## 2 Pore-Structure Characterisation and Analysis of Permeability Data
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Literature/Current**} & \multirow{2}{*}{\begin{tabular}{c} **Foam Porosity \(\upmu\)** \\ **Range, Dp [mm]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pore Diameter** \\ **Range, Dp [mm]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Mean Pore Radii,** \\ **r\({}_{\text{w}}\) [mm]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Mean Openings,** \\ **r\({}_{\text{w}}\) [mm]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Measured/\(\upmu\)CT** \\ **k\({}_{\text{o}}\)/10\({}^{\text{-9}}\) [m\({}^{2}\)]** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Predicted** \\ **k\({}_{\text{o}}\)/10\({}^{\text{-9}}\) [m\({}^{2}\)]** \\ \end{tabular} } \\ \hline \multirow{3}{*}{
\begin{tabular}{c} **[PERSON] and** \\ **[PERSON]** [33]** \\ \end{tabular} } & \multirow{2}{*}{61.2} & \multirow{2}{*}{2.0–2.5 (L-L)} & \multirow{2}{*}{1.125} & \multirow{2}{*}{0.170} & \multirow{2}{*}{1.280} & \multirow{2}{*}{1.14 [\(\upmu\)CT]} & \multirow{2}{*}{1.27} \\ \cline{3-4}  & & & & & & & 1.14 [\(\upmu\)CT] \\ \hline \multirow{3}{*}{Current} & 64.8 & 12.5 vol\%S & 0.384 & 0.137 & 0.65 [\(\upmu\)CT] & 0.98 \\  & 68.2 & 25.0 vol\%S & 0.387 & 0.120 & 1.34 [\(\upmu\)CT] & 1.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Tabular representation of pore-structure-relatedFigure 3 illustrates typical 2D velocity arrow plots for both the bimodal (50% volume in S-S) and monomodal [35,39] structures. These plots illustrate fluid flowing from the inlet to exit regions of these structures, and high intensities of colour scales were observed within the openings of these structures. Streamlined velocity plots were found to be more connected for structures with a larger capillary radius (80 \(\upmu\)m) due to their increased pore contacts, allowing a higher volume of fluid to pass, while flows through low capillary radius structures (10 \(\upmu\)m) are characterised by recirculation of fluid in the \"dead-end\" pores. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Literature/Current** & \begin{tabular}{c} **Foam Porosity \(\epsilon\)** \\ **[-1]** \\ \end{tabular} & \begin{tabular}{c} **Pore Diameter** \\ **Range, Dp [mm]** \\ \end{tabular} & \begin{tabular}{c} **Mean Pore Radii,** \\ **r\({}_{\text{p}}\) [mm]** \\ \end{tabular} & \begin{tabular}{c} **Mean Openings,** \\ **r\({}_{\text{w}}\) [mm]** \\ \end{tabular} & \
\begin{tabular}{c} **Measured/i\({}_{\text{w}}\)CT** \\ **k/10\({}^{-9}\) [m\({}^{2}\)]** \\ \end{tabular} &
\begin{tabular}{c} **Predicted** \\ **k/10\({}^{-9}\) [m\({}^{2}\)]** \\ \end{tabular} \\ \hline \multirow{2}{*}{[PERSON] et al. [35]} & 72.0 & 1.0–1.4 & 0.605 & 0.160 & 3.92 & 3.81 \\  & 75.1 & 2.5–3.15 & 1.385 & 0.350 & 20.40 & 27.92 \\ \hline \multirow{2}{*}{[PERSON] et al. [35,36]} & 70.6 & 2.0–2.5 & 1.105 & 0.323 & 13.50 & 12.31 \\  & 72.6 & 2.0–2.5 & 1.115 & 0.364 & 17.08 & 19.67 \\ \hline \multirow{2}{*}{[PERSON] et al. [3]} & 57.0 & 1.3–1.9 & 0.800 & 0.130 & 0.49 & 0.42 \\  & 60.0 & 1.3–1.9 & 0.800 & 0.155 & 0.81 & 0.83 \\  & 63.0 & 1.3–1.9 & 0.800 & 0.180 & 1.43 & 1.57 \\ \hline \multicolumn{2}{l}{Expt—Current:} & & & & & \\ \hline \multicolumn{2}{l}{NU Spherical} & 67.1 & 1.4–2.0 & 0.85 & 0.13 & 1.39 & 1.58 \\ \multicolumn{2}{l}{Hydrosoft} & 74.6 & 1.4–2.0 & 0.85 & 0.15 & 5.34 & 5.44 \\ \multicolumn{2}{l}{Granulite} & 61.8 & 3.0–4.0 & 1.75 & 0.19 & 1.85 & 1.92 \\ \hline \end{tabular}
\end{table}