Related papers: A novel phase-field model for $N$-phase problems: …
In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of…
The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase…
We present a two-phase field model and a hybrid particle-phase field model to simulate dilute colloidal sedimentation and flotation near a liquid-gas interface (or fluid-fluid interface in general). Both models are coupled to the…
Multiphase flow in porous media occurs in several disciplines including petroleum reservoir engineering, petroleum systems' analysis, and CO$_2$ sequestration. While simulations often use a fully implicit discretization to increase the time…
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
We propose a new class of phase field models coupled to viscoelasticity with large deformations, obtained from a diffuse interface mixture model composed by a phase with elastic properties and a liquid phase. The model is formulated in the…
Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are…
This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by Chapman-Enskog techniques the corresponding macroscopic equations. The singular interface…
The preferential formation of one solid over the other, as it precipitates out from the melt at specific temperatures, is often explained by invoking a competition between thermodynamic and kinetic control. A quantitative theory, however,…
In this paper, a lattice Boltzmann model is proposed to simulate solid-liquid phase change phenomena in multiphase systems. The model couples the thermal properties of the solidification front with the dynamics of the liquid droplet…
Mixtures of nematic liquid crystals and isotropic fluids display a diverse range of phase behaviors, arising from the coupling between orientational order and concentration fluctuations. In this review, we introduce a simplified…
Renewable energy sources such as wind and solar have received much attention in recent years and large amount of renewable generation is being integrated to the electricity networks. A fundamental challenge in power system operation is to…
In this work, we first propose a diffuse-interface model for the freezing processes of three-phase flows in complex geometries, and the core of the model to intergratge the Navier-Stokes equations for fluid flows, a modified phase-field…
In this study, we present the phase-space analysis of Quintessence models specified by the choice of two potentials, namely the Recliner potential and what we call the broken exponential-law potential, which is a new proposal. Using a…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only…
This paper presents a modeling framework to describe the driving mechanisms of cyclic failure in brittle and ductile materials, including cyclic plasticity and fatigue crack growth. A variational model is devised using the energetic…
We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element…
Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…