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Related papers: Degenerate Mobilities in Phase Field Models are In…

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The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary…

Analysis of PDEs · Mathematics 2020-10-20 Harald Garcke , Patrik Knopf

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Analysis of PDEs · Mathematics 2025-10-10 Monica Conti , Stefania Gatti , Andrea Giorgini , Giulio Schimperna

Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which…

Statistical Mechanics · Physics 2024-03-15 Kristian Blom , Noah Ziethen , David Zwicker , Aljaž Godec

We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only…

Analysis of PDEs · Mathematics 2019-03-07 Clément Cancès , Daniel Matthes , Flore Nabet

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling…

Condensed Matter · Physics 2009-10-30 Sanjay Puri , Alan Bray , Joel Lebowitz

Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or…

Numerical Analysis · Mathematics 2015-11-10 Christian Kahle

There are various methods for modeling phase transformations in materials science, including general classes of phase-field methods and reactive diffusion methodologies, which most importantly differ in their treatment of interface energy.…

The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…

Analysis of PDEs · Mathematics 2020-07-03 Virginie Ehrlacher , Greta Marino , Jan-Frederik Pietschmann

We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of…

Materials Science · Physics 2017-06-28 G. Boussinot , Efim A. Brener , C. Hueter , R. Spatschek

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

Analysis of PDEs · Mathematics 2024-08-15 Helmut Abels , Harald Garcke , Andrea Poiatti

In the present work, we address a class of Cahn-Hilliard equations characterized by a singular diffusion term. The problem is a simplified version with constant mobility of the Cahn-Hilliard-de Gennes model of phase separation in binary,…

Analysis of PDEs · Mathematics 2012-06-26 Giulio Schimperna , Irena Pawlow

As popular approximations to sharp-interface models, the Cahn-Hilliard type phase-field models are usually used to simulate interface dynamics with volume conservation. However, the convergence rate of the volume enclosed by the interface…

Mathematical Physics · Physics 2025-07-25 Zeyu Zhou , Wei Jiang , Tiezheng Qian , Zhen Zhang

In this work, we propose a new model for flow through deformable porous media, where the solid material has two phases with distinct material properties. The two phases of the porous material follow a Cahn-Hilliard type evolution, with…

Mathematical Physics · Physics 2021-09-09 Erlend Storvik , Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…

Numerical Analysis · Mathematics 2018-10-30 Oliver R. A. Dunbar , Kei Fong Lam , Bjorn Stinner

The Cahn-Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues. We are interested in quantifying the pressure jump at the interface in the case of incompressible flows. To do so, we…

Analysis of PDEs · Mathematics 2022-11-03 Charles Elbar , Benoît Perthame , Jakub Skrzeczkowski

The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple…

Mesoscale and Nanoscale Physics · Physics 2017-07-19 Raphael Schiedung , Reza Darvishi Kamachali , Ingo Steinbach , Fathollah Varnik

A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…

Materials Science · Physics 2008-09-04 Lynda Amirouche , Mathis Plapp

A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…

Analysis of PDEs · Mathematics 2012-01-18 Sylvie Benzoni-Gavage , Laurent Chupin , Didier Jamet , Julien Vovelle

The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by…

Materials Science · Physics 2015-06-03 Matteo Nicoli , Mathis Plapp , Hervé Henry

It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to…

Other Condensed Matter · Physics 2007-05-23 Klaus Kassner