substantially improve solute diffusion modeling in unsaturated porous media.