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Nucleation Controlled by Non-Fickian Fractional Diffusion

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  • Vyacheslav Svetukhin

    (Scientific-Manufacturing Complex “Technological Centre”, 124498 Moscow, Russia)

Abstract

Kinetic models of aggregation and dissolution of clusters in disordered heterogeneous materials based on subdiffusive equations containing fractional derivatives are studied. Using the generalized fractional Fick law and fractional Fokker–Planck equation for impurity diffusion with localization, we consider modifications of the classical models of Ham, Aaron–Kotler, and Lifshitz–Slezov for nucleation and decomposition of solid solutions. The asymptotic time dependencies of supersaturation degree, average cluster size, and other characteristics at the stages of subdiffusion-limited nucleation and coalescence are calculated and analyzed.

Suggested Citation

  • Vyacheslav Svetukhin, 2021. "Nucleation Controlled by Non-Fickian Fractional Diffusion," Mathematics, MDPI, vol. 9(7), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:740-:d:527122
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    References listed on IDEAS

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    3. Sibatov, R.T. & Svetukhin, V.V., 2015. "Fractional kinetics of subdiffusion-limited decomposition of a supersaturated solid solution," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 519-526.
    4. Giona, Massimiliano & Eduardo Roman, H., 1992. "Fractional diffusion equation for transport phenomena in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 87-97.
    5. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
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