Effective medium equations for fractional Fick's law in porous media

Francisco J. Valdes-Parada, J. Alberto Ochoa-Tapia and Jose Alvarez-Ramirez

Physica A: Statistical Mechanics and its Applications, 2007, vol. 373, issue C, 339-353

Abstract: This paper studies reaction–diffusion phenomena in disordered porous media with non-Fickian diffusion effects. The aim is to obtain an effective medium equation of the concentration dynamics having a fractional Fick's law description for the particles flux. Since the methodology is based on a volume averaging approach, a fractional spatial averaging theorem is developed to interchange averaging integration and fractional differentiation. Model structure simplifications are made on the basis of an order of magnitude analysis from physical insights. The closure problem associated with the effective diffusivity definition is also developed, showing that the macroscale diffusion parameter is affected by (i) the scaling from mesoscales to macroscales, and (ii) by the disordered structure of the porous medium.

Keywords: Non-Fickian diffusion; Fractional calculus; Reaction–diffusion; Porous media; Effective medium equations; Pseudo-homogeneous equations (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:373:y:2007:i:c:p:339-353

DOI: 10.1016/j.physa.2006.06.007

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