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| The '''Vega''' equation of state for hard (biaxial) [[Hard ellipsoids |ellipsoids]] is given by (Ref. 1 Eq. 20): | | The '''Vega''' equation of state for an isotropic fluid of hard (biaxial) [[Hard ellipsoids |ellipsoids]] is given by (Ref. 1 Eq. 20): |
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Revision as of 14:07, 30 March 2007
The Vega equation of state for an isotropic fluid of hard (biaxial) ellipsoids is given by (Ref. 1 Eq. 20):
![{\displaystyle Z=1+B_{2}^{*}y+B_{3}^{*}y^{2}+B_{4}^{*}y^{3}+B_{5}^{*}y^{4}+{\frac {B_{2}}{4}}\left({\frac {1+y+y^{2}-y^{3}}{(1-y)^{3}}}-1-4y-10y^{2}-18.3648y^{3}-28.2245y^{4}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd0233ae27caa85fa8091e121acf91e31a233963)
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
![{\displaystyle B_{3}^{*}=10+13.094756\alpha '-2.073909\tau '+4.096689\alpha '^{2}+2.325342\tau '^{2}-5.791266\alpha '\tau ',}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffc72ab17f321543a4468ce3b5e53e1b4f597760)
![{\displaystyle B_{4}^{*}=18.3648+27.714434\alpha '-10.2046\tau '+11.142963\alpha '^{2}+8.634491\tau '^{2}-28.279451\alpha '\tau '-17.190946\alpha '^{2}\tau '+24.188979\alpha '\tau '^{2}+0.74674\alpha '^{3}-9.455150\tau '^{3},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8aa5b011e7023c824746770346c647c4c7b42a4f)
and
![{\displaystyle B_{5}^{*}=28.2245+21.288105\alpha '+4.525788\tau '+36.032793\alpha '^{2}+59.0098\tau '^{2}-118.407497\alpha '\tau '+24.164622\alpha '^{2}\tau '+139.766174\alpha '\tau '^{2}-50.490244\alpha '^{3}-120.995139\tau '^{3}+12.624655\alpha '^{3}\tau ',}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0489bfa324b5488af30278d3f45cedbf72a96768)
where
,
![{\displaystyle \tau '={\frac {4\pi R^{2}}{S}}-1,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a137c9f88f699c27141c9456157564365dba9d70)
and
![{\displaystyle \alpha '={\frac {RS}{3V}}-1.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89a1587b897cb2535939f3e53763dafd9b8c43f0)
where
is
the volume,
, the surface area, and
the mean radius of curvature.
For
see B_2 for any hard convex body.
References
- Carlos Vega "Virial coefficients and equation of state of hard ellipsoids", Molecular Physics 92 pp. 651-665 (1997)