DIVISION S-1—SOIL PHYSICS Tortuosity, Diffusivity, and Permeability in the Soil Liquid and Gaseous Phases P. Moldrup,* T. Olesen, T. Komatsu, P. Schjønning, and D. E. Rolston ABSTRACT (diffusive) and pressure-driven (convective–dispersive) transport of solutes and gases in variably saturated soils. Tortuosity phenomena of pore space influence the transport of Much emphasis has been put on describing the soil water water, solutes, and gases in soil. This study presents three analyses permeability (soil hydraulic conductivity) as a function linking tortuosity and transport in unsaturated soil. The first is a diffusion-based analysis of tortuosity in the soil water and soil air of soil water content. Much less emphasis has been on phases, related to soil surface area (SA) and pore-size distribution the soil air permeability as a function of soil air content, (PSD) (characterized by Campbell b and content of pores 30 m). and on diffusive properties such as solute and gas diffu- The analysis is based on recent models to predict the diffusion coeffi- sion coefficients and their variations with fluid-phase cients, D p , of (i) a solute in soil, (ii) a gas in repacked soil, and (iii) content (soil water or soil air content), probably because a gas in undisturbed soil, each as a function of fluid-phase (soil water chemical mobility and leaching in soil historically have or soil air) content, . For use in the analysis, the relation between been assumed dominated by pressure-driven transport. SA and the threshold water content where solute diffusion ceases due However, the importance of diffusion as a controlling to disconnected water films was measured for eight soils (5–46% clay). factor for chemical mobilization and transformations The tortuosity analysis supported by measured D p () data shows that and the important interactions between diffusion-con- SA governs and has a larger impact on liquid-phase tortuosity than PSD has on gaseous-phase tortuosity. At the same value of , the trolled and convection-controlled transport domains tortuosity is typically larger in the soil water than in the soil air phase, have been acknowledged for both liquid and gaseous- and the difference becomes more pronounced with increasing SA and phase transport (e.g., van Genuchten and Wierenga, at low . In the second analysis air permeability, k a , and gas diffusivity, 1977; Brusseau, 1991). Thus, both convective (water and D P,g , are linked in the Millington and Quirk fluid flow model to de- air permeabilities) and diffusive (gas and solute diffu- scribe soil structure-forming potential and to establish a model plat- sion coefficients) transport parameters need to be con- form to describe k a as a function of D P,g and . Measurements on sidered to understand chemical transport in the soil fluid repacked, nonaggregated soil support the k a (D P,g ;) model platform, phases (the water and air phases). while measurements on repacked, aggregated soils and on undisturbed The diffusion coefficient by definition provides basic soils show that k a is greatly affected by soil aggregation and structure information about the effective, tortuous pathway of and D P,g is not. In the third analysis, a constitutive parameter model is applied to gas and solute diffusivities and air and water permeabili- the liquid or gas phase (Currie, 1960; Millington and ties in six soils along a soil texture gradient. This illustrates the different Quirk, 1964; Epstein, 1989). Thus, new insight into sol- behavior of the four transport parameters with PSD and . The liquid- ute and gas diffusivity will also probably provide valu- phase transport parameters show a steeper decrease with  compared able new insight and understanding of tortuosity in the with the gaseous-phase parameters, in part due to the higher tortuosity liquid and gaseous phases and possible links to water in the liquid phase. Also, k a in undisturbed soil exhibited a less steep and air permeability in variably saturated soils. Re- decrease with  compared with D P,g , probably due to preferential air cently, a number of conceptually based, predictive mod- flow in larger pores during convective transport. Any attempt to els for the solute and gas diffusion coefficients in soils develop a unifying and PSD-dependent model for transport parame- have been presented (Moldrup et al., 2000a, 2000b; ters in the soil liquid and gaseous phases will require careful distinction Olesen et al., 2001). The models have been developed between repacked and undisturbed soils. with careful distinction between sieved, repacked soil and undisturbed soil, and, in the case of gas diffusivity, also between dry soil and wetted soil. Parameters in- A n important goal of soil physics has been to under- cluded in the models have been degree of phase satura- stand and describe the tortuosity and connectivity tion (water content or air-filled porosity), total soil po- of the soil fluid (water and air) phases. This is a prerequi- rosity and PSD, the latter represented by the Campbell site for describing and predicting concentration-driven (1974) PSD parameter (b ) and volumetric content of large pores (represented by the air-filled porosity at P. Moldrup and T. Olesen, Dep. of Environmental Engineering, Aal- -100 cm H 2 O of soil matric head, equal to the volume borg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark; T. of pores with an equivalent pore diameter 30 m). Komatsu, Dep. of Civil and Environmental Engineering, Faculty of The new, predictive diffusivity models together with Engineering, Hiroshima Univ., 1-4-1 Kagamiyama, Higashi-Hiro- shima, 739, Japan; P. Schjønning, Dep. of Crop Physiology and Soil measured diffusivity data for different soil types enable Science, Danish Institute of Agricultural Sciences, Research Centre a closer look into the tortuosity of the liquid and gaseous Foulum, P.O. Box 50, DK-8830 Tjele, Denmark; D.E. Rolston, Soils phases of unsaturated soil. and Biogeochemistry, Dep. of Land, Air and Water Resources, Univ. This study presents three analyses concerning diffu- of California, Davis, CA 95616. Received 6 July 2000. *Corresponding author (i5pm@civil.auc.dk). Abbreviations: BET, Brunauer–Emmett–Teller; PSD, pore-size distri- bution; SA, soil surface area; WLR, water-induced linear reduction. Published in Soil Sci. Soc. Am. J. 65:613–623 (2001). 613 Published May, 2001