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
Charge transfer in thunderstorms and the surface melting of ice
M.B. Baker,J. G. Dash +1 more
TL;DR: In this paper, a mechanism for the electrification of thunderclouds was proposed, whereby charge separation in ice-hail collisions is a consequence of mass transfer between the particles due to size and growth effects in surface melting.
Journal ArticleDOI
Liquid—Vapor Interface Potential for Water
TL;DR: In this article, the water molecule has been idealized as a point dipole plus point quadrupole, encased in a spherical exclusion envelope, and classical electrostatics has been applied to the determination of the potential field surrounding such a molecule in the wide interfacial region between the liquid and vapor phases, just below the critical temperature.
Journal ArticleDOI
On the 2D Cahn–Hilliard Equation with Inertial Term
TL;DR: In this article, the authors considered an initial and boundary value problem for the Cahn-Hilliard equation in a two-dimensional bounded domain and proved a number of results related to well-posedness and large time behavior of solutions.
Journal ArticleDOI
Energetic variational approaches in modeling vesicle and fluid interactions
TL;DR: In this paper, a hydrodynamic system was established to study vesicle deformations under external flow fields, in the Eulerian formulation, involving the coupling of the incompressible flow system and a phase field equation.
Journal ArticleDOI
Multiscale modeling of solidification: phase-field methods to adaptive mesh refinement
Nikolas Provatas,Michael Greenwood,Badrinarayan P. Athreya,Nigel Goldenfeld,Jonathan A. Dantzig +4 more
TL;DR: New asymptotic analysis methods that enable phase field equations to emulate the sharp interface limit even in the case of quite diffuse phase-field interfaces are discussed, an aspect that greatly reduces computation times.
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.