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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

Gas-liquid-solid multiphase systems are ubiquitous in engineering applications, e.g. inkjet printing, spray drying and coating. Developing a numerical framework for modelling these multiphase systems is of great significance. An improved,…

Fluid Dynamics · Physics 2023-07-19 Huihuang Xia , Marc Kamlah

Thermal fluctuations cause perturbations of fluid-fluid interfaces and highly nonlinear hydrodynamics in multiphase flows. In this work, we develop a novel multiphase smoothed dissipative particle dynamics model. This model accounts for…

We develop a sharp-interface model for solid-state dewetting of double-bubble thin films using an energy variational approach based on a newly proposed interfacial energy. This model characterizes the dynamic evolution of interfaces in…

Numerical Analysis · Mathematics 2025-03-06 Meng Li , Nan Wang , Ruofan Zhao , Chunjie Zhou

In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The con- tribution is two-fold. First it participates in the…

We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…

In this work, we extend the discrete unified gas-kinetic scheme (DUGKS) [Guo et al., Phys. Rev. E 88, 033305 (2013)] to continue two-phase flows. In the framework of DUGKS, two kinetic model equations are used to solve the…

Computational Physics · Physics 2018-10-02 Chunhua Zhang , Kang Yang , Zhaoli Guo

We construct a phase field model including hydrodynamics and elasticity in one-component systems. It can be used to investigate solid-liquid and liquid-liquid phase transitions. Upon first-order phase transition, a velocity field is induced…

Soft Condensed Matter · Physics 2015-03-13 Kyohei Takae , Akira Onuki

We develop a long-wavelength theory for the linear stability of a flat interface between an active nematic and an isotropic fluid. Starting from a diffuse-interface Cahn--Hilliard--Landau--de Gennes description coupled to Brinkman-screened…

Soft Condensed Matter · Physics 2026-05-22 Rodrigo C. V. Coelho , Mykola Tasinkevych , Margarida M. Telo da Gama

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

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB…

Computational Physics · Physics 2013-05-07 Q. Li , K. H. Luo , X. J. Li

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

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

The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…

Analysis of PDEs · Mathematics 2022-10-26 Chao Zhang , Lifeng Wang

We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable…

Analysis of PDEs · Mathematics 2025-09-23 Dawei Wu , Baoming Shi , Yucen Han , Pingwen Zhang , Apala Majumdar , Lei Zhang

Surfactants reside at the interface of two-phase flows and significantly influence the flow dynamics. Numerical simulations are essential for a comprehensive understanding of such surfactant-laden flows and require a method that can…

Fluid Dynamics · Physics 2026-05-20 Shu Yamashita , Shintaro Matsushita , Tetsuya Suekane

We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids…

Fluid Dynamics · Physics 2018-03-14 Suchuan Dong

An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume…

Computational Physics · Physics 2021-03-15 Francisco J. Carrillo , Ian C. Bourg , Cyprien Soulaine

We present an effective method for simulating wall-bounded multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids with different densities, viscosities and pairwise surface tensions. The N-phase physical…

Fluid Dynamics · Physics 2017-04-05 S. Dong

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao