English
Related papers

Related papers: Approximation of surface diffusion flow: a second …

200 papers

We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only…

Analysis of PDEs · Mathematics 2019-03-07 Clément Cancès , Daniel Matthes , Flore Nabet

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

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

In this work, we propose a new model for flow through deformable porous media, where the solid material has two phases with distinct material properties. The two phases of the porous material follow a Cahn-Hilliard type evolution, with…

Mathematical Physics · Physics 2021-09-09 Erlend Storvik , Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a…

Fluid Dynamics · Physics 2017-08-02 Luca Dedè , Harald Garcke , Kei Fong Lam

We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the…

Numerical Analysis · Mathematics 2023-08-03 Elena Bachini , Veit Krause , Ingo Nitschke , Axel Voigt

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

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…

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

We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for…

Analysis of PDEs · Mathematics 2025-09-15 Pierluigi Colli , Patrik Knopf , Giulio Schimperna , Andrea Signori

We consider the Cahn-Hilliard equation, which models phase separation in binary fluids, on the two-dimen\-sional torus in the presence of advection by a given background shear flow, satisfying certain conditions and of sufficiently large…

Analysis of PDEs · Mathematics 2026-05-12 Yu Feng , Yuanyuan Feng , Anna L. Mazzucato , Xiaoqian Xu

In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two…

Numerical Analysis · Mathematics 2018-04-13 Xiaofeng Yang

This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…

Numerical Analysis · Mathematics 2022-09-20 Eric Bonnetier , Elie Bretin , Simon Masnou

In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…

Pattern Formation and Solitons · Physics 2015-06-26 Rodica Borcia , Domnic Merkt , Michael Bestehorn

In this paper, we present a new computational framework to approximate a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the…

Numerical Analysis · Mathematics 2024-12-02 Daniel Acosta-Soba , Francisco Guillén-González , J. Rafael Rodríguez-Galván , Jin Wang

A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard energy with a singular (logarithmic) potential short time…

Analysis of PDEs · Mathematics 2025-11-18 Helmut Abels , Harald Garcke , Andrea Poiatti

This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of…

Analysis of PDEs · Mathematics 2025-02-20 Harald Garcke , Patrik Knopf , Andrea Signori

The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…

Analysis of PDEs · Mathematics 2020-07-03 Virginie Ehrlacher , Greta Marino , Jan-Frederik Pietschmann

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…

Analysis of PDEs · Mathematics 2011-03-24 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Juergen Sprekels

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