http://www.sklogwiki.org/SklogWiki/api.php?action=feedcontributions&feedformat=atom&user=134.157.8.252SklogWiki - User contributions [en]2026-05-01T15:27:57ZUser contributionsMediaWiki 1.41.0http://www.sklogwiki.org/SklogWiki/index.php?title=Equations_of_state_for_hard_sphere_mixtures&diff=11598Equations of state for hard sphere mixtures2011-07-15T21:26:40Z<p>134.157.8.252: /* Mansoori, Carnahan, Starling, and Leland */</p>
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<div>The following are [[equations of state]] for [[mixtures]] of [[hard sphere model | hard spheres]].<br />
==Mansoori, Carnahan, Starling, and Leland==<br />
The Mansoori, Carnahan, Starling, and Leland equation of state is given by (Ref. 1 Eq. 7):<br />
<br />
:<math>Z = \frac{(1+\xi + \xi^2)- 3\xi(y_1 + y_2 \xi) -\xi^3y_3 }{(1-\xi)^{3}}</math><br />
<br />
where <br />
<br />
:<math>\xi = \sum_{i=1}^m \frac{\pi}{6} \rho \sigma_i^3 x_i</math><br />
<br />
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>.<br />
<br />
:<math>y_1 = \sum_{j>i=1}^m \Delta_{ij} \frac{\sigma_i + \sigma_j}{\sqrt{\sigma_i \sigma_j}} </math><br />
<br />
:<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><br />
<br />
:<math>y_3 = \left[ \sum_{i=1}^m \left(\frac{\xi_i}{\xi} \right)^{2/3} x_i^{1/3} \right]^3 </math><br />
<br />
:<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><br />
<br />
== Santos, Yuste and López De Haro==<br />
Ref. 2<br />
==Hansen-Goos and Roth==<br />
Ref. 3 Based on the [[Carnahan-Starling equation of state]]<br />
==References==<br />
#[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)]<br />
#[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)]<br />
#[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)]<br />
[[category: equations of state]]<br />
[[category: mixtures]]</div>134.157.8.252