Journal ArticleDOI
Phase separation in confined geometries: Solving the Cahn–Hilliard equation with generic boundary conditions
Rainer Kenzler,Frank Eurich,Philipp Maass,Bernd Rinn,Johannes Schropp,Erich Bohl,Wolfgang Dieterich +6 more
TLDR
In this article, the authors apply implicit numerical methods to solve the Cahn-Hilliard equation for confined systems, where the boundary conditions for hard walls are derived from physical principles.About:
This article is published in Computer Physics Communications.The article was published on 2001-01-15. It has received 116 citations till now. The article focuses on the topics: Cahn–Hilliard equation & Partial differential equation.read more
Citations
More filters
The cahn-hilliard equation
TL;DR: In this article, a phenomenological description of phase separation in spatially homogeneous systems can be obtained by energy arguments, and the free energy of a spatially heterogeneous system is given by the Gibbs free energy.
Journal ArticleDOI
The Cahn-Hilliard Equation with Logarithmic Potentials
TL;DR: In this paper, the authors discuss recent issues related with the Cahn-Hilliard equation in phase separation with the thermodynamically relevant logarithmic potentials; in particular, they are interested in the wellposedness and the study of the asymptotic behavior of the solutions (and more precisely the existence of finite-dimensional attractors).
Journal ArticleDOI
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
TL;DR: The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered in this paper, and well-posedness results are proved for the wellposedness of the Cahn Hilliard equation.
Journal ArticleDOI
Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions
Alain Miranville,Sergey Zelik +1 more
TL;DR: In this article, the Cahn-Hilliard equation with dynamic boundary conditions is interpreted as a parabolic equation on the boundary and by considering a regularized problem, the existence and uniqueness of solutions are obtained by the Leray-Schauder principle.
Journal ArticleDOI
Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
TL;DR: In this article, a solution of the Cahn-Hilliard equation and associated Caginalp problem with dynamic boundary condition is considered and it is shown that under some conditions on the potential it converges, as t ∞, to a stationary solution.
References
More filters
Book
Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Journal ArticleDOI
Theory of Dynamic Critical Phenomena
TL;DR: The renormalization group theory has been applied to a variety of dynamic critical phenomena, such as the phase separation of a symmetric binary fluid as mentioned in this paper, and it has been shown that it can explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions.
Journal ArticleDOI