Phase transitions of a phase field model

Honghu Liu

doi:10.3934/dcdsb.2011.16.883

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2011, Volume 16, Issue 3: 883-894. Doi: 10.3934/dcdsb.2011.16.883

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Phase transitions of a phase field model

Honghu Liu^1,

1.
Department of Mathematics, Indiana University, Bloomington, IN 47405

Received: June 30, 2010

Revised: January 31, 2011

Published: September 2011

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Abstract

We consider a phase field model for the mixture of two viscous incompressible uids with the same density. The model leads to a coupled Navier-Stokes/Cahn-Hilliard system. We explore the dynamics of the system near the critical point via a dynamic phase transition theory developed recently by Ma and Wang [7, 8]. Our analysis shows qualitatively the same phase transition result as the purely dissipative Cahn-Hilliard equation, which implies that the hydrodynamics does not play a role in the phase transition process of binary systems. This is different from the sharp interface situation, where numerical studies (see e.g. [3, 6]) suggest quite different behaviors between these two models.

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Mathematics Subject Classification: Primary: 82B26, 82C26, 82D15, 37L10, 35Q35.

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References

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