Vega equation of state for hard ellipsoids: Difference between revisions

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The '''Vega''' equation of state for hard (biaxial) [[Hard ellipsoids |ellipsoids]] is given by (Ref. 1 Eq. 20):
The '''Vega''' [[equations of state |equation of state]] for an isotropic fluid of hard (biaxial) [[Hard ellipsoid model |ellipsoids]] is given by
<ref>[http://dx.doi.org/10.1080/002689797169934 Carlos Vega "Virial coefficients and equation of state of hard ellipsoids", Molecular Physics '''92''' pp. 651-665 (1997)]</ref>
(Eq. 20):


:<math>
:<math>
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where <math>Z</math> is the [[compressibility factor]] and <math>y</math> is the [[volume fraction]], given by
where <math>Z</math> is the [[compressibility factor]] and <math>y</math> is the [[volume fraction]], given by
<math>y= \rho V</math> where <math>\rho</math> is the [[number density]].
<math>y= \rho V</math> where <math>\rho</math> is the [[number density]].
The virial coefficients are given by the fits
The [[Virial equation of state |virial coefficients]] are given by the fits


:<math>B_3^* =  10 + 13.094756 \alpha'  - 2.073909\tau' + 4.096689 \alpha'^2  
:<math>B_3^* =  10 + 13.094756 \alpha'  - 2.073909\tau' + 4.096689 \alpha'^2  
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</math>
</math>


where


:<math>B_n^*= B_n/V^{n-1}</math>,


where <math>B_n^*= B_n/V^{n-1}</math>,


:<math>\tau' = \frac{4 \pi R^2}{S} -1,</math>
:<math>\tau' = \frac{4 \pi R^2}{S} -1,</math>
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where <math>V</math> is
where <math>V</math> is
the volume, <math>S</math>, the surface area,  and <math>R</math> the mean radius of curvature.
the volume, <math>S</math>, the surface area,  and <math>R</math> the mean radius of curvature. These can be calculated
 
using this [[Mathematica]] notebook file for
For  <math>B_2</math> see [[B_2 for any hard convex body]].
[http://ender.quim.ucm.es/SR_B2_B3_ellipsoids.nb calculating the surface area and mean radius of curvature of an ellipsoid].
For  <math>B_2</math> see the page "[[Second virial coefficient]]".
==References==
==References==
#[http://dx.doi.org/10.1080/002689797169934 Carlos Vega "Virial coefficients and equation of state of hard ellipsoids", Molecular Physics '''92''' pp. 651-665 (1997)]
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1016/j.fluid.2007.03.026 Carl McBride and Enrique Lomba  "Hard biaxial ellipsoids revisited: Numerical results", Fluid Phase Equilibria '''255''' pp. 37-45  (2007)]
[[category: equations of state]]
[[category: virial coefficients]]
{{numeric}}

Latest revision as of 12:28, 19 February 2010

The Vega equation of state for an isotropic fluid of hard (biaxial) ellipsoids is given by [1] (Eq. 20):

where is the compressibility factor and is the volume fraction, given by where is the number density. The virial coefficients are given by the fits


and

where

,


and

where is the volume, , the surface area, and the mean radius of curvature. These can be calculated using this Mathematica notebook file for calculating the surface area and mean radius of curvature of an ellipsoid. For see the page "Second virial coefficient".

References[edit]

Related reading

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