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We present a technique to perform interface-resolved simulations of complex breakup dynamics in two-phase flows using the Cahn-Hilliard Navier-Stokes equations. The method dynamically decreases the interface thickness parameter in relevant…

We consider a system which consists of a Cahn-Hilliard equation coupled with a Cahn-Hilliard-Oono equation in a bounded domain of $\mathbb{R}^d$, $d = 2, 3$. This system accounts for macrophase and microphase separation in a polymer mixture…

Analysis of PDEs · Mathematics 2022-03-25 Andrea Di Primio , Maurizio Grasselli

Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…

Soft Condensed Matter · Physics 2015-05-20 G. Gonnella , A. Lamura , A. Piscitelli , A. Tiribocchi

We consider a diffuse interface model that describes the macro- and micro-phase separation processes of a polymer mixture. The resulting system consists of a Cahn-Hilliard equation and a Cahn-Hilliard-Oono type equation endowed with the…

Analysis of PDEs · Mathematics 2024-05-01 Bohan Ouyang

The filtration membranes are often elaborated through a phase separation process where a polymer rich phase and a polymer poor phase spontaneously form through spinodal decomposition. One process that is still not well understood from a…

The study of viscous thin film flow has led to the development of highly nonlinear partial differential equations that model how the evolution of the film height is affected by different forces. We investigate a model of interaction between…

Fluid Dynamics · Physics 2024-07-25 Steven A Kedda , Michael C Dallaston , Scott W McCue

We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents…

Analysis of PDEs · Mathematics 2026-03-12 Patrik Knopf , Andrea Poiatti , Jonas Stange , Sema Yayla

The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…

Analysis of PDEs · Mathematics 2023-07-20 Christoph Helmer , Ansgar Jüngel

In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn-Hilliard system,…

Analysis of PDEs · Mathematics 2018-03-13 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In capillary-driven fluid dynamics, simple departures from equilibrium offer the chance to quantitatively model the resulting relaxations. These dynamics in turn provide insight on both practical and fundamental aspects of thin-film…

This paper is concerned with a diffuse interface model called as Navier-Stokes/Cahn-Hilliard system. This model is usually used to describe the motion of immiscible two-phase flow with diffusion interface. For the periodic boundary value…

Analysis of PDEs · Mathematics 2021-09-06 Yazhou Chen , Hakho Hong , Xiaoding Shi

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

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

Under the condition of partial surface wettability, thin liquid films can be destabilized by small perturbations and rupture into droplets. As successfully predicted by the thin film equation (TFE), the rupture dynamics are dictated by the…

Fluid Dynamics · Physics 2024-02-14 Francesca Pelusi , Marcello Sega , Jens Harting

In this paper, we discuss a particular model arising from sinking of a rigid solid into a thin film of fluid, i.e. a fluid contained between two solid surfaces and part of the fluid surface is in contact with the air. The fluid is governed…

Analysis of PDEs · Mathematics 2024-10-30 Amrita Ghosh , Juan J. L. Velázquez

The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g., the process through which a smooth surface becomes…

Fluid Dynamics · Physics 2021-09-17 Yixin Zhang , James E. Sprittles , Duncan A. Lockerby

The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped…

Soft Condensed Matter · Physics 2015-06-11 Joshua D. McGraw , Thomas Salez , Oliver Bäumchen , Elie Raphaël , Kari Dalnoki-Veress

The van der Waals forces across a very thin liquid layer (nanofilm) in contact with a plane solid wall make the liquid nonhomogeneous. The dynamics of such flat liquid nanofilms is studied in isothermal case. The Navier-Stokes equations are…

Classical Physics · Physics 2008-09-23 Henri Gouin , Sergey Gavrilyuk

The Cahn-Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme is investigated. In place of…

Numerical Analysis · Mathematics 2017-02-28 Prerna Gera , David Salac

Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with…

Mathematical Physics · Physics 2017-01-05 Hangjie Ji , Thomas Witelski