Equations of state for hard sphere mixtures
The following are equations of state for mixtures of hard spheres.
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[edit] Mansoori, Carnahan, Starling, and Leland
The Mansoori, Carnahan, Starling, and Leland equation of state is given by (Ref. 1 Eq. 7):
\[Z = \frac{(1+\xi + \xi^2)- 3\xi(y_1 + y_2 \xi) -\xi^3y_3 }{(1-\xi)^{3}}\]
where
\[\xi = \sum_{i=1}^m \frac{\pi}{6} \rho \sigma_i^3 x_i\]
where \(m\) is the number of components, \(\sigma_i\) is the diameter of the \(i\)th component, and \(x_i\) is the mole fraction, such that \(\sum_{i=1}^m x_i =1\).
\[y_1 = \sum_{j>i=1}^m \Delta_{ij} \frac{\sigma_i + \sigma_j}{\sqrt{\sigma_i \sigma_j}} \]
\[y_2 = \sum_{j>i=1}^m \Delta_{ij} \sum_{k=1}^m \left(\frac{\xi_k}{\xi} \right) \frac{\sqrt{\sigma_i \sigma_j}}{\sigma_k} \]
\[y_3 = \left[ \sum_{i=1}^m \left(\frac{\xi_i}{\xi} \right)^{2/3} x_i^{1/3} \right]^3 \]
\[\Delta_{ij} = \frac{\sqrt{\xi_i \xi_j}}{\xi} \frac{(\sigma_i - \sigma_j)^2}{\sigma_i \sigma_j} \sqrt{x_i x_j}\]
[edit] Santos, Yuste and López De Haro
Ref. 2
[edit] Hansen-Goos and Roth
Ref. 3 Based on the Carnahan-Starling equation of state
[edit] References
- 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)
- 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)
- 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)
