Liu hard disk equation of state

The Liu equation of state for hard disks (2-dimensional hard spheres) is given by Eq. 1 of

$Z=\frac{1+{\eta }^2/8-{\eta }^4/10}{(1-\eta {)}^2}$

$Z=\frac{1+{\eta }^2/8+{\eta }^4/18-{\eta }^4/21}{(1-\eta {)}^2}$

where the packing fraction is given by $\eta =\pi \rho {\sigma }^2/4$ where $\sigma$ is the diameter of the disks.