Related papers: On a phase field model for solid-liquid phase tran…
We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
A general adsorption model is developed to describe the interactions between near-wall fluid molecules and solid surface. This model serves as a framework for the theoretical modelling of the boundary slip phenomena. Based on this…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean field formalism introduced by Saito for…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
The diffuse interface model of Cahn-Hilliard-van der Waals is often used to study various aspects of multi-phase flows such as droplets coalescence and contact line dynamics. The original model of Cahn-Hilliard-van der Waals uses an…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations challenging, especially when capillary effects are essential for the dynamics of the flow.…
The problem presented involves the development of a new analytical model for the general fluid-solid temperature jump. To the best of our knowledge, there are no analytical models that provide the accurate predictions of the temperature…
In this paper, we consider a diffuse-interface gas-liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng-Robinson equation of state and the temperature-dependent influence parameter instead of the van der…
The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…
Any interface boundary in an equilibrium system of Coulomb particles is accompanied by the existence of a finite difference in the average electrostatic potential through this boundary. The discussed interface potential drop is a…
We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an…
This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile which is divided by…
In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…
Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…
In this work we define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vapor-liquid interface area. A highly accurate density-profile equation is thus derived, which is physically favorable and…