On diffusion in fractal soil structures

Fractal models of soil structure ran be used to predict the seating propert ies of associated transport coefficients. For gas diffusion, the structure of the soil pore spade is relevant, while the structure of the solid matrix is most implicated in heat conduction. In fractal soil structures, the mag nitude of the relevant diffusivities can be written in the generic form D(r ) = A(r(-phi)), where D(r) is a Length-dependent diffusion coefficient, A i s the normalization coefficient, ris the Pythagorean length, and phi is a s tructure-dependent constant. The dependence of phi on structure has been de scribed elsewhere; however, the influence of structure on the magnitude of A has not been previously elaborated. Here, we determine the functional dep endence of A on the structural parameters of the soil. The heterogeneity an d connectivity, as quantified by the mass fractal dimension (D-m) and spect ral dimension (d), respectively, and porosity are estimated from sections o f undisturbed soil cores. For these soil structures, we demonstrate that th e magnitude of the thermal and gas diffusivities is more sensitive to the p orosity than to the scale dependency inherent in fractal structures. A meth odology is developed and applied to rank the predicted thermal and gas diff usivities for the soil structures studied.