Related papers: Phase-Field Model of Freeze Casting
It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to…
We introduce a new phase-field formulation of rapid alloy solidification that quantitatively incorporates nonequilibrium effects at the solid-liquid interface over a very wide range of interface velocities. Simulations identify a new…
This work deals with numerical simulation of water freezing and thawing in a complex three-dimensional geometry of a porous medium. The porous structure is represented by a virtual container filled with glass beads. Phase transition…
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 construct a phase field model including hydrodynamics and elasticity in one-component systems. It can be used to investigate solid-liquid and liquid-liquid phase transitions. Upon first-order phase transition, a velocity field is induced…
In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas-liquid-dendrite system is proposed through considering…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a…
Quantitative phase field models have been extensively used to study the solidification behavior of alloys under different conditions. However, a longstanding challenge of phase field models is the directional bias caused by the…
Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) is a popular sharp interface theory. Using matched asymptotic analysis, we show how to quantitatively map the sharp…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
A thermodynamically consistent phase-field model is developed to study the non-isothermal grain coalescence during the sintering process, with a potential application to the simulation in unconventional sintering techniques, e.g. spark…
A new approach is developed to derive an analytical form for mobility corrections in phase-field models for pure material solidification. Similar to the thin interface limit approach (Karma and Rappel, 1996) it seeks to remove systematic…
We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In…
Directional solidification occurs in industrial and natural processes, such as freeze-casting, metal processing, biological cryopreservation and freezing of soils. Translational temperature gradient stage allows to control the process of…
We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with…
The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer…
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…
We present a phase-field crystal (PFC) model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…