Liu hard sphere equation of state: Difference between revisions

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Hongqin Liu proposed a correction to the C-S EOS which improved accuracy by almost two order of magnitude <ref>[https://arxiv.org/abs/2010.14357]</ref>:
Hongqin Liu proposed a correction to the [[Carnahan-Starling equation of state]] which improved accuracy by almost two orders of magnitude <ref>[https://arxiv.org/abs/2010.14357 Hongqin Liu "Carnahan Starling type equations of state for stable hard disk and hard sphere fluids", arXiv:2010.14357]</ref>:


: <math>
: <math>
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</math>
</math>


The conjugate virial coefficient correlation is given by:
The conjugate [[Virial equation of state | virial coefficient]] correlation is given by:


: <math>
: <math>
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</math>
</math>


The excess Helmholtz free energy is given by:
The excess [[Helmholtz energy function]] is given by:


: <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>
</math>


The isothermal compressibility is given by:
The isothermal [[compressibility]] is given by:


: <math>
: <math>
k_T =  (\eta\frac{ dZ}{d\eta})^{-1} \rho^{-1}.
k_T =  (\eta\frac{ dZ}{d\eta} + Z)^{-1} \rho^{-1}.
</math>
</math>


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\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 }.
\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>
== References ==
<references/>
[[Category: Equations of state]]
[[category: hard sphere]]

Latest revision as of 11:21, 10 November 2020

Hongqin Liu proposed a correction to the Carnahan-Starling equation of state which improved accuracy by almost two orders of magnitude [1]:

The conjugate virial coefficient correlation is given by:

The excess Helmholtz energy function is given by:

The isothermal compressibility is given by:

where

References[edit]

  1. ↑ Hongqin Liu "Carnahan Starling type equations of state for stable hard disk and hard sphere fluids", arXiv:2010.14357
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