Excluded-Volume Analysis of Tortuosity and Diffusivity in the Gaseous Phase of Unimodal and Bimodal Porous Media.

The soil-gas diffusivity, D_p/D_o, is a key parameter for describing the fate and transport of gaseous phase chemicals through soil. The soil pore structure largely influences the magnitude and variation of D_p/D_o as a function of soil-air content, ε. As soil-water fills up the pore spaces, certain amount of air-filled pores are entrapped thus becoming inactive air-filled pore spaces where gas diffusion cannot take place.  In this study, we present an inactive pore volume analysis where we calculate the amount of the air-filled pores that is rendered inactive due to inter-connected water films between solid particles/aggregates and inside aggregates. We assume a general power law model, D_p/D_o=F(ε-ε_in)^X, where ε_in is inactive soil-air content, and F and X are tortuosity-connectivity parameters for the air-filled pore networks. F and X can be estimated from measurements at dry conditions or at a given soil-water potential where ε_n can be assumed zero. The ε_n was subsequently obtained by inverse calculations based on measured D_p/D_o in unimodal and bimodal soils. The ε_in is zero at full water saturation, increases linearly to a maximum when e equals the percolation threshold, ε_th. At ε >ε_th, data suggested a linear (for soils) or non-linear (for sands) decrease of ε_in with ε down to zero at totally dry conditions for both unimodal and bimodal media, and additionally at around -1000cm H₂O matric potential for bimodal media (corresponding to a potential where inter-aggregate pores have been drained completely). At drier conditions than -1000cm H₂O for bimodal media (intra-aggregate pores become increasingly air-filled), the estimated ε_in was small and often negligible, suggesting sequential drainage of well-connected intra-aggregate pores without significant creation of inactive air-filled porosity. A model for the gradual increase/decrease in inactive pore space with fluid saturation is developed and linked to matric potential for unimodal and bimodal porous media.