scholarly journals Phase-Field Models for Multi-Component Fluid Flows

2012 ◽  
Vol 12 (3) ◽  
pp. 613-661 ◽  
Author(s):  
Junseok Kim
Keyword(s):  
Phase Field ◽  
Fluid Flows ◽  
Surface Tension Force ◽  
Immiscible Fluids ◽  
Phase Field Method ◽  
Finite Width ◽  
Field Methods ◽  
Practical Applications ◽  
Phase Field Models ◽  
Advection Term

AbstractIn this paper, we review the recent development of phase-field models and their numerical methods for multi-component fluid flows with interfacial phenomena. The models consist of a Navier-Stokes system coupled with a multi-component Cahn-Hilliard system through a phase-field dependent surface tension force, variable density and viscosity, and the advection term. The classical infinitely thin boundary of separation between two immiscible fluids is replaced by a transition region of a small but finite width, across which the composition of the mixture changes continuously. A constant level set of the phase-field is used to capture the interface between two immiscible fluids. Phase-field methods are capable of computing topological changes such as splitting and merging, and thus have been applied successfully to multi-component fluid flows involving large interface deformations. Practical applications are provided to illustrate the usefulness of using a phase-field method. Computational results of various experiments show the accuracy and effectiveness of phase-field models.

Phase Field Simulation of the Pure Material Dendrite Growth in a Forced Flow

2012 ◽  
Vol 571 ◽  
pp. 3-7
Author(s):  
Jing Liu ◽  
Ying Shuo Wang
Keyword(s):  
Phase Field ◽  
Vertical Direction ◽  
Field Method ◽  
Dendritic Morphology ◽  
Forced Flow ◽  
Phase Field Method ◽  
Pure Material ◽  
Phase Field Models ◽  
Field Simulation ◽  
Control Equation

The phase field method is effective in simulating the formation of solidification microstructure. Based on the phase field models of coupling flow field and noise field proposed by Tong and Beckermann, using finite difference method to solve control equation, apartly simulating the dendritic morphology under the condition of convection or none convection, and drawing the following conclusions after comparing the results: in the side, the dendrite will no longer be symmetrical under the condition of countercurrent and downstream, the dendrite tip grows faster with countercurrent than that of the latter, while the dendrite grows almost naturally in the vertical direction of convection.

Phase Field Simulation on the Surface Morphology of Cu/Ti Nano Thin Film

2021 ◽  
Vol 1035 ◽  
pp. 712-717
Author(s):  
Ping Ping Wu ◽  
Bing Rui Xing
Keyword(s):  
Thin Film ◽  
Surface Roughness ◽  
Surface Morphology ◽  
Layer Thickness ◽  
Phase Field ◽  
Simulation Method ◽  
Film Structure ◽  
Phase Field Method ◽  
Practical Applications ◽  
Thin Film Structure

Cu/Ti binary thin film system has many applications for micro-/nano- electro mechanical systems (MEMS/NEMS), micro-electronics and optoelectronics. In nanoscale, the quality and many physical properties of nano thin films are strongly depended on its surface morphology. In the present paper the development of surface morphology of double layered Cu/Ti thin film heterostructure with different composition and thickness has been studied by using the phase field method. The developed method is based on solving Cahn-Hilliard equations of multi-order parameters with considering the interfacial energy and elastic energy. The simulation results show that the thickness of Ti layer and Cu layer in the double-layer thin film structure can affect the surface roughness. For the heterostructures with the Cu layer thickness was fixed at 20 nm, the surface roughness was found to vary from 0.608 nm to 0.712 nm, when the Ti layer thickness increased from 10 nm to 30 nm. The calculated surface morphology and roughness was similar to the experimentally measured values. It is believed that this simulation method is useful in designing multi-layered thin film structure for practical applications.

A Flux-Corrected Phase-Field Method for Surface Diffusion

2017 ◽  
Vol 22 (2) ◽  
pp. 422-440 ◽  
Author(s):  
Yujie Zhang ◽  
Wenjing Ye
Keyword(s):  
Surface Diffusion ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Current Phase ◽  
Field Methods ◽  
Degenerate Mobility ◽  
Shrinkage Effect ◽  
Diffusion Motion ◽  
Phase Field Methods

AbstractPhase-field methods with a degenerate mobility have been widely used to simulate surface diffusion motion. However, apart from the motion induced by surface diffusion, adverse effects such as shrinkage, coarsening and false merging have been observed in the results obtained from the current phase-field methods, which largely affect the accuracy and numerical stability of these methods. In this paper, a flux-corrected phase-field method is proposed to improve the performance of phase-field methods for simulating surface diffusion. The three effects were numerically studied for the proposed method and compared with those observed in the two existing methods, the original phase-field method and the profile-corrected phase-field method. Results show that compared to the original phase-field method, the shrinkage effect in the profile-corrected phase-field method has been significantly reduced. However, coarsening and false merging effects still present and can be significant in some cases. The flux-corrected phase field performs the best in terms of eliminating the shrinkage and coarsening effects. The false merging effect still exists when the diffuse regions of different interfaces overlap with each other. But it has been much reduced as compared to that in the other two methods.

Coupled microstructural-compositional evolution informed by a thermodynamic database using the hybrid Potts-phase field model

2013 ◽  
Vol 1524 ◽  
Author(s):  
Jordan J. Cox ◽  
Eric R. Homer ◽  
Veena Tikare
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Field Methods ◽  
Energy Functionals ◽  
Compositional Evolution ◽  
Recent Developments ◽  
Phase Field Methods

ABSTRACTA recently introduced hybrid Potts-phase field method has demonstrated the ability to evolve microstructures in conjunction with compositional fields tied to different phases. In this approach, Monte Carlo Potts methods are used to evolve the microstructure while phase field methods are used to evolve the composition, and the two fields are coupled through free energy functionals. Recent developments of the model allow different multi-component alloy systems to be simulated by using thermodynamic databases and kinetic quantities to dictate the behavior. An example of the method using the aluminum-silicon binary system is demonstrated.

scholarly journals Numerical simulation of two-dimensional Faraday waves with phase-field modelling

2011 ◽  
Vol 686 ◽  
pp. 409-425 ◽  
Author(s):  
Kentaro Takagi ◽  
Takeshi Matsumoto
Keyword(s):  
Numerical Simulation ◽  
Phase Field ◽  
Vortex Sheet ◽  
Field Method ◽  
Immiscible Fluids ◽  
Phase Field Method ◽  
Two Dimensional ◽  
Faraday Waves ◽  
Qualitative Comparison ◽  
Nonlinear Numerical Simulation

AbstractA fully nonlinear numerical simulation of two-dimensional Faraday waves between two incompressible and immiscible fluids is performed by adopting the phase-field method with the Cahn–Hilliard equation due to Jacqmin (J. Comput. Phys., vol. 155, 1999, pp. 96–127). Its validation is checked against the linear theory. In the nonlinear regime, qualitative comparison is made with an earlier vortex-sheet simulation of two-dimensional Faraday waves by Wright, Yon & Pozrikidis (J. Fluid Mech., vol. 400, 2000, pp. 1–32). The vorticity outside the interface region is studied in this comparison. The period tripling state, which is observed in the quasi-two-dimensional experiment by Jiang, Perlin & Schultz (J. Fluid Mech., vol. 369, 1998, pp. 273–299), is successfully simulated with the present phase-field method.

MULTISCALE MODELING OF SOLIDIFICATION: PHASE-FIELD METHODS TO ADAPTIVE MESH REFINEMENT

2005 ◽  
Vol 19 (31) ◽  
pp. 4525-4565 ◽  
Author(s):  
NIKOLAS PROVATAS ◽  
MICHAEL GREENWOOD ◽  
BADRINARAYAN ATHREYA ◽  
NIGEL GOLDENFELD ◽  
JONATHAN DANTZIG
Keyword(s):  
Asymptotic Analysis ◽  
Phase Field ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Field Equations ◽  
Field Methods ◽  
Dendritic Spacing ◽  
Phase Field Models ◽  
Phase Field Methods

We review the use of phase field methods in solidification modeling, describing their fundamental connection to the physics of phase transformations. The inherent challenges associated with simulating phase field models across multiple length and time scales are discussed, as well as how these challenges have been addressed in recent years. Specifically, we discuss new asymptotic analysis methods that enable phase field equations to emulate the sharp interface limit even in the case of quite diffuse phase-field interfaces, an aspect that greatly reduces computation times. We then review recent dynamic adaptive mesh refinement algorithms that have enabled a dramatic increase in the scale of microstructures that can be simulated using phase-field models, at significantly reduced simulation times. Combined with new methods of asymptotic analysis, the adaptive mesh approach provides a truly multi-scale capability for simulating solidification microstructures from nanometers up to centimeters. Finally, we present recent results on 2D and 3D dendritic growth and dendritic spacing selection, which have been made using phase-field models solved with adaptive mesh refinement.

scholarly journals Progress and opportunities in modelling environmentally assisted cracking

2021 ◽  
Vol 6 ◽  
pp. 70-77
Author(s):  
Emilio Martínez Pañeda
Keyword(s):  
Phase Field ◽  
Hydrogen Uptake ◽  
Field Variable ◽  
Field Methods ◽  
Phase Field Models ◽  
Deformation And Fracture ◽  
Environmentally Assisted Cracking ◽  
Material Environment ◽  
Recent Developments ◽  
New Generation

Environmentally assisted cracking phenomena are widespread across the transport, defence, energy and construction sectors. However, predicting environmentally assisted fractures is a highly cross-disciplinary endeavour that requires resolving the multiple material-environment interactions taking place. In this manuscript, an overview is given of recent breakthroughs in the modelling of environmentally assisted cracking. The focus is on the opportunities created by two recent developments: phase field and multi-physics modelling. The possibilities enabled by the confluence of phase field methods and electro-chemo-mechanics modelling are discussed in the context of three environmental assisted cracking phenomena of particular engineering interest: hydrogen embrittlement, localised corrosion and corrosion fatigue. Mechanical processes such as deformation and fracture can be coupled with chemical phenomena like local reactions, ionic transport and hydrogen uptake and diffusion. Moreover, these can be combined with the prediction of an evolving interface, such as a growing pit or a crack, as dictated by a phase field variable that evolves based on thermodynamics and local kinetics. Suitable for both microstructural and continuum length scales, this new generation of simulation-based, multi-physics phase field models can open new modelling horizons and enable Virtual Testing in harmful environments. 

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