Related papers: Onsager approach to 1D solidification problem and …
From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive an interface description, allowing arbitrary values of the growth velocity. Our derivation leads to exact expressions for the…
The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
A brief review of the Stefan problem of solidification from a mixture, and its main numerical solution methods is given. Simulation of this problem in 2D or 3D is most practically done on a regular grid, where a sharp solid-liquid interface…
Solidification structures are determined by the interaction between the interfacial processes and transport processes of heat and solute. In this paper, we investigate planar instability in directional solidification. Firstly, the…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid,…
Topographical and diffuse interface reconfigurations occur with a change in the solidification rate. In this article we pursue the hypothesis that the interface configuration during solidification is determined by the rate of entropy…
We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation of the Discrete Nonlinear Schr\"odinger equation. This model is characterized by two conserved quantities, namely mass…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation, to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three…
We discuss melting of alloys along grain boundaries as a free boundary problem for two moving solid-liquid interfaces. One of them is the melting front and the other is the solidification front. The presence of the triple junction plays an…
Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
In this paper, we consider the capillarity-driven evolution of a solid toroidal island on a flat rigid substrate, where mass transport is controlled by surface diffusion. This problem is representative of the geometrical complexity…
A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…
This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories…
In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…