## 2 Materials and Methods
Key parameters are shown below in Table 2. The Kozeny-Carman equation was used to define the permeability of the electrodes as a function of porosity. Data published by [PERSON] et al. [31] for carbon felt electrodes at various states of compression was used for electrical conductivity and porosity parameters, as shown below in Table 3.  
Electrochemical properties used are summarised in Table 4 for reference. A Bruggeman correction was applied to diffusion coefficients and electrical conductivity parameters. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Outlet pressure & \(P\) & 0 & Pa \\ Temperature & T & 293.15 & K \\ Current density & \(i\) & 160 & mA cm\({}^{-2}\) \\ ate of Charge & SOC & 90 & - \\ Domain width & w & \(4\times 10^{-3}\) & m \\ Current collector thickness & h & \(1.0\times 10^{-3}\) & m \\ Membrane thickness & \(d\) & \(0.1\times 10^{-3}\) & m \\ \hline \end{tabular}
\end{table} 
Table 1: General operating parameters. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Dynamic viscosity (negative electrolyte) & \(\mu_{-}\) & 0.0025 & Pa s \\ Dynamic viscosity (positive electrolyte) & \(\mu_{+}\) & 0.005 & Pa s \\ Density (negative electrolyte) & \(\rho_{-}\) & 1300 & kg m\({}^{-3}\) \\ Density (positive electrolyte) & \(\rho_{+}\) & 1350 & kg m\({}^{-3}\) \\ Mean pore radius & \(r_{p}\) & \(50.3\times 10^{-6}\) & m \\ Kozeny-Carman constant & \(k_{\text{CC}}\) & 180 & – \\ Conductivity of current collector & \(\sigma_{s}^{\text{CC}}\) & 1000 & S m\({}^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Model parameters from [PERSON] et al. [14]. \begin{table}
\begin{tabular}{c c c c} \hline
**Thickness** & **Compression** & **Conductivity** & **Porosity** \\ \hline
**mm** & **mm** & **\%** & **S/m** & \\ \hline
4.0 & 0.0 & 0\% & 5.9 & 0.95 \\
3.6 & 0.4 & 10\% & 14.3 & 0.90 \\
3.2 & 0.8 & 20\% & 20.0 & 0.89 \\
2.8 & 1.2 & 30\% & 50.0 & 0.87 \\ \hline \end{tabular}
\end{table} 
Table 3: Carbon felt electrode data adapted from [PERSON] et al. [31]. The full-cell model used for this research showed good agreement with the published experimental data with parameters defined by [PERSON] et al. [12]. This includes a small voltage correction which the researchers used to account for considerations that are not included in the simplified model, such as contact resistances. With 150 mV added to each value, the average error over the range 10% to 90% SOC was 1%, and the maximum error at 10% was 3%. Experimental and simulated charge curves are shown in Figure 3 below. Performance parameters were obtained through post-processing in COMSOL, with derived values providing the minimum V\({}^{3+}\) concentration over the negative electrode cross-section. The electric potential was measured at the current collector boundary at the positive half-cell, implemented with a boundary probe. This boundary was defined as an electrode current set at the applied average current density, while the negative was given an electric ground boundary condition. Differential pressure values were extracted by subtracting the inlet boundary average absolute pressure from that at the outlet