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Related papers: Phase separation for the 2D Cahn-Hilliard equation…

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The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…

Statistical Mechanics · Physics 2009-11-10 E. V. L. de Mello , Otton Teixeira da Silveira Filho

The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…

Numerical Analysis · Mathematics 2026-05-26 Yi Liu , Shuting Gu

In the present work, we address a class of Cahn-Hilliard equations characterized by a singular diffusion term. The problem is a simplified version with constant mobility of the Cahn-Hilliard-de Gennes model of phase separation in binary,…

Analysis of PDEs · Mathematics 2012-06-26 Giulio Schimperna , Irena Pawlow

We prove existence and regularity for the solutions to a Cahn-Hilliard system describing the phenomenon of phase separation for a material contained in a bounded and regular domain. Since the first equation of the system is perturbed by the…

Analysis of PDEs · Mathematics 2020-05-05 Michele Colturato

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…

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

We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of…

Fluid Dynamics · Physics 2017-04-06 Prasad Perlekar , Nairita Pal , Rahul Pandit

We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions. We employ the standard semi-implicit numerical scheme which treats the linear fourth-order dissipation term implicitly and…

Numerical Analysis · Mathematics 2021-06-21 Dong Li , Tao Tang

This paper is concerned with the evolution of the periodic boundary value problem and the mixed boundary value problem for a compressible mixture of binary fluids modeled by the Navier-Stokes-Cahn-Hilliard system in one dimensional space.…

Analysis of PDEs · Mathematics 2018-06-08 Yazhou Chen , Qiaolin He , Ming Mei , Xiaoding Shi

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

Analysis of PDEs · Mathematics 2024-08-15 Helmut Abels , Harald Garcke , Andrea Poiatti

We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the…

Numerical Analysis · Mathematics 2021-11-12 Dong Li

In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock…

Numerical Analysis · Mathematics 2013-12-24 Amanda E. Diegel , Xiaobing H. Feng , Steven M. Wise

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

In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…

Numerical Analysis · Mathematics 2020-11-02 Chen Liu , Deep Ray , Christopher Thiele , Lu Lin , Beatrice Riviere

We study phase separation in thin films using the Navier--Stokes Cahn--Hilliard equations in the lubrication approximation, modeling substrate-film interactions with a van der Waals potential. We investigate the thin-film equations…

Fluid Dynamics · Physics 2007-12-12 Lennon O Naraigh , Jean-Luc Thiffeault

We consider a class of Cahn-Hilliard equation that characterizes phase separation phenomena of binary mixtures in a bounded domain $\Omega \subset \mathbb{R}^d$ $(d\in \{2,3\})$ with non-permeable boundary. The equations in the bulk are…

Analysis of PDEs · Mathematics 2024-06-03 Maoyin Lv , Hao Wu

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

Analysis of PDEs · Mathematics 2021-04-27 Patrik Knopf , Kei Fong Lam , Chun Liu , Stefan Metzger

A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are…

Analysis of PDEs · Mathematics 2023-01-25 Nitu Lakhmara , Hari Shankar Mahato

Differences in activities in colloidal particles are sufficient to drive phase separation between active and passive (or less active) particles, even if they have only excluded volume interactions. In this paper, we study the phase…

Soft Condensed Matter · Physics 2020-05-27 Efe Ilker , Jean-François Joanny

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…

Numerical Analysis · Mathematics 2019-10-21 B. Aymard , U. Vaes , M. Pradas , S. Kalliadasis