Related papers: Thin interface limit for phase-field models of sol…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
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,…
Drift-diffusion plasma fluid models are commonly used to simulate electric discharges. Such models can computationally be very efficient if they are combined with explicit time integration. This paper deals with two issues that often arise…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…
We construct gradient structures for free boundary problems with nonlinear elasticity and study the impact of moving contact lines. In this context, we numerically analyze how phase-field models converge to certain sharp-interface limits…
A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…
In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn-type equation, which distinguishes the body from the…
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…
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…
The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models,…
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…
Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits…
In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with…
The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials…
Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter $\epsilon$, representing the interface thickness between the tumorous and non tumorous cells,…
The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the…