Nucleation Controlled by Non-Fickian Fractional Diffusion

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-04, Vol.9 (7), p.740
Main Author: Svetukhin, Vyacheslav
Format: Article
Language:English
Subjects:
anomalous diffusion
cluster
Coalescing
Decomposition
diffusion-limited process
Fokker-Planck equation
Food science
fractional equation
Grain boundaries
Kinetics
Laplace transforms
Monte Carlo simulation
Nanostructured materials
Nucleation
Solid solutions
Supersaturation
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9070740