Interfacial area based variable tortuosity‐connectivity for unsaturated media: A comparison using Miller–Miller scaling and Arya–Paris model

Abstract

The tortuosity and/or pore connectivity factor, τ, in unsaturated media is typically represented by Seɛ, where Se = effective saturation. The exponent ɛ is treated as an optimized parameter with typical values of 0.5 and 2, respectively, for Mualem and Burdine‐type models. In this study, the tortuosity and/or connectivity term in Mualem and Burdine models is replaced by a normalized ratio, τ(Se = 1) / τ(Se); τ(Se) is the ratio of air–water interfacial area for a soil sample to the interfacial area for the corresponding idealized capillary bundle. The interfacial area for a soil sample is based on Leverett's (1941) thermodynamic considerations and is obtained by integrating the area under the laboratory‐measured moisture retention curve. In addition to Miller–Miller scaling used in an earlier work, the idealized medium retention curve in this study is based on translation via the Arya–Paris (AP) model of the particle size distribution data for a soil sample into its pore size distribution. The saturation‐dependent, variable tortuosity concept is tested for 24 fine‐textured samples in addition to 22 coarse‐textured samples considered in the earlier study. For both fine‐ and coarse‐textured samples, the interfacial area based variable τ(Se) formulation provides at least as good a fit of the measured and predicted unsaturated hydraulic conductivities, K, as a function of moisture content, θ, as the standard Brooks–Corey–Burdine and van Genuchten–Mualem models. Specifically, for the fine‐textured samples, Brooks–Corey–Burdine K(θ) predictions based on the variable τ(Se) model compare well with K(θ) measurements, with an r2 of 0.86, a regression slope of 1.02, and a relatively low residual mean squared deviation of 1.13. Unlike the Burdine (Se2) and Mualem (Se0.5) empirical models, the τ(Se)‐based model parameters have explicit physical significance because the interfacial area in unsaturated media can be measured using interfacial tracers. The use of the AP model to represent the idealized medium retention data suggests its broader applicability for both fine‐ and coarse‐textured media.