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The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

We perform computer simulations of a Cahn-Hilliard model of phase separation which has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function which is order…

Soft Condensed Matter · Physics 2009-10-31 Rajeev Ahluwalia

We consider a diffuse interface model describing a ternary system constituted by a conductive diblock copolymer and a homopolymer acting as solvent. The resulting dynamics is modeled by two Cahn--Hilliard--Oono equations for the copolymer…

Analysis of PDEs · Mathematics 2024-11-07 Helmut Abels , Andrea Di Primio , Harald Garcke

We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary…

Materials Science · Physics 2009-11-10 R. Folch , M. Plapp

We consider the sharp interface limit of a coupled Stokes/Cahn\textendash Hilliard system in a two dimensional, bounded and smooth domain, i.e., we consider the limiting behavior of solutions when a parameter $\epsilon>0$ corresponding to…

Analysis of PDEs · Mathematics 2020-04-02 Helmut Abels , Andreas Marquardt

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…

Analysis of PDEs · Mathematics 2016-09-16 Christian Heinemann , Christiane Kraus

We study both diffuse and sharp liquid-vapor interfaces. The equilibrium equation of fluids is derived by using the principle of virtual work in a domain including the interfaces. For diffuse interfaces, the surface tension coefficient…

Mathematical Physics · Physics 2026-05-27 Sergey L. Gavrilyuk , Henri Gouin

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of…

Analysis of PDEs · Mathematics 2017-02-03 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and…

Analysis of PDEs · Mathematics 2022-07-20 Yu Feng , Yuanyuan Feng , Gautam Iyer , Jean-Luc Thiffeault

We introduce a new phase-field model which allows for simulation of incoherent solid/solid transformations. Contrary to previous models which impose coherency at the interface, the zero shear-stress condition characteristic of incoherent…

Materials Science · Physics 2007-05-23 Jerome Paret

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…

Analysis of PDEs · Mathematics 2023-07-03 Mathis Kelm , Carina Bringedal , Bernd Flemisch

In this paper, we study the slow patterns of multilayer dislocation dynamics modeled by a multiscale parabolic equation in the half-plane coupled with a dynamic boundary condition on the interface. We focus on the influence of bulk dynamics…

Analysis of PDEs · Mathematics 2025-02-11 Yuan Gao , Stefania Patrizi

The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…

Cell Behavior · Quantitative Biology 2023-06-30 Sebastian Aland , Claudia Wohlgemuth

We study the mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyze…

Fluid Dynamics · Physics 2018-02-14 Juan J. Hidalgo , Marco Dentz

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…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Analysis of PDEs · Mathematics 2024-10-31 Rômulo Damasclin Chaves dos Santos , Jorge Henrique de Oliveira Sales

We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…

Analysis of PDEs · Mathematics 2025-12-30 Andrea Giorgini , Jingning He , Hao Wu

We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…

Analysis of PDEs · Mathematics 2024-02-08 Maoyin Lv , Hao Wu

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

We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…

Numerical Analysis · Mathematics 2026-05-07 Ziqian Li , Enrique Zuazua