Liu hard sphere equation of state: Difference between revisions

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: <math>
: <math>
A^{ex} = \frac{ A - A^{id}}{Nk_b}= \frac{ 188\eta - 126\eta^2 - 13\eta^4 }{52(1-\eta)^2} - \frac{5}{13} ln(1-\eta).
A^{ex} = \frac{ A - A^{id}}{Nk_b}= \frac{ 188\eta - 126\eta^2 - 13\eta^4 }{52(1-\eta)^2} - \frac{5}{13} ln(1-\eta).
</math>
The isothermal compressibility is given by:
: <math>
k_T =  (\eta\frac{ dZ}{d\eta})^{-1} \rho^{-1}.
</math>
where
: <math>
\frac{ dZ}{d\eta} =  \frac{ 4 + 4\eta - \frac {11}{13} \eta^2 -  \frac{52}{13}\eta^3 + \frac {7}{2}\eta^4 - \eta^5 }{(1-\eta)^4 }.
</math>
</math>

Revision as of 00:21, 9 November 2020

Hongqin Liu proposed a correction to the C-S EOS which improved accuracy by almost two order of magnitude [1]:

The conjugate virial coefficient correlation is given by:

The excess Helmholtz free energy is given by:

The isothermal compressibility is given by:

where