Equations of state for hard sphere mixtures: Difference between revisions

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Mixtures of [[hard sphere model | hard spheres]].
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

Revision as of 15:49, 22 April 2008

Mixtures of hard spheres.

Mansoori, Carnahan, Starling, and Leland

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

Ref. 2

Hansen-Goos and Roth

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

References

  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)