\section{Enskog solutions with a hard sphere potential}
For comparison with the predictions made by the implementation of the Enskog solutions with a Mie potential, presented in Section \ref{sec:enskog_valid}, the same computations were made with a hard sphere potential. In all cases, the hard sphere diameter was set equal to the Mie potential $\sigma$-parameter. The results using a hard sphere potential are discussed in Section \ref{sec:enskog_valid}, and are collected here for reference.

\begin{figure}[htb!]
    \centering
    \includegraphics[width=.8\textwidth]{appendix/figures/noble_gases_hs.eps}
        \caption{Predicted and measured diffusion coefficients of noble-gas mixtures at $p = \SI{1}{\atm}$, densities supplied to the Enskog solutions were computed using the SAFT-VR Mie EoS, predictions made using a hard sphere potential. Helium mixtures contain 98.5 \% Helium, the remaining mixtures contain 99 \% of the first component. Data reported by Hogervorst.\cite{noble_gas_diffusion}}
    \label{fig:D12_noble_gases_hs}
\end{figure}

\begin{figure}[htb!]
    \centering
    \includegraphics[width=.75\textwidth]{appendix/figures/water_hs.eps}
    \caption{Self-diffusion coefficient of supercritical water at several isotherms. Lines are predictions by the Enskog solutions with a hard sphere potential, marks are data reported by Yoshida et al.\cite{water_self_diffusion}}
    \label{fig:D12_water_hs}
\end{figure}

\begin{figure}[htb!]
    \centering
    \includegraphics[width=.75\textwidth]{appendix/figures/conductivity_hs.pdf}
    \caption{Conductivity of noble gases and noble gas mixtures at varying density. Predictions by the Enskog solutions with a hard sphere potential. All measurements at \SI{35}{\celsius}.$^{(a)}x_{\ce{He}} = 0.2172$, $^{(b)}x_{\ce{He}} = 0.4662$, $^{(c)}x_{\ce{He}} = 0.6823$, $^{(d)}x_{\ce{He}} = 0.7156$, $^{(e)}x_{\ce{Ar}} = 0.4088$, $^{(f)}x_{\ce{Ar}} = 0.7059$. Measurements reported by Assael et al.\cite{noble_gas_conductivity}}
    \label{fig:noble_gas_conductivity_hs}
\end{figure}