Equations of state for hard sphere mixtures: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
No edit summary
 
(4 intermediate revisions by one other user not shown)
Line 1: Line 1:
Mixtures of [[hard sphere model | hard spheres]].
The following are [[equations of state]] for [[mixtures]] of [[hard sphere model | hard spheres]].
==Mansoori,  Carnahan, Starling, and Leland==
==Mansoori,  Carnahan, Starling, and Leland==
Ref. 1
The Mansoori,  Carnahan, Starling, and Leland  equation of state is given by (Ref. 1 Eq. 7):
 
:<math>Z = \frac{(1+\xi + \xi^2)- 3\xi(y_1 + y_2 \xi) -\xi^3y_3 }{(1-\xi)^{3}}</math>
 
where
 
:<math>\xi = \sum_{i=1}^m \frac{\pi}{6} \rho \sigma_i^3 x_i</math>
 
where <math>m</math> is the number of components, <math>\sigma_i</math> is the diameter of the <math>i</math>th component, and <math>x_i</math> is the mole fraction, such that <math>\sum_{i=1}^m  x_i =1</math>.
 
:<math>y_1 = \sum_{j>i=1}^m \Delta_{ij} \frac{\sigma_i + \sigma_j}{\sqrt{\sigma_i \sigma_j}} </math>
 
:<math>y_2 = \sum_{j>i=1}^m \Delta_{ij} \sum_{k=1}^m \left(\frac{\xi_k}{\xi} \right) \frac{\sqrt{\sigma_i \sigma_j}}{\sigma_k} </math>
 
:<math>y_3 =  \left[ \sum_{i=1}^m \left(\frac{\xi_i}{\xi} \right)^{2/3} x_i^{1/3}  \right]^3 </math>
 
:<math>\Delta_{ij}  = \frac{\sqrt{\xi_i \xi_j}}{\xi} \frac{(\sigma_i - \sigma_j)^2}{\sigma_i \sigma_j} \sqrt{x_i x_j}</math>
 
== Santos, Yuste and López De Haro==
== Santos, Yuste and López De Haro==
Ref. 2
Ref. 2
Line 11: Line 28:
#[http://dx.doi.org/10.1063/1.2187491      Hendrik Hansen-Goos and Roland Roth "A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres", Journal of Chemical Physics '''124''' 154506 (2006)]
#[http://dx.doi.org/10.1063/1.2187491      Hendrik Hansen-Goos and Roland Roth "A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres", Journal of Chemical Physics '''124''' 154506 (2006)]
[[category: equations of state]]
[[category: equations of state]]
[[category: mixtures]]

Latest revision as of 22:26, 15 July 2011

The following are equations of state for mixtures of hard spheres.

Mansoori, Carnahan, Starling, and Leland[edit]

The Mansoori, Carnahan, Starling, and Leland equation of state is given by (Ref. 1 Eq. 7):

where

where is the number of components, is the diameter of the th component, and is the mole fraction, such that .

Santos, Yuste and López De Haro[edit]

Ref. 2

Hansen-Goos and Roth[edit]

Ref. 3 Based on the Carnahan-Starling equation of state

References[edit]

  1. G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, Jr. "Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres", Journal of Chemical Physics 54 pp. 1523-1525 (1971)
  2. Andrés Santos; Santos Bravo Yuste; Mariano López De Haro "Equation of state of a multicomponent d-dimensional hard-sphere fluid", Molecular Physics 96 pp. 1-5 (1999)
  3. Hendrik Hansen-Goos and Roland Roth "A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres", Journal of Chemical Physics 124 154506 (2006)