Equations of state for hard sphere mixtures: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
(New page: Mixtures of hard spheres. ==References== #[http://dx.doi.org/10.1063/1.1675048 G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, Jr. "Equilibriu...)
 
 
(5 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==
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==
Ref. 2
==Hansen-Goos and  Roth==
Ref. 3 Based on the [[Carnahan-Starling equation of state]]
==References==
==References==
#[http://dx.doi.org/10.1063/1.1675048    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)]
#[http://dx.doi.org/10.1063/1.1675048    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)]
#[http://dx.doi.org/10.1080/002689799165936 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)]
#[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)