On Diffusion in Fractal Soil Structures

Abstract

Fractal models of soil structure can be used to predict the scaling properties of associated transport coefficients. For gas diffusion, the structure of the soil pore space is relevant, while the structure of the solid matrix is most implicated in heat conduction. In fractal soil structures, the magnitude of the relevant diffusivities can be written in the generic form , where D(r) is a length‐dependent diffusion coefficient, A is the normalization coefficient, r is the Pythagorean length, and ϕ is a structure‐dependent constant. The dependence of ϕ on structure has been described elsewhere; however, the influence of structure on the magnitude of A has not been previously elaborated. Here, we determine the functional dependence of A on the structural parameters of the soil. The heterogeneity and connectivity, as quantified by the mass fractal dimension (Dm) and spectral dimension (d), respectively, and porosity are estimated from sections of undisturbed soil cores. For these soil structures, we demonstrate that the magnitude of the thermal and gas diffusivities is more sensitive to the porosity than to the scale dependency inherent in fractal structures. A methodology is developed and applied to rank the predicted thermal and gas diffusivities for the soil structures studied.

Pore structure changes during decomposition of fresh residue: X-ray tomography analyses

“…For 2D images, the mass fractal dimension is a number between 1 and 2 which is inversely proportional to the irregularity of the soil porous systems (Crawford and Matsui, 1996). Although it is difficult to interpret the nature of differences in mass fractal dimension between different soils (Velde, 1999), it has been successfully used as a sensitive indicator of the structural differences among soils (Rasiah and Aylmore, 1998;Gantzer and Anderson, 2002), and to model water retention, bypass flow or gas diffusion (Anderson et al, 2000). Velde (1999Velde ( , 2001 noted that the mass fractal dimension was (linearly) related to the total porosity of a sample, but that this relation was different for different soils or at different places within a drying soil core.…”

A review of model applications for structured soils: a) Water flow and tracer transport

“…Sources: g. modified after Graf and Therrien (2006), h. modified after Vogel (2002), i. modified after Deurer et al (2003), j. Anderson et al (2000), reprinted with permission from the Soil Science Society of America, k. Vogel et al (2006), reprinted with permission of the authors.…”

The relationship between fractal properties of solid matrix and pore space in porous media

“…To obtain images, they placed thin sections as negatives in a photograph chamber and used SEM and TEM (transmission electron microscopy) for high resolutions. Using black and white photographs from soil thin sections, Anderson et al (1996Anderson et al ( , 2000 measured the mass dimension of the solid and the pore phase, respectively, and in addition the spectral dimension. Gimenez et al (1998) measured the mass fractal dimension of the pore phase and the fractal dimension of the pore surface.…”