Application of the kirkwoodbuff solution formalism and the hard sphere expansion method with the modified mean density approximation to predict solubility of solutes in supercritical fluids

1997 ◽  
Vol 14 (3) ◽  
pp. 184-191 ◽  
Author(s):  
Yong Jung Kwon ◽  
Joon Yong Lee ◽  
Ki-Chang Kim
Keyword(s):  
Supercritical Fluids ◽  
Hard Sphere ◽  
Expansion Method ◽  
Density Approximation ◽  
Hard Sphere Expansion

Mean density approximation and hard sphere expansion theory: A review

1987 ◽  
Vol 37 ◽  
pp. 1-27 ◽  
Author(s):  
Li-Jen Chen ◽  
James F. Ely ◽  
G. Ali Mansoori
Keyword(s):  
Hard Sphere ◽  
Density Approximation ◽  
Expansion Theory ◽  
Hard Sphere Expansion

Discrete versus continuum relaxation modes of a hard sphere gas

1984 ◽  
Vol 62 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Bernard Shizgal
Keyword(s):  
Discrete Spectrum ◽  
Cross Section ◽  
Cross Sections ◽  
Hard Sphere ◽  
Expansion Method ◽  
Gas Mixture ◽  
Discrete Ordinate Method ◽  
Discrete Ordinate ◽  
Relaxation Modes ◽  
The Continuum

The nature of the discrete spectrum of the linear Boltzmann collision operators for a simple gas and for a gas mixture is studied numerically with a discrete ordinate method. The discrete ordinate method is found to give a large number of discrete eigenvalues whereas the expansion method with Burnett functions yields only a few converged eigenvalues. The hard sphere cross section is used in the present paper although the methods employed are readily applicable to other cross sections. The approach of the eigenvalues to the continuum boundary is studied in detail and a comparison with a previous asymptotic Wentzell–Kramers–Brillouin (WKB) analysis yields excellent agreement.

SEGREGATION OF FLUIDIZED BINARY HARD-SPHERE SYSTEMS UNDER GRAVITY

2005 ◽  
Vol 19 (04) ◽  
pp. 763-774
Author(s):  
SOON-CHUL KIM
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Local Density ◽  
Measure Theory ◽  
Density Approximation ◽  
Brazil Nut ◽  
Density Oscillation ◽  
Analytic Expression ◽  
Dynamics Simulations ◽  
Fundamental Measure Theory

We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.

Modified weighted density approximation for binary hard-sphere solid mixtures

1998 ◽  
Vol 58 (4) ◽  
pp. 5171-5174 ◽  
Author(s):  
Guiomar Ruiz ◽  
Carlos F. Tejero
Keyword(s):  
Hard Sphere ◽  
Density Approximation ◽  
Weighted Density ◽  
Weighted Density Approximation

scholarly journals Correlation of Solubilities of High Boiling Compounds in Supercritical Fluids Using Perturbed-Hard-Sphere Equation of State.

1991 ◽  
Vol 4 (2) ◽  
pp. 7-14
Author(s):  
Kenji MISHIMA ◽  
Shigeki AOKI ◽  
Masanori NAGATANI ◽  
Masayuki WATANABE ◽  
Chikashi NISHINO ◽  
...  
Keyword(s):  
Equation Of State ◽  
Supercritical Fluids ◽  
Hard Sphere ◽  
Sphere Equation

The mean density approximation for hard sphere Yukawa systems

1997 ◽  
Vol 91 (2) ◽  
pp. 377-379
Author(s):  
I. L. McLAUGHLIN
Keyword(s):  
Hard Sphere ◽  
Density Approximation ◽  
The Mean
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