Suppression of Anomalous Interface Effects by Localization of Solute Redistribution in Thin Interface Phase-Field Modeling of Solidification

2005 ◽  
Vol 475-479 ◽  
pp. 3197-3202
Author(s):  
Won Tae Kim ◽  
Seong Gyoon Kim
Keyword(s):  
Phase Field ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Field Calculation ◽  
Solute Redistribution ◽  
Grid Spacing ◽  
Potential Jump ◽  
Narrow Region ◽  
Enhanced Surface ◽  
Interface Effects

A phase field model for alloy solidification was developed to suppress the anomalous interface effects such as enhanced surface diffusion, chemical potential jump and surface stretching by localizing the solute redistribution into a narrow region within the phase-field interface. Application of this model to a free dendritic growth in an undercooled liquid yields quantitatively the same results as previously reported anti-trapping model. By localization of the solute redistribution into a region of single grid spacing the anomalous interfacial effects can be effectively suppressed. This model can be used for quantitative phase field calculation with an enhanced computational efficiency.

scholarly journals Lattice Phase Field Model for Nanomaterials

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7317
Author(s):  
Pingping Wu ◽  
Yongfeng Liang
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Lattice Parameter ◽  
Grid Spacing ◽  
Field Equations ◽  
Future Directions ◽  
Superlattice Structure ◽  
Field Modeling ◽  
Phase Field Equations

The lattice phase field model is developed to simulate microstructures of nanoscale materials. The grid spacing in simulation is rescaled and restricted to the lattice parameter of real materials. Two possible approaches are used to solve the phase field equations at the length scale of lattice parameter. Examples for lattice phase field modeling of complex nanostructures are presented to demonstrate the potential and capability of this model, including ferroelectric superlattice structure, ferromagnetic composites, and the grain growth process under stress. Advantages, disadvantages, and future directions with this phase field model are discussed briefly.

scholarly journals Time-Fractional Phase Field Model of Electrochemical Impedance

2021 ◽  
Vol 5 (4) ◽  
pp. 191
Author(s):  
Pavel E. L’vov ◽  
Renat T. Sibatov ◽  
Igor O. Yavtushenko ◽  
Evgeny P. Kitsyuk
Keyword(s):  
Phase Field ◽  
Chemical Potential ◽  
Electrochemical Impedance ◽  
Phase Field Model ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Warburg Impedance ◽  
Cahn Hilliard Equation ◽  
Dimensional Cell ◽  
Additional Calculation

In this paper, electrochemical impedance responses of subdiffusive phase transition materials are calculated and analyzed for one-dimensional cell with reflecting and absorbing boundary conditions. The description is based on the generalization of the diffusive Warburg impedance within the fractional phase field approach utilizing the time-fractional Cahn–Hilliard equation. The driving force in the model is the chemical potential of ions, that is described in terms of the phase field allowing us to avoid additional calculation of the activity coefficient. The derived impedance spectra are applied to describe the response of supercapacitors with polyaniline/carbon nanotube electrodes.

On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case

2020 ◽  
Vol 30 (12) ◽  
pp. 2263-2297
Author(s):  
Xiaoli Li ◽  
Jie Shen
Keyword(s):  
Error Analysis ◽  
Phase Field ◽  
Field Model ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Auxiliary Variable ◽  
Field Variable ◽  
Second Order ◽  
Navier Stokes ◽  
Order Error

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase-field variable, chemical potential, velocity and pressure in different discrete norms for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.

scholarly journals Phase field model with a variable chemical potential

2002 ◽  
Vol 132 (4) ◽  
pp. 993-1019 ◽  
Author(s):  
Yoshihiro Tonegawa
Keyword(s):  
Phase Field ◽  
Hausdorff Distance ◽  
Mean Curvature ◽  
Field Model ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Hilliard Equation ◽  
Variable Chemical ◽  
Energy Bound ◽  
Cahn Hilliard Equation

We study some asymptotic behaviour of phase interfaces with variable chemical potential under the uniform energy bound. The problem is motivated by the Cahn-Hilliard equation, where one has a control of the total energy and chemical potential. We show that the limit interface is an integral varifold with generalized Lp mean curvature. The convergence of interfaces as 0 is in the Hausdorff distance sense.

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