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The Cahn-Hilliard equation is one of the most common models to describe phase separation processes in mixtures of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Numerical Analysis · Mathematics 2023-01-23 Stefan Metzger

The alternative approach to the displacement of gas/liquid equilibrium is developed on the basis of the Clapeyron equation. The phase transition in the system with well-established properties is taken as a reference process to search for…

Chemical Physics · Physics 2010-06-15 Vladimir Kh. Dobruskin

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

We consider a phase-field model for the incompressible flow of two immiscible fluids. This model extends widespread models for two fluid phases by including a third, solid phase, which can evolve due to e.g. precipitation and dissolution.…

Analysis of PDEs · Mathematics 2022-05-18 Lars von Wolff , Iuliu Sorin Pop

Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field…

Computational Physics · Physics 2019-10-23 Henning Bonart , Christian Kahle , Jens-Uwe Repke

A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a…

patt-sol · Physics 2025-02-25 Morton E. Gurtin , Debra Polignone , Jorge Vinals

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling…

Condensed Matter · Physics 2009-10-30 Sanjay Puri , Alan Bray , Joel Lebowitz

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…

Soft Condensed Matter · Physics 2015-05-20 G. Gonnella , A. Lamura , A. Piscitelli , A. Tiribocchi

In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are based on suitable combinations of existing schemes for the…

Numerical Analysis · Mathematics 2021-04-07 Mattia Martini , Giacomo Enrico Sodini

Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial…

Soft Condensed Matter · Physics 2020-06-26 Martin Meere , Giuseppe Pontrelli , Sean McGinty

This paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the entropy balance and equilibrium equations for the microforces. The related system is highly nonlinear and admits singular potentials…

Analysis of PDEs · Mathematics 2019-01-30 Pierluigi Colli , Shunsuke Kurima

A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…

Analysis of PDEs · Mathematics 2019-06-14 Gianluca Favre , Giulio Schimperna

We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for…

Analysis of PDEs · Mathematics 2026-01-22 Peter Howard , Adam Larios , Quyuan Lin

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where…

We present a numerical scheme for solving a sixth-order Cahn-Hilliard type equation that captures the dynamics of phase transitions in a ternary mixture consisting of two immiscible fluids and a surface active molecule that is amphiphilic.…

Numerical Analysis · Mathematics 2025-04-01 Natasha S. Sharma , Giordano Tierra

We study a system describing the dynamics of a two-phase flow of incompressible viscous fluids influenced by the convective heat transfer of Caginalp-type. The separation of the fluids is expressed by the order parameter which is of diffuse…

Analysis of PDEs · Mathematics 2023-08-15 Šárka Nečasová , John Sebastian H. Simon

Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced…

Mathematical Physics · Physics 2013-11-22 Markus Schmuck , Marc Pradas , Gregorios A. Pavliotis , Serafim Kalliadasis

This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard equations, both of which consist of equations for the (total)…

Analysis of PDEs · Mathematics 2013-11-04 Heinrich Freistuhler , Matthias Kotschote

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation. We…

Soft Condensed Matter · Physics 2015-05-14 Lennon O Naraigh , Jean-Luc Thiffeault