Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility

The coarsening dynamics of the Cahn-Hilliard equation with order-parameter dependent mobility, \(\lambda(\phi) \propto (1-\phi^2)^\alpha\), is addressed at zero temperature in the Lifshitz-Slyozov limit where the minority phase occupies a vanishingly small volume fraction. Despite the absence of bul...

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Bibliographic Details
Published in:arXiv.org 1995-03
Main Authors: Bray, A J, Emmott, C L
Format: Article
Language:English
Subjects:
Coarsening
Order parameters
Size distribution
Online Access:Get full text
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Summary:The coarsening dynamics of the Cahn-Hilliard equation with order-parameter dependent mobility, \(\lambda(\phi) \propto (1-\phi^2)^\alpha\), is addressed at zero temperature in the Lifshitz-Slyozov limit where the minority phase occupies a vanishingly small volume fraction. Despite the absence of bulk diffusion for \(\alpha>0\), the mean domain size is found to grow as \( \propto t^{1/(3+\alpha)}\), due to subdiffusive transport of the order parameter through the majority phase. The domain-size distribution is determined explicitly for the physically relevant case \(\alpha = 1\).
ISSN:2331-8422
DOI:10.48550/arxiv.9503168