HYDRAULIC CONDUCTIVITY OF POROUS-MEDIA AT LOW WATER-CONTENT

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 behaviour 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. -Authors