Measurement and approximate critical path analysis of the pore‐scale‐induced anisotropy factor of an unsaturated porous medium

Nonspherical particles aligned parallel to preferential bedding planes form sedimentary rocks and soils, which are anisotropic in their resistance to flow of fluids, solutes, heat, and electrical current at the microscopic scale. Understanding the extent of the anisotropy of an unsaturated medium, containing both water and air, and its quantification is of major importance for improving our prediction capability of pollutant transport occurring in those media. The anisotropy factor is defined as the ratio of the conductivities parallel to the bedding plane and perpendicular to it. Measurements of the anisotropy factor of the apparent electrical conductivity in initially saturated packings of platy mica particles resulted in an initial moderate increase of the anisotropy factor with desaturation, followed by its decrease when approaching the drier region of residual moisture contents. The anisotropy factor for the hydraulic conductivity is expected to follow a pattern similar to that found for the apparent electrical conductivity. This behavior is opposite to that predicted by previous theoretical models, which suggest a possible initial decrease of the anisotropy factor of the hydraulic conductivity with desaturation, followed by its divergence to infinity toward the dry end. A critical path analysis of a simplified three-dimensional pore network model, based on different characterization of the pores parallel and normal to the bedding plane, served to evaluate the saturation degree-dependent anisotropy factors. The critical path analysis reconstructed the experimentally determined pattern qualitatively and helped to explain the observed dependence of the apparent electrical conductivity's anisotropy factor on saturation degree. The critical path analysis also provided an indication of the anisotropy factor for hydraulic conductivity, which is expected to be of higher magnitude than that of the apparent electrical conductivity.

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