Prediction of grain-size transition during solidification of hypoeutectic Al-Si alloys by an improved three-dimensional sharp-interface model

2022 ◽  
Vol 203 ◽  
pp. 111131
Author(s):  
Zhe Ren ◽  
Zhenpeng Pu ◽  
Dong-Rong Liu
Keyword(s):  
Grain Size ◽  
Three Dimensional ◽  
Sharp Interface ◽  
Interface Model ◽  
Sharp Interface Model

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.

scholarly journals A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

2020 ◽  
pp. 1-35
Author(s):  
Christian Rohde ◽  
Lars von Wolff
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Solid Phase ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Navier Stokes ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

2020 ◽  
Vol 229 (19-20) ◽  
pp. 2899-2909
Author(s):  
L. V. Toropova ◽  
P. K. Galenko ◽  
D. V. Alexandrov ◽  
M. Rettenmayr ◽  
A. Kao ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Three Dimensions ◽  
Interface Model ◽  
Sharp Interface Model
Sign in / Sign up

Export Citation Format

Share Document