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Related papers: A diffuse interface model for two-phase incompress…

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We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…

Analysis of PDEs · Mathematics 2014-06-09 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

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

We consider the Cahn--Hilliard/Navier--Stokes system with non-degenerate mobility in the space-periodic case, describing the flow of two viscous immiscible and incompressible Newtonian fluids with matched densities. We identify sufficient…

Analysis of PDEs · Mathematics 2024-08-06 Stefanos Georgiadis

We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…

Analysis of PDEs · Mathematics 2024-01-15 Helmut Abels , Harald Garcke , Andrea Poiatti

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

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…

Analysis of PDEs · Mathematics 2020-07-28 Zhilei Liang , Dehua 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

The motion of two contiguous incompressible and viscous fluids is described within the diffuse interface theory by the so-called Model H. The system consists of the Navier-Stokes equations, which are coupled with the Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2024-12-10 Andrea Giorgini , Alain Miranville , Roger Temam

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…

Analysis of PDEs · Mathematics 2026-01-13 Andrea Giorgini , Jingning He , Hao Wu

We investigate a non-isothermal diffuse-interface model that describes the dynamics of two-phase incompressible flows with thermo-induced Marangoni effect. The governing PDE system consists of the Navier--Stokes equations coupled with…

Analysis of PDEs · Mathematics 2023-07-28 Hao Wu

In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…

Analysis of PDEs · Mathematics 2025-05-13 Helmut Abels , Andrea Poiatti

We study an initial-boundary value problem for the incompressible Navier-Stokes-Cahn-Hilliard system with non-constant density proposed by Abels, Garcke and Gr\"{u}n in 2012. This model arises in the diffuse interface theory for binary…

Analysis of PDEs · Mathematics 2023-02-21 Helmut Abels , Harald Garcke , Andrea Giorgini

In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid…

Analysis of PDEs · Mathematics 2025-03-12 Yinghua Li , Yuanxiang Yan , Xijun Yin

We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…

Analysis of PDEs · Mathematics 2015-05-13 Helmut Abels , Matthias Röger

This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2020-04-22 Martin Kalousek , Sourav Mitra , Anja Schlömerkemper

We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid-fluid-solid contact lines. Allowing for motion of such contact…

Numerical Analysis · Mathematics 2024-07-09 T. H. B. Demont , S. K. F. Stoter , C. Diddens , E. H. van Brummelen

In this paper we derive a class of thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. The class of mixture models is fully compatible with the continuum theory of mixtures. The resulting…

Fluid Dynamics · Physics 2023-02-21 M. ten Eikelder , K. van der Zee , D. Schillinger

A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…

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

This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface…

Fluid Dynamics · Physics 2026-03-02 Chunhua Zhang , Peiyao Liu , Cheng Peng , Lian-Ping Wang , Zhaoli Guo

We consider a model for the evolution of a mixture of two incompressible and partially immiscible Newtonian fluids in two dimensional bounded domain. More precisely, we address the well-known model H consisting of the Navier-Stokes equation…

Analysis of PDEs · Mathematics 2013-04-04 Stefano Bosia , Stefania Gatti