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Journal ArticleDOI

Free Energy of a Nonuniform System. I. Interfacial Free Energy

John W. Cahn, +1 more
- 01 Feb 1958 - 
- Vol. 28, Iss: 2, pp 258-267
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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.

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Citations
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Journal ArticleDOI

On a Cahn-Hilliard type phase field system related to tumor growth

TL;DR: For positive viscosity coefficients, the authors in this article proved an existence and uniqueness result and studied the long time behavior of the solution by assuming the nonlinearities to be rather general.
Journal ArticleDOI

On Phase-Separation Models: Asymptotics and Qualitative Properties

TL;DR: In this article, bound state solutions of a class of two-component nonlinear elliptic systems with a large parameter tending to infinity were studied and the profile of bound state solution near the interface was obtained.
Journal ArticleDOI

Linear Stability of Steady States for Thin Film and Cahn-Hilliard Type Equations

TL;DR: In this article, the linear stability of smooth steady states of the evolution equation under both periodic and Neumann boundary conditions was studied under both Neumann and Gaussian boundary conditions, where a = 0 and f = 1.
Journal ArticleDOI

A mass-conserving lattice Boltzmann method with dynamic grid refinement for immiscible two-phase flows

TL;DR: The proposed AMR-LBM is a promising tool for direct numerical simulation of two-phase flows and the Kelvin-Helmholtz instability of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids.
Journal ArticleDOI

Celebrating Soft Matter's 10th Anniversary: Cell division: a source of active stress in cellular monolayers.

TL;DR: It is shown that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by the modeling approach and the fingering instabilities induced by cell division are compared to experimental observations on the expansion of MDCK cell cultures.
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

R. Becker
- 01 Jan 1938 - 
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

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.
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