MODELING DIFFUSION AND REACTION IN SOILS: VII. PREDICTING GAS AND ION DIFFUSIVITY IN UNDISTURBED AND SIEVED SOILS

Abstract

The classical Penman (1940) and Millington-Quirk (1960, 1961) diffusivity models were transformed into general form by introducing a tortuosity parameter, m. Compared with measured diffusivities close to phase saturation (soil-water and soil-air saturation for ion and gas diffusivity, respectively), the Penman (1940) model was superior to the Millington-Quirk models independent of diffusion type. The combined use of the Penman model to predict the diffusivity at phase saturation together with a general Millington-Quirk model to predict relative decrease in diffusivity with decreasing phase content was labeled the Penman-Millington-Quirk (PMQ) model. The best fit of the new PMQ model to measured data was obtained with m = 3 (high tortuosity) and m = 6 (medium tortuosity) for gas diffusivity in undisturbed and sieved soils, respectively, and m = 1 (high tortuosity) for ion diffusivity. Measurements did not suggest a significant difference between ion diffusivity in undisturbed, sieved, or aggregated soils. The differences in m-values between diffusion types are likely caused by different diffusion pathways and geometries for ion and gas diffusivity as well as a large effect of soil heterogeneity and spatial variability on gas diffusivity. The PMQ model predicted gas diffusivity in sieved and undisturbed soil well, but a soil-type dependent model (Part IV of this series) was superior for predicting ion diffusivity. The new models seem promising for more accurately predicting gas and ion diffusion and, therefore, for improving simulations of diffusion-constrained chemical and biological reactions in soils.