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Effective medium equation for fractional Cattaneo's diffusion and heterogeneous reaction in disordered porous media

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

Abstract

This paper focuses on the reaction-diffusion problem in a disordered porous medium. The objective is to obtain an effective medium description of the concentration dynamics having a fractional Cattaneo's law equation as the flux constitutive equation. The methodology is based on a volume averaging procedure, and simplifications are made on the basis of an order of magnitude analysis with physical grounds. Sufficient conditions to obtain pseudo-homogeneous models are given. The closure problem associated with the effective diffusivity definition results to be the same that the one corresponding to Fickian diffusion.

Suggested Citation

  • Valdes-Parada, Francisco J. & Alberto Ochoa-Tapia, J. & Alvarez-Ramirez, Jose, 2006. "Effective medium equation for fractional Cattaneo's diffusion and heterogeneous reaction in disordered porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 318-328.
    • Handle: RePEc:eee:phsmap:v:369:y:2006:i:2:p:318-328
    DOI: 10.1016/j.physa.2006.02.030
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    Cited by:

    1. Fernandez-Anaya, G. & Valdes-Parada, F.J. & Alvarez-Ramirez, J., 2011. "On generalized fractional Cattaneo’s equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4198-4202.

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