Nucleation Controlled by Non-Fickian Fractional Diffusion

Vyacheslav Svetukhin
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Vyacheslav Svetukhin: Scientific-Manufacturing Complex “Technological Centre”, 124498 Moscow, Russia

Mathematics, 2021, vol. 9, issue 7, 1-11

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.

Keywords: anomalous diffusion; fractional equation; cluster; nucleation; diffusion-limited process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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