A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics

2017 ◽  
Vol 19 (2) ◽  
pp. 141-182 ◽  
Author(s):  
Elie Bretin ◽  
Simon Masnou
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
New Phase

A new phase-field model for strongly anisotropic systems

2009 ◽  
Vol 465 (2105) ◽  
pp. 1337-1359 ◽  
Author(s):  
Solmaz Torabi ◽  
John Lowengrub ◽  
Axel Voigt ◽  
Steven Wise
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Anisotropic Surface ◽  
Sharp Corners ◽  
New Phase

We present a new phase-field model for strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn–Hilliard-type equations. Such problems arise during the growth and coarsening of thin films. When the anisotropic surface energy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn–Hilliard equations become ill-posed. Our models contain a high-order Willmore regularization, where the square of the mean curvature is added to the energy, to remove the ill-posedness. The regularized equations are sixth order in space. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. Using the method of matched asymptotic expansions, we show the convergence of our phase-field model to the general sharp-interface model. We present two- and three-dimensional numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the dynamics of the new phase-field model and the sharp-interface model. The computed equilibrium shapes using the new model also match a recently developed analytical sharp-interface theory that describes the rounding of the sharp corners by the Willmore regularization.

A new phase-field model for a water–oil-surfactant system

2014 ◽  
Vol 229 ◽  
pp. 422-432 ◽  
Author(s):  
Ana Yun ◽  
Yibao Li ◽  
Junseok Kim
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Surfactant System ◽  
New Phase

The Phase-Field Simulation of the Grain Growth under External Field

2011 ◽  
Vol 299-300 ◽  
pp. 69-72
Author(s):  
Li Li Zhang ◽  
Ming Gao ◽  
Shao Nan Tang
Keyword(s):  
External Field ◽  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Grain Number ◽  
Grain Distribution ◽  
2D And 3D ◽  
The Relationship ◽  
New Phase

A new phase field model coupled with external field was used to simulate 2D and 3D grain growth processing. The simulation results showed that 2D grain size distribution under external field was inhomogeneous. The evolutions of 2D grain under different external field strength were roughly the same, but the grain number was obviously different with the changes of external fields. Under the external field, the relationship between 2D grain area and time was linear. 3D grain distribution was inhomogeneous in the direction of the external field gradient. The nucleation gradually decreased in the direction of change.

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