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In this paper, the sharp interface limit for the compressible non-isentropic Navier-Stokes/Allen-Cahn system is derived by the method of matched asymptotic expansion. We show that the leading order problem satisfies the compressible…

Analysis of PDEs · Mathematics 2021-02-09 Chen Yazhou , He Qiaolin , Shi Xiaoding , Wang Xiaoping

We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2014-04-16 Sergio Frigeri , Maurizio Grasselli , Elisabetta Rocca

We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the…

Numerical Analysis · Mathematics 2015-10-09 E. H. van Brummelen , M. Shokrpour-Roudbari , G. J. van Zwieten

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 article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…

Numerical Analysis · Mathematics 2021-12-09 Yali Gao , Daozhi Han , Xiaoming He , Ulrich Rüde

From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping…

Soft Condensed Matter · Physics 2009-11-07 Tiezheng Qian , Xiao-Ping Wang , Ping Sheng

Static droplets serve as fundamental benchmarks for interface-resolved simulations of two-phase flows. However, their accurate representation in phase-field models remains elusive due to persistent numerical artifacts. This work rigorously…

Fluid Dynamics · Physics 2025-08-22 Jun Lai

We consider a model of a two phase flow proposed by Anderson, McFadden and Wheeler taking into account possible thermal fluctuations. The mathematical model consists of the compressible Navier-Stokes system coupled with the Cahn-Hilliard…

Analysis of PDEs · Mathematics 2018-04-17 Eduard Feireisl , Madalina Petcu

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 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

In this paper, we propose an improved phase field model for interface capturing in simulating two-phase incompressible flows. The model incorporates a second-order diffusion term, which utilizes a nonlinear coefficient to assess the degree…

Fluid Dynamics · Physics 2025-01-20 Jing-Wei Chen , Chun-Yu Zhang , Hao-Ran Liu , Hang Ding

Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced…

Mathematical Physics · Physics 2013-11-22 Markus Schmuck , Marc Pradas , Gregorios A. Pavliotis , Serafim Kalliadasis

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…

Numerical Analysis · Mathematics 2023-09-27 Yerbol Palzhanov , Alexander Zhiliakov , Annalisa Quaini , Maxim Olshanskii

Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…

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

We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…

Analysis of PDEs · Mathematics 2026-05-26 Lingxi Chen , Hao Wu

Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of…

Computational Physics · Physics 2020-03-02 Guangpu Zhu , Jisheng Kou , Shuyu Sun , Jun Yao , Aifen Li

We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth energy potential. We establish the existence of optimal solutions and present two…

Optimization and Control · Mathematics 2019-07-10 Carmen Gräßle , Michael Hintermüller , Michael Hinze , Tobias Keil

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field…

Computational Physics · Physics 2019-10-23 Henning Bonart , Christian Kahle , Jens-Uwe Repke

We present a two-phase field model and a hybrid particle-phase field model to simulate dilute colloidal sedimentation and flotation near a liquid-gas interface (or fluid-fluid interface in general). Both models are coupled to the…

Soft Condensed Matter · Physics 2024-10-01 Alexandra J. Hardy , Abdallah Daddi-Moussa-Ider , Elsen Tjhung