Related papers: Diffusion in a two Phases System: Application to I…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
Two-phase flow in porous media is a ubiquitous phenomenon that has been studied for well over a century. However, we still lack a successful theory that predicts flow on a macroscopic length scale (the so-called Darcy scale) on the basis of…
This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories…
The glass transition can simply be viewed as the point at which the viscosity of a structurally disordered liquid reaches 10^{13} Poise [1]. This definition is operational but it sidesteps fundamental controversies about the glass: Is the…
We construct a mean-field formulation of the thermodynamics of ion solvation in immiscible polar binary mixtures. Assuming an equilibrium planar interface separating two semi-infinite regions of different constant dielectric medium, we…
An analytical solution based on a diffuse interface model is presented for an isothermal evaporation problem under sub-saturation pressure. The macroscopic equations are derived from the free-energy method, widely recognized in the lattice…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…
The analytical solutions of the equations describing impurity diffusion due to migration of nonequilibrium impurity interstitials were obtained for the impurity redistribution during ion implantation at elevated temperatures and for…
A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step…
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first…
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…
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…
The available sites for ions in a typical disordered ionic conductor are determined. For this purpose we devised a straightforward algorithm which via cluster analysis identifies these sites from long time ionic trajectories below the glass…
Glass-to-glass and liquid-to-liquid phase transitions are observed in bulk and confined water, with or without applied pressure. They result from the competition of two liquid phases separated by an enthalpy difference depending on…
Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly-interacting environment, leading to the formation of discrete layers of charges at interfaces. Here, we propose a continuum theory that captures the…
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…
An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…