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A review of non-fickian reaction-diffusion equations

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  • Zhokh, O.O.
  • Strizhak, P.E.

Abstract

A review of the recent advances in the field of non-Fickian reaction-diffusion systems is presented. The macroscopic mathematical representation of the models coupling non-Fickian diffusive transport and a chemical reaction is explored, as well as the basics of the underlying physics are highlighted. The relevant equations are based on continuous time random walks, Levy flights, fractal environment, Cattaneo flux, and Feynman-Kac formalism. The direct relevance of the non-Fickian reaction-diffusion problem in chemical reactor engineering is discussed. The steady-state form of the non-Fickian reaction-diffusion equations is also revisited. The effect of the non-Fickian diffusion on the engineering parameters, e.g., Thiele modulus and effectiveness factor, is considered.

Suggested Citation

  • Zhokh, O.O. & Strizhak, P.E., 2026. "A review of non-fickian reaction-diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:chsofr:v:203:y:2026:i:c:s0960077925016868
    DOI: 10.1016/j.chaos.2025.117673
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