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

Author

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

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.

Suggested Citation

  • Valdes-Parada, Francisco J. & Alberto Ochoa-Tapia, J. & Alvarez-Ramirez, Jose, 2007. "Effective medium equations for fractional Fick's law in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 339-353.
    • Handle: RePEc:eee:phsmap:v:373:y:2007:i:c:p:339-353
    DOI: 10.1016/j.physa.2006.06.007
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    Cited by:

    1. Wei, Song & Chen, Wen & Hon, Y.C., 2016. "Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1244-1251.
    2. Palanivel, J. & Suresh, K. & Premraj, D. & Thamilmaran, K., 2018. "Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 35-43.

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