Related papers: Solving Free Boundary Problems in Alloy Solidifica…
A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation…
We establish a quantitative homogenization result for an interface moving through a field of sufficiently sparse but possibly impenetrable random obstacles. From a physical viewpoint, such problems arise e.g. in the context of the motion of…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
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…
In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary,…
Understanding rapid solidification behavior at velocities relevant to additive manufacturing (AM) is critical to controlling microstructure selection. Although in-situ visualization of solidification dynamics is now possible, systematic…
In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven…
We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…
Frequently, the design of physicochemical processes requires screening of large numbers of alternative designs with complex geometries. These geometries may result in conformal meshes which introduce stability issues, significant…
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…
Fluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many applications, fluid flow is non-parallel to the fluid-porous…
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the…
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…
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using…
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…