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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.

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.

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.

This paper gives unique perspectives to future directions of research on this topic.

In this work, with a goal to ultimately forward the advancement of additive manufacturing research, the author applies the Wheeler-Boettinger-McFadden model through a progressive series of increasingly complex solidification problems illustrating the evolution of both dendritic as well as columnar growth morphologies. For purposes of convenience, the author assumes idyllic solutions (i.e. the excess energies associated with mixing solid and liquid phases can be neglected).

In this work, the author applied the phase-field model through a progressive series of increasingly complex solidification problems, illustrating the evolution of both dendritic as well as columnar growth morphologies. Beginning with a non-isothermal treatment of pure Ni, the author further examined the isothermal and directional solidification of Cu–Ni binary alloys.

(1) Consistent with previous simulation results, solidification simulations from each of the three cases revealed the presence of parabolic, dendrite tips evolving along directions of maximum interface energy. (2) For pure Ni simulations, changes in the anisotropy and noise magnitudes resulted in an increase of secondary dendritic branches and changes in the direction of propagation. The overall shape of the primary structure tended also to elongate with increased anisotropy. (3) For simulations of isothermal solidification of Ni–Cu binary alloys, the development of primary and secondary dendrite arm formation followed similar patterns associated with a pure substance. Calculations of dendrite tip velocity tended to increase monotonically with increasing anisotropy in accordance with previous research. (4) Simulations of directional solidification of Ni–Cu binary alloys with a linear temperature profile demonstrated the presence of cellular dendrites with relatively weak side-branching. The occurrence of solute trapping was also apparent between the primary dendrite columns. Dendrite tip velocities increased with increasing cooling rate.

This research, particularly the section devoted to directional solidification of binary alloys, describes a novel numerical framework and platform for the parametric analysis of various microstructural related quantities, including the effects due to changes in temperature gradient and cooling rate. Both the evolution of the phase and concentration are resolved.

This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method.

A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case.

The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented.

A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

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.

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.

The results show an influence scale on directional phase front propagation dynamics and how significant are stochastic thermal noises in micro-scale freezing.

The numerical calculation has modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.

Proper selection of the stability parameter determines the accuracy of dendrite tip kinetics at a single crystal scale. Recently developed sophisticated phase field modelling of a single grain evolution provides evidence that this parameter is not constant during the process. Nevertheless, in the commonly used micro-macroscopic simulations of alloy solidification, it is a common practice to use a constant value of the stability parameter, resulting from the marginal stability theory. This paper aims to address the issue of how this inaccuracy in modelling crystal growth kinetics can influence numerically predicted zones of columnar and equiaxed dendrites and the macro-segregation formation.

Using the original authors’ micro-macroscopic computer simulation model of binary alloy solidification, the calculations have been performed for the Kurz-Giovanola-Trivedi (KGT) crystal growth kinetics with two different values of the stability parameter, and for two different compositions of Al-Cu alloys. The computational model is based on single domain-based formulation of transport equations, which are discretized on control-volume mesh. To identify zones of different grain structures, developing within the two-phase liquid-solid region, an envelope of columnar dendrite tips is tracked on a fixed non-orthogonal, triangular control volume grid. The models of porous and slurry media are used, along with the concept of the switching function, to account for diverse flow resistances in the columnar and equiaxed crystal zones. The numerical predictions are carefully studied to address the question of how the chosen stability parameter influences macroscopic structures of a cast, the most important issue from the engineering point of view.

The carried-out comprehensive numerical analysis shows that the value of the stability parameter of the KGT-constrained dendrite growth model does not have a direct significant impact on the macrosegregation formation. It, however, visibly influences the undercooling along the front, separating different dendritic structures and the size of the undercooled melt region where the equiaxed grains can develop. It also affects the amount of eutectic phase created.

To the best of the authors’ knowledge, this is the first attempt at estimating the influence of some inaccuracies, caused by possible ambiguities in choosing the stability constant of the KGT law, on numerically predicted macroscopic fields of solute concentration, the developing zones of columnar and equiaxed crystals and the macrosegregation patterns.

In the present work, a numerical method, based on the well established enthalpy technique, is developed to simulate the growth of binary alloy equiaxed dendrites in presence of melt convection. The paper aims to discuss these issues.

The principle of volume-averaging is used to formulate the governing equations (mass, momentum, energy and species conservation) which are solved using a coupled explicit-implicit method. The velocity and pressure fields are obtained using a fully implicit finite volume approach whereas the energy and species conservation equations are solved explicitly to obtain the enthalpy and solute concentration fields. As a model problem, simulation of the growth of a single crystal in a two-dimensional cavity filled with an undercooled melt is performed.

Comparison of the simulation results with available solutions obtained using level set method and the phase field method shows good agreement. The effects of melt flow on dendrite growth rate and solute distribution along the solid-liquid interface are studied. A faster growth rate of the upstream dendrite arm in case of binary alloys is observed, which can be attributed to the enhanced heat transfer due to convection as well as lower solute pile-up at the solid-liquid interface. Subsequently, the influence of thermal and solutal Peclet number and undercooling on the dendrite tip velocity is investigated.

As the present enthalpy based microscopic solidification model with melt convection is based on a framework similar to popularly used enthalpy models at the macroscopic scale, it lays the foundation to develop effective multiscale solidification.

The purpose of this paper is to demonstrate a method for modeling of cellular structures by means of Voronoi tessellation and to conduct a validation by comparison with real metal foam structures.

Heat propagation behavior of open-pore metal foams is studied for both experimental as well as computer-modeled structures showing excellent agreement. The 3D open-pore structure of the real foam is reconstructed from 2D light microscope images in-depth.

An algorithm to create synthetic open-pore foam structures has been developed.

The algorithm for modeling synthetic open-pore cellular structures allows the random distribution of the individual pores close to reality.

A fundamental principle of materials engineering is that the microstructure of a material controls the properties. The phase transformation is an important phenomenon that determines the final microstructure. Recently, many analytical and numerical methods were used for modeling of phase transformation, but some limitations can be seen in relation to the choice of the shape of growing grains, introduction of varying grain growth rate and modeling of diffusion phenomena. There are also only few comprehensive studies that combine the final microstructure with the actual conditions of its formation. Therefore, the objective of the work is a development of a new hybrid model based on lattice Boltzmann method (LBM) and cellular automata (CA) for modeling of the diffusional phase transformations. The model has a modular structure and simulates three basic phenomena: carbon diffusion, heat flow and phase transformation. The purpose of this study is to develop a model of heat flow with consideration of enthalpy of transformation as one of the most important parts of the proposed new hybrid model. This is one of the stages in the development of the complex model, and the obtained results will be used in a combined solution of heat flow and carbon diffusion during the modeling of diffusion phase transformations.

Different values of overheating/overcooling affect different values in the enthalpy of transformation and thus the rate of transformation. CA and LBM are used in the hybrid model in part related to heat flow. LBM is used for modeling of heat flow, while CA is used for modeling of the microstructure evolution during the phase transformation.

The use of LBM and CA in one numerical solution creates completely new possibilities for modeling of phase transformations. CA and LBM in comparison with commonly used approaches significantly simplify interface and interaction between different parts of the model, which operates in a common domain. The CA can be used practically for all possible processes that consist of nucleation and grains growth. The advantages of the LBM method can be well used for the simulation of heat flow during the transformation, which is confirmed by numerical results.

The developed heat flow model will be combined with the carbon diffusion model at the next stage of work, and the new complex hybrid model at the final stage will provide new solutions in numerical simulation of phase transformations and will allow comprehensive modeling of the diffusional phase transformations in many processes. Heating, annealing and cooling can be considered.

The paper presents the developed model of heat flow (temperature module), which is one of the main parts of the new hybrid model devoted to modeling of phase transformation. The model takes into account the enthalpy of transformation, and the connection with the model of microstructure evolution was obtained.

The aim of this study is to apply an enthalpy-based lattice Boltzmann method with multi distribution function model, to investigate melting process with natural convection inside a cavity with an obstacle. The cavity is filled with water (ice)-based nanofluid containing copper nanoparticles.

This methodology eliminates the requirement of satisfying conditions at the phase change front. The combination of lattice D2Q9 and D2Q5 models is implemented to determine the density, velocity and temperature fields. The simulations are carried out for Rayleigh number of 105, various volume fractions of the nanoparticles and various positions of the cubic obstacle.

The predicated results demonstrate that the use of nanoparticles leads to enhancement of thermal conductivity of nano-enhanced phase change materials in comparison with conventional PCMs. When the position of the obstacle changes from the top to the bottom of the cavity the melting rate increases 75 percent. The numerical study indicates that by increasing the solid concentration from 0 to 0.04, the heat release enhances 52.7, 41.2 and 30 percent when the obstacle is located on the top, middle and bottom sections of the cavity, respectively. It is also observed that, the employment of nanoparticles is more effective when the heat conduction dominates.

The main unacceptable property of most PCMs is their low thermal conductivity, and hence, heat transfer enhancement using nanofluid will be useful for thermal energy storage applications.

The purpose of this study is to establish a finite element (FE) model with the random distribution of the Nylon12/hydroxyapatite (PA12/HA) composite material in selective laser sintering (SLS) process for considering the material anisotropy, which aims to obtain the law of temperature and stress changes in PA12/HA sintering.

By using python script in Abaqus, the FE model is established in which the two materials are randomly distributed and are assigned to their intrinsic temperature-dependent physical parameters. Molten pool sizes at various process parameters were evaluated in terms of numerical simulation and scanning electron microscope analysis, identifying a good agreement between them. Evaluation of temperature and stress distribution under the condition of different HA contents was also conducted.

It shows that the uneven distribution and quantity of HA powder play a vital role in stress concentration and temperature increase. Additionally, the influence of HA addition on the mechanical performance of SLS-fabricated parts shows that it is conducive to improve compressive strength when the HA ratio is less than 5% because an excess of HA powder tends to bring about a certain amount of microspores resulting in a decrease in part density.

The FE model of the PA12/HA composite material with parameterized random distribution in SLS can be applied in other similar additive manufacturing technologies. It provides a feasible guideline for the numerical analysis of properties of composite materials.