Editing Vega equation of state for hard ellipsoids

The '''Vega''' equation of state for hard (biaxial) [[Hard ellipsoids |ellipsoids]] is given by (Ref. 1 Eq. 20):

:<math>
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)
</math>
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]].
The virial coefficients are given by the fits

:<math>B_3^* =  10 + 13.094756 \alpha'  - 2.073909\tau' + 4.096689 \alpha'^2 
        +  2.325342\tau'^2 - 5.791266\alpha' \tau',</math>


:<math>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,</math>

and

:<math>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',
</math>



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

:<math>\tau' = \frac{4 \pi R^2}{S} -1,</math>

and

:<math>\alpha' = \frac{RS}{3V}-1.</math>

where <math>V</math> is
the volume, <math>S</math>, the surface area,  and <math>R</math> the mean radius of curvature.

For  <math>B_2</math> see [[B_2 for any hard convex body]].
==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)]
@@ Line 1: / Line 1: @@
-The '''Vega''' [[equations of state |equation of state]] for an isotropic fluid of hard (biaxial) [[Hard ellipsoid model |ellipsoids]] is given by
+The '''Vega''' equation of state for hard (biaxial) [[Hard ellipsoids |ellipsoids]] is given by (Ref. 1 Eq. 20):
-<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>
@@ Line 10: / Line 8: @@
 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]].
-The [[Virial equation of state |virial coefficients]] are given by the fits
+The virial coefficients are given by the fits
 :<math>B_3^* =  10 + 13.094756 \alpha'  - 2.073909\tau' + 4.096689 \alpha'^2
@@ Line 29: / Line 27: @@
 </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>
@@ Line 41: / Line 38: @@
 where <math>V</math> is
-the volume, <math>S</math>, the surface area,  and <math>R</math> the mean radius of curvature. These can be calculated
+the volume, <math>S</math>, the surface area,  and <math>R</math> the mean radius of curvature.
-using this [[Mathematica]] notebook file for
-[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 [[B_2 for any hard convex body]].
-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)]
-'''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}}