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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

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

The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…

Mathematical Physics · Physics 2009-03-12 Tian Ma , Shouhong Wang

In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion type dynamics is derived on the basis…

Materials Science · Physics 2016-02-03 Gyula I. Toth , Mojdeh Zarifi , Bjorn Kvamme

In the present work, we address a class of Cahn-Hilliard equations characterized by a nonlinear diffusive dynamics and possibly containing an additional sixth order term. This model describes the separation properties of oil-water mixtures,…

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

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…

The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced to model interactions of the materials with…

Analysis of PDEs · Mathematics 2021-10-12 Patrik Knopf , Andrea Signori

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

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

Analysis of PDEs · Mathematics 2021-06-03 Pierluigi Colli , Takeshi Fukao , Luca Scarpa

The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…

Analysis of PDEs · Mathematics 2022-06-22 Hao Wu

We show short-time well-posedness of 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 2026-05-01 Helmut Abels , Jonas Haselböck

The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…

Fluid Dynamics · Physics 2014-12-23 Lennon O'Naraigh , Selma Shun , Aurore Naso

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…

Numerical Analysis · Mathematics 2018-10-30 Oliver R. A. Dunbar , Kei Fong Lam , Bjorn Stinner

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching…

Fluid Dynamics · Physics 2025-04-01 M. F. P. ten Eikelder

We analyze a coupled Cahn-Hilliard-Forchheimer system featuring concentration-dependent mobility, mass source and convective transport. The velocity field is governed by a generalized quasi-incompressible Forchheimer equation with…

Numerical Analysis · Mathematics 2026-02-05 Aaron Brunk , Marvin Fritz

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase field approach is…

Analysis of PDEs · Mathematics 2019-12-20 Christian Rohde , Lars von Wolff

In this paper we discuss a family of viscous Cahn-Hilliard equations with a non-smooth viscosity term. This system may be viewed as an approximation of a "forward-backward" parabolic equation. The resulting problem is highly nonlinear,…

Analysis of PDEs · Mathematics 2018-10-03 Elena Bonetti , Pierluigi Colli , Luca Scarpa , Giuseppe Tomassetti

We study a diffuse-interface model for a binary incompressible mixture in a periodically perforated porous medium, described by a time-dependent Navier-Stokes-Cahn-Hilliard (NSCH) system posed on the pore domain…

Analysis of PDEs · Mathematics 2026-03-17 Amartya Chakrabortty , Haradhan Dutta , Hari Shankar Mahato

The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…

Analysis of PDEs · Mathematics 2025-05-09 Helmut Abels , Harald Garcke , Julia Wittmann

The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss…

Fluid Dynamics · Physics 2017-10-26 Lennon O Naraigh , Jean-Luc Thiffeault