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We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal…

Analysis of PDEs · Mathematics 2020-10-14 Helmut Abels , Josef Weber

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

The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between both fluids. Spherical particles with a given…

Fluid Dynamics · Physics 2020-10-28 Michael Eigenbrod , Steffen Hardt

When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a…

Fluid Dynamics · Physics 2026-01-09 Andreu F. Gallen , Joan Muñoz Biosca , Mario Castro , Aurora Hernández-Machado

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu

This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…

Fluid Dynamics · Physics 2024-11-05 Joris Labarbe

This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take…

Analysis of PDEs · Mathematics 2016-09-21 David Lannes

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually…

Soft Condensed Matter · Physics 2015-03-20 Timm Krüger , Stefan Frijters , Florian Günther , Badr Kaoui , Jens Harting

This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…

Computational Physics · Physics 2022-03-15 Tim Wallis , Philip Barton , Nikolaos Nikiforakis

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

We investigate a novel Marangoni-induced instability that arises exclusively in diffuse fluid interfaces, absent in classical sharp-interface models. Using a validated phase-field Navier-Stokes-Allen-Cahn framework, we linearize the…

Fluid Dynamics · Physics 2026-01-14 Xiangwei Li , Dongdong Wan , Haohao Hao , Christian Diddens , Mengqi Zhang , Huanshu Tan

In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible…

Analysis of PDEs · Mathematics 2021-06-09 Martin Kalousek , Sourav Mitra , Anja Schlömerkemper

The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea interface at geophysically relevant Reynolds numbers. It…

We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel $\mathbb{T} \times \mathbb{R}$. Under a simple spectral…

Analysis of PDEs · Mathematics 2018-04-24 Emmanuel Grenier , Toan T. Nguyen , Frédéric Rousset , Avy Soffer

We study a diffuse interface model describing the motion of two viscous fluids driven by the surface tension in a Hele-Shaw cell. The full system consists of the Cahn-Hilliard equation coupled with the Darcy's law. We address the physically…

Analysis of PDEs · Mathematics 2019-03-12 Andrea Giorgini

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to…

Fluid Dynamics · Physics 2026-03-11 Rahul Bhattacharjee , Henning Struchtrup , Anirudh Singh Rana

We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle…

Analysis of PDEs · Mathematics 2024-05-07 Eduardo García-Juárez , Po-Chun Kuo , Yoichiro Mori

With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the non-linear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model…

Classical Physics · Physics 2018-11-14 Claire Lestringant , Basile Audoly

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

Analysis of PDEs · Mathematics 2023-10-25 Andrea Giorgini , Patrik Knopf

Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…

Fluid Dynamics · Physics 2025-07-15 Zhong-Han Xue , Jacques Magnaudet , Jie Zhang