Hydraulic conductivity of porous media at low water content
Toledo, P.G. | Novy, R.A. | Davis, H.T. | Scriven, L.E.
Matric potential and hydraulic conductivity at low water content often obey power laws in low water content, but the exponents of these are largely empirical. Theories of fractal geometry and of thin-film physics provide a basis for the observed power-law behavior of matric potential and hydraulic conductivity. Specifically, the lead to matric potential is proportional to low water content 1/(3-D) and hydraulic conductivity is proportional to 3/m(3-D), where D is the Hausdorff dimension of the surface between the pore space and grains or matrix, and m is the exponent in the relation of disjoining pressure II and film thickness h, i.e., II is proportional to h m. These power laws may increase the reliability of extrapolating measurements of matric potential and hydraulic conductivity at low water content. Using the data of Nimmo and Akstin (1988) to test our ideas, we found that, in the case of water in soils, m < 1 and, across length scales between 5 micrometer and 20 micrometer, 2.1 < D < 2.7. In the limit of smooth pore walls, D = 2. The measured hydraulic conductivities lie between upper and lower bounds of hydraulic conductivity (low water content) that we computed using three trial distributions of pore radius.
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