On diffusion in fractal soil structures

Anderson, A.N., Crawford, J.W. and McBratney, A.B. (2000) On diffusion in fractal soil structures. Soil Science Society of America Journal, 64(1), pp. 19-24. (doi: 10.2136/sssaj2000.64119x)

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 D(r) = A(r(-φ)), 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 (D(m)) 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Crawford, Professor John
• Authors: Anderson, A.N., Crawford, J.W., and McBratney, A.B.
• College/School: College of Social Sciences > Adam Smith Business School > Management
• Journal Name: Soil Science Society of America Journal
• Publisher: Wiley for Soil Science Society of America
• ISSN: 0361-5995
• ISSN (Online): 1435-0661

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