scholarly journals Solutions to a three phase-field model for solidification

2021 ◽  
Author(s):  
yangxin Tang ◽  
Wei Gao
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Three Dimension ◽  
Parabolic Differential Equations ◽  
Phase Field Models ◽  
Multiphase Alloy ◽  
Three Phase ◽  
Temporal And Spatial ◽  
Maximum Theorem ◽  
The Galerkin Method

In this paper we present the phase-field models to describe nonisothermal solidification of ideal multicomponent and multiphase alloy systems. Governing equations are developed for the temporal and spatial variation of three phase-field functions, as well as the temperature field. The global existence of weak solutions to parabolic differential equations in three dimension was proved by the Galerkin method. The existence of a maximum theorem are also extensively studied.

scholarly journals Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Zhan Chen
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Lagrangian Formulation ◽  
Global Minimizer ◽  
Solvation Model ◽  
Phase Field Models ◽  
Eulerian Formulation ◽  
Solvation Models ◽  
Similarity And Difference ◽  
Nonpolar Solvation

AbstractIn this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.

Phase-Field Numerical Simulation of Pure Free Dendritic Growth Using Wheeler and Karma Model

2011 ◽  
Vol 421 ◽  
pp. 90-97 ◽  
Author(s):  
Yun Chen ◽  
Na Min Xiao ◽  
Xiu Hong Kang ◽  
Dian Zhong Li
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Dendrite Growth ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Two Phase ◽  
Phase Field Models ◽  
Careful Comparison ◽  
Undercooled Melts

To understand the dendrite formation during solidification phase-field model has become a powerful numerical method of simulating crystal growth in recent years. Two phase-field models due to Wheeler et al. and Karma et al., respectively, have been employed for modeling the dendrite growth worldwidely. The comparison of the two models was performed. Then using the adaptive finite element method, both models were solved to simulate a free dendrite growing from highly undercooled melts of nickel at various undercoolings. The simulated results showed that the discrepancy between the two phase-field models is negligible. Careful comparison of the phase-filed simulations with LKT(BCT) theory and experimental data were carried out, which demonstrated that the phase-field models are able to quantitatively simulate the dendrite growth of nickel at low undercoolings, however, at undercoolings above ten percent of the melting point (around 180K), the simulated velocities by Wheeler and Karma model as well as the analytical predictions overestimated the reported experiment results.

Mass and Volume Conservation in Phase Field Models for Binary Fluids

2013 ◽  
Vol 13 (4) ◽  
pp. 1045-1065 ◽  
Author(s):  
Jie Shen ◽  
Xiaofeng Yang ◽  
Qi Wang
Keyword(s):  
Phase Field ◽  
Numerical Study ◽  
Mixing Layer ◽  
Phase Field Model ◽  
Fluid Phase ◽  
Binary Fluids ◽  
Fluid Mixture ◽  
Volume Fractions ◽  
Phase Field Models ◽  
Constraints Model

AbstractThe commonly used incompressible phase field models for non-reactive, binary fluids, in which the Cahn-Hilliard equation is used for the transport of phase variables (volume fractions), conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when densities of two components are different. In this paper, we formulate the phase field theory for mixtures of two incompressible fluids, consistent with the quasi-compressible theory [28], to ensure conservation of mass and momentum for the fluid mixture in addition to conservation of volume for each fluid phase. In this formulation, the mass-average velocity is no longer divergence-free (solenoidal) when densities of two components in the mixture are not equal, making it a compressible model subject to an internal con-straint. In one formulation of the compressible models with internal constraints (model 2), energy dissipation can be clearly established. An efficient numerical method is then devised to enforce this compressible internal constraint. Numerical simulations in confined geometries for both compressible and the incompressible models are carried out using spatially high order spectral methods to contrast the model predictions. Numerical comparisons show that (a) predictions by the two models agree qualitatively in the situation where the interfacial mixing layer is thin; and (b) predictions differ significantly in binary fluid mixtures undergoing mixing with a large mixing zone. The numerical study delineates the limitation of the commonly used incompressible phase field model using volume fractions and thereby cautions its predictive value in simulating well-mixed binary fluids.

3D Simulation of Coarsening of γ′ Precipitates in a Ni-Al Alloy

1999 ◽  
Vol 580 ◽  
Author(s):  
V. Vaithyanathan ◽  
L.Q. Chen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Lattice Mismatch ◽  
Phase Field Model ◽  
Particle Morphology ◽  
3D Simulation ◽  
Al Alloy ◽  
Three Dimension ◽  
Spatial Correlations ◽  
Two Dimension

AbstractPrecipitation of γ′ particles from a disordered γ matrix in a Ni-Al alloy is studied. A continuum phase-field model is employed in three-dimension(3D). The focus is on the evolution of γ′ particle morphology and development of spatial correlations during coherent nucleation, growth and coarsening. The effect of lattice mismatch on the rate of coarsening is investigated. The results are compared with those obtained from two-dimension(2D) simulations.

Prediction of biofilm deformation and detachment using shear rheometry, phase-field modeling, and OCT

2020 ◽  
Author(s):  
Mengfei Li ◽  
Karel Matouš ◽  
Robert Nerenberg
Keyword(s):  
Mechanical Properties ◽  
Fluid Flow ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Viscoelastic Behavior ◽  
Biofilm Control ◽  
Viscoelastic Parameters ◽  
Water Solvent ◽  
Phase Field Models

<p>In many environmental systems, such as membrane filtration systems, biofilm control is essential, but costly and requiring harsh chemicals. More effective biofilm control may be obtained using a “materials science” approach.  Biofilms can be characterized as viscoelastic materials, and biofilm “disruptors” can be characterized for their weakening effect on biofilm mechanical strength. By using a novel mathematical model that incorporates biofilm mechanical properties, fluid flow, and diffusion and reaction of disruptors, better cleaning strategies can be devised.</p> <p> </p> <p>Phase-field models, where the biofilm is treated like a viscoelastic fluid, are one of the few types of models that can predicting deformation and detachment based on mechanical properties. While several related studies have proposed phase-field models for predicting biofilm deformation, there has not been any validation of these models with experimental data. As a first step towards developing a material science strategy for biofilm control, this study validated the ability of a phase-field model to capture biofilm viscoelastic behavior.</p> <p> </p> <p>In this study, a two-dimensional continuum biofilm model was implemented with finite element method (FEM) using COMSOL Multiphysics (COMSOL v5.4, Comsol Inc, Burlington, MA). We applied the phase-field model with the Cahn-Hilliard equation to simulate biofilm mechanical behavior under fluid flow. The Oldroyd-B model, the simplest viscoelastic constitutive model, was applied to capture biofilm viscoelasticity. The biofilm was modeled as an incompressible viscoelastic fluid, with EPS and a water solvent. The phase-field physics were adapted from previous studies and applied to biofilm-fluid interactions. Two types of incompressible, immiscible fluids (EPS and water solvent) were studied as two components of a single fluid, with a fluid-fluid interface between the two.</p> <p> </p> <p>Homogeneous alginate was used as a synthetic biofilm for the experimental validation. The viscoelastic parameters of alginate were obtained by shear rheometry using stress relaxation tests. In experimental tests, the deformation behavior was observed in real time using optical coherence tomography (OCT). By importing the 2-D geometry from OCT and viscoelastic parameters from rheometry, the model was simulated and compared with real deformation in the flow cell.</p> <p> </p> <p>With the applied constant flow (Re=6), biofilm demonstrated viscoelastic behavior.The same behavior was observed in modeling as well. By tracking the movements of several locations of the biofilm geometry, it was concluded that the deformation of alginate biofilms was consistent with the computational results of phase-field models. The relative error between experiment and model for this certain location were 12.8%. Heterotrophic counter-diffusional biofilms cultured in membrane-aerated biofilm reactors were also tested in this study, with a relative error of 22.2%.</p> <p> </p> <p>In conclusion, the phase-field model, coupled with Oldroyd-B equation, could properly capture biofilm viscoelastic behavior. In a complex system, the phase-field model could be used as a tool to characterize the viscoelastic parameters from the observed deformation. With this information, the model can be used to predict the required disruptor dose to achieve high amounts of biofilm removal with a minimal amount of chemical addition. This can reduce operating costs and minimize the use of harsh chemicals.</p>

scholarly journals Development of phase-field model for gas-liquid-solid three-phase flow

2014 ◽  
Vol 2014.27 (0) ◽  
pp. 593-594
Author(s):  
Tetsuya Sakakibara ◽  
Tomohiro Takaki ◽  
Masaki Kurata
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Phase Flow ◽  
Three Phase ◽  
Three Phase Flow
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