An adaptive finite volume method is presented for solving incompressible heat flow problems with an unknown melt/solid interface, mainly in solidification applications, using primitive variables on a fixed collocated grid. A phase-field variable is introduced to treat the melt/solid interface, which is assumed to be diffusive, so that the complicated interfaces and phase change (using the entha...

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evap...

The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growt...

In this work, Boltzmann transform has been used to analyze the problem of freezing of pure Aluminum in semi-infinite domain. The uniqueness of solution (solidification front location) has been proved using the characteristics of the functions appeared in solution. The effect of density change on temperature distribution and errors resulting from ignoring this change have been investigated. The ...

the rapid melting of a semi- infinite body due to the absorption of a cw laser beam radiation has been studied. the enthalpy technique for the solution of phase change problems has been used in an explicit finite difference form to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. the technique has been modified so that it is not ne...

We present a unified description of interface kinetic effects in phase-field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase-field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross-coupling generalizes the phenomenology of kinetic effects and was omitted until re...

mobile carrier properties of two schiff base ligands, named bis(2-hydroxypropiophenone)-1,2-propanediimine (n2o2) and bis(1'-hydroxy-2'-acetonaphthone)-2,2'-diiminodiethylamine (n3o2), dissolved in dichloromethane for the extraction of copper(ii) ions from an ammonium buffer feed phase into a nitric acid solution (receiving phase) were investigated and compared. the parameters influencing the t...

Hydrodynamics of multiple rising bubbles as a fundamental two-phase phenomenon is studied numerically by lattice Boltzmann method and using Lee two-phase model. Lee model based on Cahn-Hilliard diffuse interface approach uses potential form of intermolecular forces and isotropic finite difference discretization. This approach is able to avoid parasitic currents and leads to a stable procedure t...

A general class of anisotropic multi-phase-eld models is proposed to describe the motion of multiple interfaces that may intersect at multiple junctions. The model reduces to classical sharp interface models in the limit of vanishing interfacial thickness. Numerical simulations show that our model is capable to recover generic features of grain growth such as crystalline curvature ow, an anisot...

We show that under equilibrium conditions, an anisotropic phase-eld model of a diiuse interface leads to the notion of a divergence-free tensor, whose components are negligible away from the interface. Near the interface, it plays the r^ ole of a stress tensor, and involves the phase-eld generalisation of the Cahn-Hooman-vector. We show that this tensor may be used to derive the equilibrium con...