2022: SklogWiki celebrates 15 years on-line

Vega equation of state for hard ellipsoids

From SklogWiki
Jump to: navigation, search

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

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)

where Z is the compressibility factor and y is the volume fraction, given by y= \rho V where \rho is the number density. The virial coefficients are given by the fits

B_3^* =  10 + 13.094756 \alpha'  - 2.073909\tau' + 4.096689 \alpha'^2 
        +  2.325342\tau'^2 - 5.791266\alpha' \tau',

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,


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',


B_n^*= B_n/V^{n-1},

\tau' = \frac{4 \pi R^2}{S} -1,


\alpha' = \frac{RS}{3V}-1.

where V is the volume, S, the surface area, and R 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 B_2 see the page "Second virial coefficient".


Related reading

40px-Stop hand nuvola.svg.png This page contains numerical values and/or equations. If you intend to use ANY of the numbers or equations found in SklogWiki in any way, you MUST take them from the original published article or book, and cite the relevant source accordingly.