# American Institute of Mathematical Sciences

October  2011, 16(3): 883-894. doi: 10.3934/dcdsb.2011.16.883

## Phase transitions of a phase field model

 1 Department of Mathematics, Indiana University, Bloomington, IN 47405, United States

Received  July 2010 Revised  February 2011 Published  June 2011

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.
Citation: Honghu Liu. Phase transitions of a phase field model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 883-894. doi: 10.3934/dcdsb.2011.16.883
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##### References:
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