Phase-field modeling of multicomponent and multiphase flows in microfluidic systems: a review

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Somnath Santra ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Phase Field ◽  
Order Parameter ◽  
Multiphase Flows ◽  
Field Method ◽  
Phase Field Method ◽  
Phase Field Modeling ◽  
Field Function ◽  
Content Type ◽  
Forcing Function ◽  
Field Modeling

Purpose The purpose of this study is to perform a detailed review on the numerical modeling of multiphase and multicomponent flows in microfluidic system using phase-field method. The phase-field method is of emerging importance in numerical computation of transport phenomena involving multiple phases and/or components. This method is not only used to model interfacial phenomena typical to multiphase flows encountered in engineering and nature but also turns out to be a promising tool in modeling the dynamics of complex fluid-fluid interfaces encountered in physiological systems such as dynamics of vesicles and red blood cells). Intrinsically, a priori unknown topological evolution of interfaces offers to be the most concerning challenge toward accurate modeling of moving boundary problems. However, the numerical difficulties can be tackled simultaneously with numerical convenience and thermodynamic rigor in the paradigm of the phase field method. Design/methodology/approach The phase-field method replaces the macroscopically sharp interfaces separating the fluids by a diffuse transition layer where the interfacial forces are smoothly distributed. As against the moving mesh methods (Lagrangian) for the explicit tracking of interfaces, the phase-field method implicitly captures the same through the evolution of a phase-field function (Eulerian). In contrast to the deployment of an artificially smoothing function for the interface as used in the volume of a fluid or level set method, however, the phase-field method uses mixing free energy for describing the interface. This needs the consideration of an additional equation for an order parameter. The dynamic evolution of the system (equation for order parameter) can be described by Allen–Cahn or Cahn–Hilliard formulation, which couples with the Navier–Stokes equation with the aid of a forcing function that depends on the chemical potential and the gradient of the order parameter. Findings In this review, first, the authors discuss the broad motivation and the fundamental theoretical foundation associated with phase-field modeling from the perspective of computational microfluidics. They subsequently pinpoint the outstanding numerical challenges, including estimations of the model-free parameters. They outline some numerical examples, including electrohydrodynamic flows, to demonstrate the efficacy of the method. Finally, they pinpoint various emerging issues and futuristic perspectives connecting the phase-field method and computational microfluidics. Originality/value This paper gives unique perspectives to future directions of research on this topic.

scholarly journals Fracture Propagation in Brazilian Discs with Multiple Pre-existing Notches by Using a Phase Field Method

2018 ◽  
Author(s):  
Shuwei Zhou
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Peak Load ◽  
Vertical Direction ◽  
Field Method ◽  
Phase Field Method ◽  
Phase Field Modeling ◽  
Direct Tension ◽  
Field Modeling ◽  
Splitting Test

The crack propagation in the Brazilian discs with multiple pre-existing notches is investigated by using a phase field method. The phase field modeling is verified by applying a direct tension test and an indirect splitting test on a Brazilian specimen with no pre-existing notches where the simulated results are in good agreement with previous numerical and experimental results. The influence of the notch number and spacing on the crack propagation in the Brazilian discs with multiple vertically and horizontally arranged notches is studied. Outer cracks initiate from the notch tips and propagate at a small angle with the vertical direction, finally coalescing with the ends of the discs. The strength of the specimen decreases as the notches increases. The Brazilian discs with horizontally arranged pre-existing notches only have outer cracks when the notch number is 1, 3, and 5 and have both outer and inner cracks for two and four notches. The peak load of the Brazilian discs with horizontally arranged notches increases as the notch spacing increases. The final crack patterns obtained by the phase field modeling are consistent with those by previous numerical simulations and experimental tests.

scholarly journals Machine learning-assisted high-throughput exploration of interface energy space in multi-phase-field model with CALPHAD potential

2022 ◽  
Vol 6 (1) ◽  
Author(s):  
Vahid Attari ◽  
Raymundo Arroyave
Keyword(s):  
Machine Learning ◽  
High Throughput ◽  
Phase Field ◽  
Interface Energy ◽  
Energy Space ◽  
Supervised Machine Learning ◽  
Phase Field Method ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Multi Phase

AbstractComputational methods are increasingly being incorporated into the exploitation of microstructure–property relationships for microstructure-sensitive design of materials. In the present work, we propose non-intrusive materials informatics methods for the high-throughput exploration and analysis of a synthetic microstructure space using a machine learning-reinforced multi-phase-field modeling scheme. We specifically study the interface energy space as one of the most uncertain inputs in phase-field modeling and its impact on the shape and contact angle of a growing phase during heterogeneous solidification of secondary phase between solid and liquid phases. We evaluate and discuss methods for the study of sensitivity and propagation of uncertainty in these input parameters as reflected on the shape of the Cu6Sn5 intermetallic during growth over the Cu substrate inside the liquid Sn solder due to uncertain interface energies. The sensitivity results rank σSI,σIL, and σIL, respectively, as the most influential parameters on the shape of the intermetallic. Furthermore, we use variational autoencoder, a deep generative neural network method, and label spreading, a semi-supervised machine learning method for establishing correlations between inputs of outputs of the computational model. We clustered the microstructures into three categories (“wetting”, “dewetting”, and “invariant”) using the label spreading method and compared it with the trend observed in the Young-Laplace equation. On the other hand, a structure map in the interface energy space is developed that shows σSI and σSL alter the shape of the intermetallic synchronously where an increase in the latter and decrease in the former changes the shape from dewetting structures to wetting structures. The study shows that the machine learning-reinforced phase-field method is a convenient approach to analyze microstructure design space in the framework of the ICME.

The numerical modeling of cell freezing in binary solution under subcooling conditions

2019 ◽  
Vol 30 (6) ◽  
pp. 3005-3025
Author(s):  
Przemysław Smakulski ◽  
Sławomir Pietrowicz ◽  
Jun Ishimoto
Keyword(s):  
Numerical Modeling ◽  
Free Energy ◽  
Numerical Calculation ◽  
Phase Field ◽  
Field Method ◽  
Energy Functional ◽  
Phase Field Method ◽  
Phase Front ◽  
Content Type ◽  
Free Energy Functional

Purpose This paper aims to describe and investigate the mathematical models and numerical modeling of how a cell membrane is affected by a transient ice freezing front combined with the influence of thermal fluctuations and anisotropy. Design/methodology/approach The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics and how it influences the freezing process of a single red blood cell. The numerical calculation has been modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional. Findings The results show an influence scale on directional phase front propagation dynamics and how significant are stochastic thermal noises in micro-scale freezing. Originality/value The numerical calculation has modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.

Phase-Field Modeling of the Microstructure Evolutions in Fe-Cu Base Alloys

2007 ◽  
Vol 539-543 ◽  
pp. 2383-2388 ◽  
Author(s):  
Toshiyuki Koyama ◽  
Hidehiro Onodera
Keyword(s):  
Phase Field ◽  
Structural Phase ◽  
Alloy System ◽  
Phase Field Method ◽  
Phase Decomposition ◽  
Phase Field Modeling ◽  
Rich Phase ◽  
Microstructure Changes ◽  
Field Modeling ◽  
Bcc Phase

The phase transformations and the microstructure developments in Fe-Cu base alloys during isothermal aging are simulated based on the phase-field method. Since the chemical free energy used in this simulation is obtained from the thermodynamic database of phase diagrams, the calculated microstructure changes are directly related to the phase diagram of the real alloy system. Firstly the phase decomposition and the microstructure changes in the Fe-Cu binary alloy system are demonstrated as the simple example of the phase-field modeling, i.e., the phase decomposition in bcc phase where the Cu-rich phase forms, the structural phase transformation from bcc to fcc phase in the Cu-rich nano-particle, and the shape change of fcc-Cu precipitates from sphere to rod. Secondly, the phase decomposition in bcc phase of the multi-component alloys such as the Fe-Cu-X (X=Mn,Ni) ternary system and the Fe-Cu-Mn-Ni quaternary alloy is simulated. At the early stage of aging, the Cu-rich zone with bcc structure begins to nucleate, and the component X (=Mn, Ni) is partitioned to the Cu-rich phase. When the Cu composition in the precipitate reaches equilibrium, the component X inside the precipitates moves toward to the interface region between the precipitate and matrix. Finally, there appears the shell structure that the Cu precipitates surrounded by the thin layer with high concentration of component X.

scholarly journals A practical phase field method for an elliptic surface PDE

2020 ◽  
Author(s):  
John W Barrett ◽  
Klaus Deckelnick ◽  
Vanessa Styles
Keyword(s):  
Phase Field ◽  
Numerical Test ◽  
Quadrature Rule ◽  
Field Method ◽  
Grid Size ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Finite Element Scheme ◽  
Field Function ◽  
Spatial Grid

Abstract We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to implement compared to other approaches. We estimate the error in natural norms in terms of the spatial grid size, the interface width and the order of the underlying quadrature rule. Numerical test calculations are presented, which confirm the form of the error bounds.

A Phase Field Method for Numerical Simulation of Boiling Heat Transfer

2020 ◽  
Author(s):  
Zhicheng Wang ◽  
Xiaoning Zheng ◽  
George Karniadakis
Keyword(s):  
Heat Transfer ◽  
Level Set ◽  
Phase Field ◽  
Boiling Heat Transfer ◽  
Level Set Methods ◽  
Field Method ◽  
Phase Field Method ◽  
Two Phase ◽  
Field Function ◽  
High Reynolds

Abstract The Cahn-Hilliard phase field method for two-phase flow has gained particular attention due to its unique features including its flexibility for complex morphological and topological changes, the intrinsic property of conserving mass, and the natural approach to account for the surface tension. The essential idea of the method is to use a phase field function to describe the two-phase system, while a thin smooth transition layer (interfacial area) connects the two immiscible fluids, where the value of phase field function varies continuously. The application of phase field method to two-phase flows has become more widespread recently, but to the best of our knowledge, very little progress has been made for the method being applied to the two-phase flows with phase change. This includes evaporation, condensation and boiling, which plays an important role in enhanced heat transfer in power electronics, energy, and aerospace engineering. In previous work, in order to face the challenge of large density contrast and high Reynolds number of practical engineering problems, we developed a stabilized phase field method that can handle two-phase flow with density ratio over 1000, at high Reynolds number over 10,000, and applied the method to simulate slug initiation in a long circular pipe. In this paper, inspired by the boiling model widely used in the level-set method, we propose a new boiling model that assumes that boiling takes place in the whole interfacial layer. The method is then used to solve the non-solenoidal Navier-Stokes equations. The boiling model is validated by simulating a vapor bubble growing in super-heated liquid. For this case, the growth rate of the bubble has an analytical solution, and it is used as a benchmark case in volume of fluid (VOF) and level-set methods extensively. For three different refrigerants, namely water, R134a and HFE7100, our phase field method with the boiling model can obtain accurate simulation results. Moreover, the method and model are applied to predict the three-dimensional boiling heat transfer in a rectangular micro-channel that contains a water vapor bubble with various inlet super-heat conditions. We found that the predicted bubble shape is very similar to that visualized in existing experiment. From our simulation of boiling flow using the phase field method, We have found that the required mesh resolution for the phase field method is comparable with that of VOF and level-set methods.

Optimal shape design of flux barriers in IPM synchronous motors using the phase field method

2014 ◽  
Vol 33 (3) ◽  
pp. 998-1016 ◽  
Author(s):  
Jae Seok Choi ◽  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki ◽  
Heeseung Lim ◽  
...  
Keyword(s):  
Phase Field ◽  
Numerical Technique ◽  
Optimization Method ◽  
Field Method ◽  
Phase Field Method ◽  
Content Type ◽  
Synchronous Motors ◽  
Diffuse Interfaces ◽  
Interior Permanent Magnet ◽  
Rotor Flux

Purpose – The purpose of this paper is to present an optimization method for flux barrier designs in interior permanent magnet (IPM) synchronous motors that aims to produce an advantageous sinusoidal flux density distribution in the air-gap. Design/methodology/approach – The optimization is based on the phase field method using an Allen-Cahn equation. This approach is a numerical technique for tracking diffuse interfaces like the level set method based on the Hamilton-Jacobi equation. Findings – The optimization results of IPM motor designs are highly dependent on the initial flux barrier shapes. The authors solve the optimization problem using two different initial shapes, and the optimized models show considerable reductions in torque pulsation and the higher harmonics of back-electromotive force. Originality/value – This paper presents the optimization method based on the phase field for the design of rotor flux barriers, and proposes a novel interpolation scheme of the magnetic reluctivity.

Phase-Field Simulation of γ"(D022) Precipitation in Ni Base Superalloys

2007 ◽  
Vol 561-565 ◽  
pp. 2287-2292 ◽  
Author(s):  
Toshiyuki Koyama ◽  
Hidehiro Onodera
Keyword(s):  
Phase Field ◽  
Strain Energy ◽  
Lattice Mismatch ◽  
Elastic Strain Energy ◽  
Field Method ◽  
Phase Field Method ◽  
Two Phase ◽  
Field Modeling ◽  
Fe Alloys ◽  
Key Parameter

Although the γ"(D022) phase has been known as a strengthen phase for the turbine disk of wrought Ni-base superalloys, the computer simulation of the γ"(D022) precipitation is hardly performed. In this study, it is demonstrated that the phase-field modeling of the complex microstructure developments including γ"(D022) precipitation in Ni-V-X (X=Co,Nb,Fe) alloys. The simulation results obtained are as follows: (1) The complex morphologies of the γ(A1)+γ"(D022) two-phase microstructure, such as the maze-microstructure, the chessboard-microstructure, and the chessboard-like microstructure, in Ni-V-X (X=Co,Nb,Fe) alloys are simulated reasonably by using phase-field method. (2) The morphology of the microstructure is mainly controlled by the elastic strain energy induced from the lattice mismatch. In particular, the tetragonal distortion is a key parameter to control and understand the complex microstructure changes.

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