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Related papers: On a diffuse interface model for diblock copolymer…

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The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding…

Numerical Analysis · Mathematics 2024-03-11 Amlan K. Barua , Ray Chew , Shuwang Li , John Lowengrub , Andreas Münch , Barbara Wagner

We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…

Analysis of PDEs · Mathematics 2011-04-01 Helmut Abels

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation…

Fluid Dynamics · Physics 2013-03-25 Uwe Thiele , Santiago Madruga , Lubor Frastia

We introduce a diffuse interface model for the phenomenon of electrowetting on dielectric and present an analysis of the arising system of equations. Moreover, we study discretization techniques for the problem. The model takes into account…

Numerical Analysis · Mathematics 2011-12-30 Ricardo H. Nochetto , Abner J. Salgado , Shawn W. Walker

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…

Soft Condensed Matter · Physics 2016-08-31 R. M. L. Evans , W. C. K. Poon

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2024-08-27 Helmut Abels , Harald Garcke , Jonas Haselböck

We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…

Analysis of PDEs · Mathematics 2026-04-30 Mingwen Fei , Xiang Fei , Yadong Liu , Hao Wu

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…

Analysis of PDEs · Mathematics 2015-06-03 Helmut Abels , Daniel Depner , Harald Garcke

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…

Materials Science · Physics 2023-04-03 Yue Li , Lei Wang , Junjie Li , Jincheng Wang , Zhijun Wang

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…

Analysis of PDEs · Mathematics 2023-02-15 Harald Garcke , Patrik Knopf , Robert Nürnberg , Quan Zhao

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…

Numerical Analysis · Mathematics 2022-06-15 Yuzhe Qin , Huaxiong Huang , Yi Zhu , Chun Liu , Shixin Xu

This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…

Analysis of PDEs · Mathematics 2024-11-15 Yadong Liu , Dennis Trautwein

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…

Fluid Dynamics · Physics 2010-11-03 Helmut Abels , Harald Garcke , Günther Grün

In this paper, we analytically investigate multi-component Cahn-Hilliard and Allen-Cahn systems which are coupled with elasticity and uni-directional damage processes. The free energy of the system is of the form…

Analysis of PDEs · Mathematics 2015-02-23 Christian Heinemann , Christiane Kraus

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

Analysis of PDEs · Mathematics 2015-06-01 Sergio Frigeri

We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…

Analysis of PDEs · Mathematics 2024-07-23 Clément Cancès , Jean Cauvin-Vila , Claire Chainais-Hillairet , Virginie Ehrlacher

This paper is concerned with a diffuse interface model called as Navier-Stokes/Cahn-Hilliard system. This model is usually used to describe the motion of immiscible two-phase flow with diffusion interface. For the periodic boundary value…

Analysis of PDEs · Mathematics 2021-09-06 Yazhou Chen , Hakho Hong , Xiaoding Shi

In this paper, we study a hydrodynamic phase-field system modeling the deformation of functionalized membranes in incompressible viscous fluids. The governing PDE system consists of the Navier-Stokes equations coupled with a convective…

Analysis of PDEs · Mathematics 2022-06-22 Hao Wu , Yuchen Yang

Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded domain. One phase is assumed to be magnetic, the other phase…

Analysis of PDEs · Mathematics 2025-07-08 Samuel Lanthaler , Franziska Weber