An Air–Water Interfacial Area Based Variable Tortuosity Model for Unsaturated Sands

A new variable tortuosity definition is introduced that is based on the immiscible fluid (air–water) interfacial area. Unsaturated media tortuosity (τ a ) is defined as the ratio of a aw to a aw,o where a aw is the estimated air–water interfacial area in a real unsaturated medium (i.e., a soil sample), and a aw,o is the same variable for the corresponding, idealized capillary bundle. The air–water interfacial area for both real and idealized media is directly proportional to the area under their respective retention curves. With τ being the saturated tortuosity, we relate the variable tortuosity ratio (τ/τ a ) to the S e ε term in Mualem's (ε = 0.5) and Burdine's (ε = 2) pore‐size distribution models. Thus, instead of using tortuosity and pore connectivity formulations, which have empirical exponents of either 0.5 or 2, the new model depends on a variable interfacial area for varying saturation and soil texture, as reflected in the measured retention data. We tested the new definition of tortuosity to predict unsaturated hydraulic conductivity, K , as a function of volumetric moisture content, θ, for 22 repacked Hanford sediments that are comprised of mostly coarse and fine sands but some also contain a sizeable fraction (as high as 27%) of fines (silt and clay). Replacing the S e ε term in van Genuchten–Mualem (VGM) model by the tortuosity ratio τ/τ a , and still using saturated hydraulic conductivity and moisture retention parameters as used in the conventional approach, we obtained τ a ‐based K (θ) predictions that are nearly identical to the conventional VGM model predictions. We also compared the τ a ‐based K (θ) predictions with the standard Brooks–Corey–Burdine (BCB) model predictions. In comparison to the VGM model predictions, τ a ‐based BCB K (θ) predictions appear to be less biased relative to the measured K for the coarse‐textured samples.