Related papers: Boundary Dynamics of Sweeping Interface
A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…
We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a diffuse-interface concept. Precisely, we suggest a compressible Navier--Stokes--Allen--Cahn model. Basic properties of the model…
The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high performance computing systems and/or accelerators. However, these systems…
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation…
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…
There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping,…
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 derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The…
We simulate the mesoscopic dynamics of droplets formed by phase separated fluids at nanometer scales where thermal fluctuations are significant. Both spherical droplets fully immersed in a second fluid and sessile droplets which are also in…
Atomistic computer simulations are applied to investigate the atomic structure, thermal stability, and diffusion processes in Al-Si interphase boundaries as a prototype of metal-ceramic interfaces in composite materials. Some of the most…
We study the pinning phase transition for discrete surface dynamics in random environments. A renormalization procedure is devised to prove that the interface moves with positive velocity under a finite size condition. This condition is…
We consider approximations of the Stefan-type condition by imbalances of volume closely around the inner interface and study convergence of the solutions of the corresponding semilinear stochastic moving boundary problems. After a…
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions.…
Diffusion through semipermeable interfaces has a wide range of applications, ranging from molecular transport through biological membranes to reverse osmosis for water purification using artificial membranes. At the single-particle level,…