Liu hard sphere equation of state

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


Z =  \frac{ 1 + \eta + \eta^2 -  \frac{8}{13}\eta^3 - \eta^4 + \frac{1}{2}\eta^5 }{(1-\eta)^3 }.

The conjugate virial coefficient correlation is given by:


B_n =  0.9423n^2 + 1.28846n - 1.84615,  n > 3.

The excess Helmholtz free energy is given by:


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).

The isothermal compressibility is given by:


k_T =  (\eta\frac{ dZ}{d\eta})^{-1} \rho^{-1}.

where


\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 }.
  1. [1]
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