scispace - formally typeset
Search or ask a question

Showing papers by "Fu Jen Catholic University published in 1976"


Journal ArticleDOI
TL;DR: In this article, a molecular theory of surface tension is developed for a liquid-gas interface of a one component system and the Helmholtz free energy is obtained from a rigorous expansion in powers of derivatives of density ρ and is minimized by the calculus of variations.
Abstract: A molecular theory of surface tension is developed for a liquid–gas interface of a one component system. The Helmholtz free energy, the quantity minimized in the van der Waals approach, is obtained here from a rigorous expansion in powers of derivatives of density ρ and is minimized by the calculus of variations. The coefficient A (ρ) of the term in the square of the density gradient is (kT/6) Fdr r2C (r,ρ), C being the direct correlation function. In the case in which ρ varies in one direction x only, the solution of the Euler–Lagrange differential equation is analyzed in detail. This describes the cases of a single phase and of two coexisting phases and leads to the equal area Maxwell construction. The effect of an external field on the solution is discussed. The Euler–Lagrange differential equation provides a differential statement of Bernoulli’s theorem. In a three dimensional treatment the stress tensor formula is obtained from the corresponding Euler–Lagrange partial differential equation. A (differ...

447 citations


Journal ArticleDOI
TL;DR: The van der Waals theory of surface tensions is generalized to multicomponent systems in this paper, where the local free energy density consists of a "local equilibrium" free energy (i.e., equilibrium free energy of a uniform mixture having species densities equal to the local species density) plus a quadratic form in the gradients of the local densities.
Abstract: The van der Waals theory of surface tensions is generalized to multicomponent systems. The local free energy density consists of a ’’local equilibrium’’ free energy (i.e., equilibrium free energy of a uniform mixture having species densities equal to the local species densities) plus a quadratic form in the gradients of the species densities. The coefficients in this quadratic form depend on the local species densities through the density dependence of the second moment of the local multicomponent direct correlation function. The requirement that the free energy be a minimum yields a system of partial differential equations (one for each component). A particular linear combination of the differential equations is the condition for mechanical equilibrium. It can be interpreted as a microscopic statement of the multicomponent Young–Laplace equation for the pressure variation across a curved interface. For two component systems the theory is a generalization of the treatment of Cahn and Hilliard in that it allows for pressure variations. If the local pressure fluctuations are suppressed, the differential equation for the concentration is very similar to theirs, except that the total density may vary across the interface. Similarly, when the theory is applied to liquid–vapor equilibrium in a binary system, the differential equation for the total number density reduces to that of a single component system when the local chemical potential difference (μ=μ1−μ2) is held constant.

50 citations


Journal ArticleDOI
TL;DR: In this paper, a subcritical viscosity anomaly is reported in binary mixtures of Na 2 O-SiO 2, and the results are discussed qualitatively in terms of inhomogeneities which are present in the system.

2 citations