Related papers: Sharp interface limits of phase-field models
We perform a rigorous examination of the sharp interface limit of a coupled Navier-Stokes and mass-conserving Allen-Cahn system in a two-dimensional, bounded, and smooth domain as the parameter $\varepsilon > 0$, representing the thickness…
We develop a phase-field model for evaporation from a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases…
We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Particular emphasis is put on Stefan problems, and their quasi-static variants, with…
Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…
We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the…
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…
We consider the problem of minimizing the Willmore energy connected surfaces with prescribed surface area which are confined to a finite container. To this end, we approximate the surface by a phase field function $u$ taking values close to…
Consider the Allen-Cahn equation on the $d$-dimensional torus, $d=2,3$, in the sharp interface limit. As it is well known, the limiting dynamics is described by the motion by mean curvature of the interface between the two stable phases.…
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…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field…
This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi's…
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…
We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes.…
We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the…