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The purpose of this paper is to develop a numerical model for the simulation of the dynamics of nanoparticles (NPs) at liquid–liquid interfaces. Two cases have been studied, NPs smaller than the interfacial thickness, and NPs greater than the interfacial thickness.

The model is based on the molecular dynamics (MD) simulation in addition to phase field (PF) method, through which the discrete model of particles motion is superimposed on the continuum model of fluids which is a new ide a in numerical modeling. The liquid–liquid interface is modeled using the diffuse interface model.

For NPs smaller than the interfacial thickness, the results obtained show that the concentration gradient of one fluid in the other gives rise to a hydrodynamic drag force that drives the NPs to agglomerate at the interface. Whereas, for spherical NPs greater than the interfacial thickness, the results show that such NPs oscillate at the interface which agrees with some experimental studies.

The results are important in the field of numerical modeling, especially that the model is general and can be used to study different systems. This will be of great interest in the field of studying the behavior of NPs inside fluids and near interfaces, which enters in many industrial applications.

The idea of superimposing the molecular dynamic method on the PF method is a new idea in numerical modeling.

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.

The purpose of this paper is to investigate the diffusion behaviors of different atoms at the Cu/Cu3Sn interface and the vacancy formation energy, diffusion energy barrier and vacancy diffusion activation energy.

The diffusion behaviors of different atoms at the Cu/Cu3Sn interface are analyzed, and the vacancy formation energy, diffusion energy barrier and vacancy diffusion activation energy are obtained using molecular dynamics simulation. The nudged elastic band method is used to evaluate diffusion energy barrier for Cu/Cu3Sn system.

It is found that the vacancies in the Cu/Cu3Sn interface promote the interfacial diffusion, and the formation energy of Cu vacancy in the Cu crystal is larger than that in Cu3Sn crystal. In addition, the formation energies of Cu1 vacancy and Cu2 vacancy are close to each other in Cu3Sn crystal, and they are all less than the formation energy of Sn vacancy. Furthermore, the vacancy diffusion barrier and vacancy diffusion activation energy of the Cu/Cu3Sn interface are calculated, and the results show that the vacancy diffusion activation energy of Sn was higher than that of Cu. Finally, by comparison of diffusion activation energies of different diffusion mechanisms, Cu→Cu1vac is the most possible migration path at all temperatures.

It is concluded that the vacancies in Cu/Cu3Sn interface promote interfacial diffusion, and the activation energy of vacancy diffusion in most diffusion mechanisms decreases with the increase of temperature.

During thermal laser processes, heat transfer and fluid flow in the melt pool are primary driven by complex physical phenomena that take place at liquid/vapor interface. Hence, the choice and setting of front description methods must be done carefully. Therefore, the purpose of this paper is to investigate to what extent front description methods may bias physical representativeness of numerical models of laser powder bed fusion (LPBF) process at melt pool scale.

Two multiphysical LPBF models are confronted: a Level-Set (LS) front capturing model based on a C++ code and a front tracking model, developed with COMSOL Multiphysics® and based on Arbitrary Lagrangian–Eulerian (ALE) method. To do so, two minimal test cases of increasing complexity are defined. They are simplified to the largest degree, but they integrate multiphysics phenomena that are still relevant to LPBF process.

LS and ALE methods provide very similar descriptions of thermo-hydrodynamic phenomena that occur during LPBF, providing LS interface thickness is correctly calibrated and laser heat source is implemented with a modified continuum surface force formulation. With these calibrations, thermal predictions are identical. However, the velocity field in the LS model is systematically underestimated compared to the ALE approach, but the consequences on the predicted melt pool dimensions are minor.

This study fulfils the need for comprehensive methodology bases for modeling and calibrating multiphysical models of LPBF at melt pool scale. This paper also provides with reference data that may be used by any researcher willing to verify their own numerical method.

This paper aims to propose a new smoothed particle hydrodynamics (SPH)-finite element (FE) algorithm to study fluid–structure interaction (FSI) problems.

The fluid domain is discretized based on the theory of SPH), and solid part is solved through FE method, similar to other SPH-FE methods in the previous studies. Instead of master-slave technique, the interpolating (kernel) functions of immersed boundary method are implemented to couple fluid and solid domains. The procedure of modeling completely follows the classic IB framework where forces and velocities are transferred between interacting parts. Three benchmark FSI problems are simulated and the results are compared with those of similar numerical and experimental works.

The proposed SPH-FE algorithm with promising and acceptable results can be utilized as a reliable method to simulate FSI problems.

Contrary to most SPH-FE algorithms, the calculation of contact force is not required at interacting boundaries and no iterative process is proposed to calculate forces, velocities and positions at new time step.

The purpose of this paper is to develop and validate a numerical model to study the effect of changing hydraulic parameters on saltwater intrusion in coastal aquifers.

The numerical model SEAWAT is validated and applied to a hypothetical case (Henry problem) and a real case study (Biscayne aquifer, Florida, USA) for different values of hydraulic parameters including; hydraulic conductivity, porosity, dispersion, diffusion, fluid density and solute concentration. The dimensional analysis technique is used to correlate these parameters with the intrusion length.

The results show that the hydraulic parameters have a clear effect on saltwater intrusion as they increase the intrusion in some cases and decrease it in some other cases. The results indicate that changing hydraulic parameters may be used as a control method to protect coastal aquifers from saltwater intrusion.

The results of the application of the model to the Biscayne aquifer in Florida showed that the intrusion can be reduced to 50 percent when the hydraulic conductivity is reduced to 50 percent. Decreasing hydraulic conductivity by injecting some relatively cheap materials such as bentonite can help to reduce the intrusion of saltwater. So the saltwater intrusion can be reduced with relatively low cost through changing some hydraulic parameters.

A relationship to calculate intrusion length in coastal aquifer is developed and the impact of different hydraulic parameters on saltwater intrusion is highlighted. Control of saltwater intrusion using relatively cheap method is presented.

This paper aims to demonstrate the capabilities of a diffuse interface free energy lattice Boltzmann method to perform direct numerical simulations of liquid–liquid dispersions in a well-controlled turbulent environment. The goal of this research study is to develop numerical techniques that can visualize and quantify drop interaction with the turbulent vortices. The obtained information will be used for the development of sub-models of drop breakup for multi-scale simulations.

A pure binary liquid system is considered that is subject to fully developed statistically stationary turbulent flow field in a cubic fully periodic box with the edge size of 300 lattice units. Three turbulent flow fields with varying energy input are examined and their coherent structures are visualized using a normalized Q-criterion. The evolution of the liquid–liquid interface is tracked as a function of time. The detailed explanation of the numerical method is provided with a highlight on a choice of the numerical parameters.

Drop breakup mechanisms differ depending on energy input. Drops break due to interaction with the vortices. Quantification of turbulent structures shows that the size of vortices increases with the decrease of energy input. Drop interacts simultaneously with multiple vortices of the size comparable to or smaller than the drop size. Vortices of the size smaller than the drop size disturb drop interface and pinch off the satellites. Vortices of the size comparable to the drop size tend to elongate the drop and tear it apart producing daughter drops and satellites. Addition of the second phase enhances turbulent dissipation at the high wavenumbers. To obtain physically realistic two-phase energy spectra, the multiple-relaxation-time collision operator should be used.

Detailed information of drop breakup in the turbulent flow field is crucial for the development of drop breakup sub-models that are necessary for multi-scale numerical simulations. The improvement of numerical methods that can provide these data and produce reliable results is important. This work made one step towards a better understanding of how drops interact with the turbulent vortices.

The purpose of this paper is to provide an experimental basis for studying the effects of laser remelting on the surface modification of arc-sprayed Al coating.

A layer of arc-sprayed Al coating on S355 steel was remelted with a CO₂ laser, and the surface-interface morphologies, compositions of chemical elements and phases of Al coating were analyzed with scanning electron microscopy, energy disperse spectroscopy and X-ray diffraction, respectively. The effects of laser remelting on compositions of chemical elements and bonding performance of Al coatings were discussed.

The result shows that there are some pores existing on the Al coating surface after arc spraying, and the combination mode of coating interface is primarily composed of mechanical bonding. The pores on the Al coating reduce after laser remelting, which improves the compact performance, and the mechanical binding mode by arc spraying is changed into metallurgical bonding. The Fe and Al atoms at the coating interface are distributed with gradient, and the stratified enrichment is evident, which improves binding performance of the Al coating. The Al coating exhibits general corrosion before laser remelting and local corrosion after laser remelting, which improves the corrosion resistance of Al coating.

The arc-sprayed Al coating is remelted by CO₂ laser, improving its microstructures and bonding mode with the substrate.

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.

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.

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.

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.

This paper aims to analyze the morphology transformation on the Cu₃Sn grains during the formation of full Cu₃Sn solder joints in electronic packaging.

Because of the infeasibility of analyzing the morphology transformation intuitively, a novel equivalent method is used. The morphology transformation on the Cu₃Sn grains, during the formation of full Cu₃Sn solder joints, is regarded as equivalent to the morphology transformation on the Cu₃Sn grains derived from the Cu/Sn structures with different Sn thickness.

During soldering, the Cu₃Sn grains first grew in the fine equiaxial shape in a ripening process until the critical size. Under the critical size, the Cu₃Sn grains were changed from the equiaxial shape to the columnar shape. Moreover, the columnar Cu₃Sn grains could be divided into different clusters with different growth directions. With the proceeding of soldering, the columnar Cu₃Sn grains continued to grow in a feather of the width growing at a greater extent than the length. With the growth of the columnar Cu₃Sn grains, adjacent Cu₃Sn grains, within each cluster, merged with each other. Next, the merged columnar Cu₃Sn grains, within each cluster, continued to merge with each other. Finally, the columnar Cu₃Sn grains, within each cluster, merged into one coarse columnar Cu₃Sn grain with the formation of full Cu₃Sn solder joints. The detailed mechanism, for the very interesting morphology transformation, has been proposed.

Few researchers focused on the morphology transformation of interfacial phases during the formation of full intermetallic compounds joints. To bridge the research gap, the morphology transformation on the Cu₃Sn grains during the formation of full Cu₃Sn solder joints has been studied for the first time.