MODELING DIFFUSION AND REACTION IN SOILS: X. A UNIFYING MODEL FOR SOLUTE AND GAS DIFFUSIVITY IN UNSATURATED SOIL

Abstract

Diffusion processes in the soil water and air phases often govern transport and fate of nutrients, pesticides, and toxic chemicals in the vadose zone. This final paper in a 10-part series on diffusion-reaction processes in soils concerns the development of a unifying model platform for predicting solute and gas diffusion coefficients as functions of fluid-phase (water or air) content and pore-size distribution in unsaturated soils. We find that the Buckingham (1904) expression predicts solute diffusivities in water-saturated porous media more accurately than other classical expressions and, extended with a pore-size distribution-based term, yields a new and accurate model for solute diffusivity in unsaturated soil. The same was shown for gas diffusivity in undisturbed soil in Part IX of this series. Thus, the predictive diffusivity models can be rewritten in a common form with two model parameters that vary between solute and gas diffusivity and, in the case of gas diffusivity, also between undisturbed and repacked soil. It is suggested that the two parameters in this unified diffusivity model (UDM) represent porous media (solids-induced) tortuosity (T) and water-induced fluid phase disconnectivity (W), respectively, with W increasing with clay content for solute diffusion but being constant (repacked soil) or decreasing (undisturbed soil) for gas diffusion. Tested against data for 77 soils, the UDM model was markedly more accurate than commonly used soil-type independent models, with 35–50% (gas diffusivity) and 75% (solute diffusivity) reduction in root mean square error of prediction. The use of the new UDM to predict effective diffusion of sorbing chemicals in the soil water and air phases is illustrated. The UDM concept enables a new definition of the relative diffusion coefficient in soil, i.e. relative to the diffusion coefficient in a fluid-saturated porous media instead of in free water or air. This provides new possibilities for analyzing tortuosity phenomena in the soil water and air phases and their effects on diffusive and convective transport parameters in unsaturated soil.