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An analog of the continuum Widom-Rowlinson model is introduced and studied. Its two-component version is a gas of point particles of types 0 and 1 placed in $\mathds{R}^d$, in which like particles do not interact and unlike particles…
In the turbulent boundary layer of multicomponent fluid mixtures, the species-specific mass flux is determined by the combination of turbulent-diffusiophoretic diffusion and diffusion due to gradients in supplementary fields (e.g.…
In this paper we propose an extension of the Cahn method to binary mixtures and study the problem of wetting near a two-phase critical point without any assumption on the form of intermolecular potentials. A comparison between Cahn's method…
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to determine the collisional moments of second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms…
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: i) atoms attract each other by van der Waals forces that generate a liquid-gas…
A van der Waals (vdW) density functional was implemented in the mixed basis approach previously developed for studying two dimensional systems, in which the vdW interaction plays an important role. The basis functions here are taken to be…
Several aspects of the theory of the coexistence of phases and equilibrium forms are discussed. In section 1, the problem is studied from the point of view of thermodynamics. In section 2, the statistical mechanical theory is introduced. We…
We propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second…
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…
We consider the van der Waals' free energy functional, with a scaling small parameter epsilon, in the plane domain given by the first quadrant, and inhomogeneous Dirichlet boundary conditions. The boundary data are chosen in such a way that…
Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate…
We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…
A simple two dimensional model of a phase growing on a substrate is introduced. The model is characterized by an adsorption rate q, and a desorption rate p. It exhibits a wetting transition which may be viewed as an unbinding transition of…
Fluid mixture models are essential for describing a wide range of physical phenomena, including wave dynamics and spinodal decomposition. However, there is a lack of consensus in the modeling of compressible mixtures, with limited…
A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a…
We propose a new class of phase field models coupled to viscoelasticity with large deformations, obtained from a diffuse interface mixture model composed by a phase with elastic properties and a liquid phase. The model is formulated in the…
The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary…
The first principles approaches, density functional theory (DFT) and quantum Monte Carlo, have been used to examine the balance between van der Waals (vdW) forces and hydrogen (H) bonding in ambient and high pressure phases of ice. At…
To describe highly heterogeneous systems using the Cahn-Hilliard equation, the standard form of the thermodynamic potential with a constant coefficient in the gradient term and a polynomial of the fourth degree may not be sufficient. The…