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We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…

Analysis of PDEs · Mathematics 2023-01-23 Abramo Agosti , Pierluigi Colli , Harald Garcke , Elisabetta Rocca

We consider a class of nonlocal Cahn-Hilliard equations in a bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, subject to a nonlocal kinetic rate dependent dynamic boundary condition. This diffuse interface model describes phase…

Analysis of PDEs · Mathematics 2024-12-11 Maoyin Lv , Hao Wu

This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…

Materials Science · Physics 2020-05-11 Arne Claus Hansen-Dörr , Franz Dammaß , René de Borst , Markus Kästner

In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of…

Mathematical Physics · Physics 2017-05-24 Shuonan Wu , Jinchao Xu

A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…

Analysis of PDEs · Mathematics 2011-02-22 Pierluigi Colli , Sergio Frigeri , Maurizio Grasselli

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…

Soft Condensed Matter · Physics 2009-10-31 K. R. Elder , Martin Grant , Nikolas Provatas , J. M. Kosterlitz

We study the existence of weak solutions and the corresponding sharp interface limit of an anisotropic Cahn-Hilliard equation with disparate mobility, i.e., the mobility is degenerate in one of the two pure phases, making the diffusion in…

Analysis of PDEs · Mathematics 2025-09-08 Charles Elbar , Andrea Poiatti

This paper deals with a conserved phase field system that couples the energy balance equation with a Cahn--Hilliard type system including temperature and the inertial term for the order parameter. In the case without inertial term, the…

Analysis of PDEs · Mathematics 2025-05-28 Pierluigi Colli , Shunsuke Kurima

We study a nonlocal variant of a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. The model is described by a Navier--Stokes--Cahn--Hilliard system that…

Analysis of PDEs · Mathematics 2025-12-15 Kin Shing Chan , Kei Fong Lam

In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn-Hilliard equations. The main challenge in solving the system numerically is…

Numerical Analysis · Mathematics 2017-03-20 Xiaofeng Yang

We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In…

Materials Science · Physics 2007-05-23 Seong Gyoon Kim , Won Tae Kim , Toshio Suzuki

We consider a diffuse interface model describing a ternary system constituted by a conductive diblock copolymer and a homopolymer acting as solvent. The resulting dynamics is modeled by two Cahn--Hilliard--Oono equations for the copolymer…

Analysis of PDEs · Mathematics 2024-11-07 Helmut Abels , Andrea Di Primio , Harald Garcke

An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…

Analysis of PDEs · Mathematics 2012-02-24 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Jürgen Sprekels

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.…

Analysis of PDEs · Mathematics 2014-11-13 Wolfgang Dreyer , Jan Giesselmann , Christiane Kraus

Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or…

Numerical Analysis · Mathematics 2015-11-10 Christian Kahle

The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link interacting particle systems and continuous descriptions, has…

Analysis of PDEs · Mathematics 2024-07-08 Charles Elbar , Jakub Skrzeczkowski

The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH) equation. In this paper, based on the exponential…

Numerical Analysis · Mathematics 2023-07-27 Xiaoqing Meng , Aijie Cheng , Zhengguang Liu

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

Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato

As popular approximations to sharp-interface models, the Cahn-Hilliard type phase-field models are usually used to simulate interface dynamics with volume conservation. However, the convergence rate of the volume enclosed by the interface…

Mathematical Physics · Physics 2025-07-25 Zeyu Zhou , Wei Jiang , Tiezheng Qian , Zhen Zhang