Variable pore connectivity factor model for gas diffusivity in unsaturated, aggregated soil

The soil gas diffusion coefficient (D-p) and its variations with soil air content (epsilon) and soil water matric potential (psi) control vadose zone transport and emissions of volatile organic chemicals and greenhouse gases. This study revisits the 1904 Buckingham power-law model where D-p is proportional to E with X characterizing the tortuosity and connectivity of air-filled pore space. One hundred years later, most models linking D-p (epsilon) to Soil water retention and pore size distribution still assume that the pore connectivity factor, X, is a constant for a given soil. We show that X varies strongly with both epsilon and matric potential [given as pF = log(psi, cm H2O)] for individual soils ranging from undisturbed sand to aggregated volcanic ash soils (Andisols). For Andisols with bimodal pore size distribution, the X-pF function appears symmetrical. The minimum X value is typically around 2 and was observed close to psi of -1000 cm H2O (pF 3) when inter-aggregate voids are drained. To link D-p with bimodal pore size distribution, we coupled a two-region van Genuchten soil water retention model with the Buckingham D-p (epsilon) model, assuming X to vary symmetrically around a given pF. The coupled model well described D-p as a function of both epsilon and psi for both repacked and undisturbed Andisols and for other soil types. By merely using average values of the three constants in the proposed symmetrical X-pF expression, predictions of D-p were better than with traditional models.