Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
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TLDR
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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Fluid-fluid phase separation in colloid-polymer mixtures studied with small angle light scattering and light microscopy
TL;DR: In this paper, the phase separation kinetics of this fluid-fluid phase separation is studied for different compositions of the colloid-polymer mixtures, and at several degrees of supersaturation, with small angle light scattering and with light microscopy.
Journal ArticleDOI
Protein-Polysaccharide Interactions to Alter Texture
TL;DR: This review focuses on the physical interactions between proteins and polysaccharides that form the basis for the microstructure and texture of semisolid and soft-solid foods.
Journal ArticleDOI
The meshless local collocation method for solving multi-dimensional Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations
Mehdi Dehghan,Mostafa Abbaszadeh +1 more
TL;DR: In this article, a linear combination of shape functions of local radial basis functions collocation method and moving Kriging interpolation technique is proposed for solving problems that have shock (advection problems) or the discontinuous initial condition.
Journal ArticleDOI
Liquid–vapor phase transition: Thermomechanical theory, entropy stable numerical formulation, and boiling simulations
TL;DR: In this article, a new continuum mechanics modeling framework for liquid-vapor flows, with particular focus on the van der Waals fluid, was developed, by invoking microforce theory, the Coleman-Noll procedure was generalized to derive consistent constitutive relations in the presence of nonlocal effects.
Journal ArticleDOI
The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property
TL;DR: In this article, the authors considered the nonlocal Cahn-Hilliard equation with singular potential and constant mobility, and established the validity of the strict separation property in dimension two.
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.