The role of degenerate mobilities in Cahn‐Hilliard models
Abstract: The present work provides an insight into the role of degenerate mobilities in phase field models and in particular their influence on the evolution of the interface. The equation of interest is the Cahn‐Hilliard equation (in two space dimensions) with a polynomial double well free energy and different order‐parameter dependent, degenerate mobilities. According to the preliminary work [1], considering an anisotropic version of the equation, the asymptotic sharp interface limit subtly dependents on the degeneracy of the mobility. Whilst a quadratic degenerate mobility leads to a sharp interface model where bulk diffusion is present at the same asymptotic order as surface diffusion, a bi‐quadratic degenerate mobility leads to a sharp interface model where bulk diffusion is subdominant. The present study continues the preliminary work and shows that the type of the degeneracy has a qualitative impact on the evolution: Considering numerical simulations of the dewetting process of a thin solid film with four‐fold anisotropic surface energy, the evolution with bi‐quadratic degenerate mobility turns out to be more effective for film pinch‐off than with quadratic degenerate mobility. An extension to the isotropic Cahn‐Hilliard equation ensures that the characteristic difference in the pinch‐off behavior is in fact mobility‐dependent.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
The role of degenerate mobilities in Cahn‐Hilliard models ; volume:19 ; number:1 ; year:2019 ; extent:2
Proceedings in applied mathematics and mechanics ; 19, Heft 1 (2019) (gesamt 2)
- Creator
-
Dziwnik, Marion
- DOI
-
10.1002/pamm.201900396
- URN
-
urn:nbn:de:101:1-2022072207291392592499
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
15.08.2025, 7:28 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Dziwnik, Marion
Other Objects (12)
Degenerate Nucleation in the Cahn-Hilliard-Cook Model
Degenerate nucleation in the Cahn-Hilliard-Cook model
From Vlasov Equation to Degenerate Nonlocal Cahn-Hilliard Equation
A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow
Energy identity for the incompressible Cahn–Hilliard/Navier–Stokes system with non–degenerate mobility
Parameter Identification in Cahn-Hilliard Systems
Nonisothermal Cahn–Hilliard Navier–Stokes system
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
Phase separation in stochastic Cahn-Hilliard models
Fast iterative solvers for Cahn-Hilliard problems
Computational methods for Cahn-Hilliard variational inequalities
Degenerate Nucleation in the Cahn-Hilliard-Cook Model
Degenerate nucleation in the Cahn-Hilliard-Cook model
From Vlasov Equation to Degenerate Nonlocal Cahn-Hilliard Equation
A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow
Energy identity for the incompressible Cahn–Hilliard/Navier–Stokes system with non–degenerate mobility
Parameter Identification in Cahn-Hilliard Systems
Nonisothermal Cahn–Hilliard Navier–Stokes system
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
Phase separation in stochastic Cahn-Hilliard models
Fast iterative solvers for Cahn-Hilliard problems
Computational methods for Cahn-Hilliard variational inequalities
Degenerate Nucleation in the Cahn-Hilliard-Cook Model
Degenerate nucleation in the Cahn-Hilliard-Cook model
From Vlasov Equation to Degenerate Nonlocal Cahn-Hilliard Equation
A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow
Energy identity for the incompressible Cahn–Hilliard/Navier–Stokes system with non–degenerate mobility
Parameter Identification in Cahn-Hilliard Systems
Nonisothermal Cahn–Hilliard Navier–Stokes system
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems
Phase separation in stochastic Cahn-Hilliard models
Fast iterative solvers for Cahn-Hilliard problems