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Wet-End Deviations from Scaling of the Water Retention Characteristics of Fractal Porous Media

CIRES, Univ. of Colorado, Boulder, CO 80309

View larger version (15K): [in a new window]   Fig. 1. Results for log(K) (vertical) vs. S (horizontal) of a representative soil due to capillary flow using fractal scaling for large , and percolation scaling for near the percolation threshold. Here, D was chosen to be 2.85, t as 0.08, and as 0.44. From Eq. [6], t turns out to be t + 0.062. The inverted triangles represent the composite calculation for K. The open circles give the percolation scaling treatment extension into the fractal scaling regime, and the fractal scaling extension into the percolation scaling regime. The vertical line gives t, and the vertical arrow points to the crossover in validity from Eq. [2] to Eq. [4] for K at t as determined from Eq. [6].

View larger version (24K): [in a new window]   Fig. 2. Determinations of wet-end moisture contents () at which deviation from fractal scaling of water retention occurs for four soils. The vertical axis is the tension (h). The open circles are theory, the solid circles experiment. The fractal dimensionality for the pore space was determined in Hunt and Gee (2002a) from the particle-size distribution and the porosity, and the air-entry head (hA) was used as an adjustable parameter. The wet-end deviations from fractal scaling are indicated with arrows. Two soils from Hunt and Gee (2002a) are used for which the wet-end deviation could clearly be seen, FLTF D11-06 (Fig. 2a) and VOC 3-0652 (Fig. 2b). For a number of the ITS soils, such as 2-2227 shown here, w was better determined from the pressure applying Eq. [8] as experimental values of h tend to rise above the theoretical curve at large .

View larger version (21K): [in a new window]   Fig. 3. Correlation of predicted and observed wet-end deviations from fractal scaling. (Upper right) VOC, (lower right) FLTF, (upper left) other, and (lower left) ITS soils. The predicted value is equal to t, which is deduced from d using Eq. [6].

View larger version (17K): [in a new window]   Fig. 4. Correlation of predicted and observed wet-end deviations from fractal scaling for all soils. The predicted value is equal to t, which is deduced from d using Eq. [6].

View larger version (19K): [in a new window]   Fig. 5. Comparison of the values of - w and t (deduced from d) with c as predicted from Eq. [3] for the moisture content at which solute diffusion vanishes, and inferred to be the critical volume fraction for percolation. In this comparison the calculated value of A/V from the particle size distribution was used as described in Hunt and Gee (2002b), but the unknown proportionality constant was uniformly taken to be 1/6 to facilitate comparison.