Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
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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.Abstract:
It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find 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 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.read more
Citations
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Journal ArticleDOI
On a generalized Cahn-Hilliard equation with biological applications
TL;DR: In this paper, the authors studied the asymptotic behavior of a generalization of the Cahn-Hilliard equation with a proliferation term and with Neumann boundary conditions, and showed that the relevant, from a biological point of view, solutions converge to $1$ as time goes to infinity.
Journal ArticleDOI
Benchmark problems for numerical implementations of phase field models
TL;DR: Two benchmark problems are proposed that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model.
Journal ArticleDOI
Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations
TL;DR: The idea in [33] is used to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows.
PatentDOI
Biodegradable foams for cell transplantation
TL;DR: A structurally rigid biodegradable foam scaffold useful for cell transplantation is provided and can be loaded with nutrients and/or drugs that elute from the foam during transplant to promote growth of the cells.
Journal ArticleDOI
Accurate contact angle boundary conditions for the Cahn–Hilliard equations
Hyun Geun Lee,Junseok Kim +1 more
TL;DR: In this paper, a novel contact angle boundary formulation based on a characteristic interpolation for the Cahn-Hilliard equation is proposed. But the method is not suitable for the case of a two-phase interface and a solid surface.
References
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Journal ArticleDOI
The Principle of Corresponding States
TL;DR: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of liquid and the triple point temperature and pressure, the heat capacity of liquid, and the surface tension of liquid as mentioned in this paper.
Book ChapterDOI
Zur Theorie des Austauschproblems und der Remanenzerscheinung der Ferromagnetika
TL;DR: The Slatersche Methode as mentioned in this paper is an analog zur Jordan-Kleinschen Theorie in eine nichtlineare Wellengleichung im dreidimensionalen Raum, wobei das Absolutquadrat der Wellenfunktion anschaulich als Spindichte gedeutet werden kann.
Journal ArticleDOI
Die Keimbildung bei der Ausscheidung in metallischen Mischkristallen
TL;DR: In this article, ausscheidung in einem ubersattigten binaren Mischkristall is considered, das die Energie eines Misch-kristalls durch einfache Addition of Nachbarbindungen berechnet werden darf.
Journal ArticleDOI
Domain Structure of Rochelle Salt and K H 2 P O 4
Toshito Mitsui,Jiro Furuichi +1 more
TL;DR: In this paper, it has been shown that rochelle salt in the ferroelectric state consists of many domains and that the domain structure in an annealed crystal is caused by the electrostatic self energy.