Weak solutions and simulations to a new phase-field model with periodic boundary

2020 ◽  
pp. 1-16
Author(s):  
Lixian Zhao ◽  
Jiawei Mai ◽  
Fang Cheng
Keyword(s):  
Phase Field ◽  
Weak Solutions ◽  
Periodic Boundary ◽  
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
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