Phase field models frequently provide insight into phase transitions and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via surface diffusion is the long-time, sharp interface limit of microscopic phase field models such as the Cahn-Hilliard equation with a degenerate mobility function. Contrary to this conventional wisdom, we show that the long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free energy undergoes coarsening, reflecting the presence of bulk diffusion, rather than pure surface diffusion. This reveals an important limitation of phase field models that are frequently used to model surface diffusion.
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24 August 2015
Research Article|
August 27 2015
Degenerate mobilities in phase field models are insufficient to capture surface diffusion
Alpha A. Lee;
Alpha A. Lee
Mathematical Institute,
University of Oxford
, Oxford OX2 6GG, United Kingdom
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Andreas Münch
;
Andreas Münch
Mathematical Institute,
University of Oxford
, Oxford OX2 6GG, United Kingdom
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Endre Süli
Endre Süli
Mathematical Institute,
University of Oxford
, Oxford OX2 6GG, United Kingdom
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Appl. Phys. Lett. 107, 081603 (2015)
Article history
Received:
May 23 2015
Accepted:
August 16 2015
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A related article has been published:
Comment on “Degenerate mobilities in phase field models are insufficient to capture surface diffusion” [Appl. Phys. Lett. 107, 081603 (2015)]
Citation
Alpha A. Lee, Andreas Münch, Endre Süli; Degenerate mobilities in phase field models are insufficient to capture surface diffusion. Appl. Phys. Lett. 24 August 2015; 107 (8): 081603. https://doi.org/10.1063/1.4929696
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