Gaseous Diffusion in Porous Media: Comparison of Universal Scaling With Experiments.

Gaseous diffusion in porous media: Comparison of universal scaling with experiments

 

Behzad Ghanbarian and Allen G. Hunt

Abstract

Diffusion in disordered media deviates from Einstein’s traditional theory, and is known to be anomalous where the mean squared displacement becomes a nonlinear function of time. In percolation clusters, anomalous diffusion follows a universal scaling near the percolation threshold of the medium and does not depend on the system’s details. However, “near” has not been well defined. In this study, we compare the results of universal scaling of anomalous diffusion in percolation clusters with measured gas diffusion data in soil samples with different textures. The universal power law is a function of the air-filled porosity (less a threshold value) with an exponent of 2.00. We digitized measured data from four databases e.g., Moldrup et al. (2000a,b), databases 1 and 2, Moldrup et al. (2003), database 3, and Moldrup et al. (2004), database 4. Our results indicated that the experimental exponent was 1.91, 2.00, 1.98, and 2.12 for database 1 to 4 with R² value greater than 0.90. As we demonstrated before (Ghanbarian-Alavijeh and Hunt, 2012), the air-filled threshold can be predicted reasonably well from the wet end of soil water retention curve data. Therefore, not only the universal scaling is confirmed, but also it is capable to predict gas diffusion in porous media.