Hydraulic Conductivity of Porous Media at Low Water Content
1990
Toledo, Pedro G. | Novy, Robert A. | Davis, H Ted | Scriven, L. E.
Matric potential ψ and hydraulic conductivity K at low water content θ often obey power laws in θ, 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 ψ and K. Specifically, they lead to ψ ∝ θ⁻¹/⁽³⁻ᴰ⁾ and K ∝ θ³/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 ∝ h⁻ᵐ. These power laws may increase the reliability of extrapolating measurements of ψ and K at low θ. 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 µm and 20 µm, 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 K(θ) that we computed using three trial distributions of pore radius.
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