## 5 Simulation of Future VST Experiments with Pb-Li Using Literature-Averaged Dissolution Parameters
During the system transient, the aforementioned difference between BCs experienced by \"wet\" and \"dry\" steel surfaces implies that the flux through wet surfaces will be lower than through dry surfaces. Additionally, since future experiments with Pb-Li in the UC are designed with the height of liquid metal around 20.0 mm, the WALL surface that is wet is only \(\approx\)20% of the total. Thus, as a _mass-transport-system simplification_, radial diffusion was neglected through WALL sections covered by Pb-Li. Figure 11 shows the evolution of atomic concentrations in the Pb-Li and the BASE for a simulation run at 450 \({}^{\circ}\)C and initial pressure of 780 mbar. Notice that the interface between Pb-Li and steel is represented in different positions in each graph; the interface concentrations are displayed at the abscissa \(x=18\) mm in Figure 11a, and abscissa \(x=0\) mm in Figure 11b. As previously explained, this interface concentration in Pb-Li is considerably lower than in steel; however, the deuterium flux is nevertheless directed from the former towards the latter because of the different chemical potential (represented by Sieverts' concentrations) of deuterium in each medium. \begin{table}
\begin{tabular}{c c c c c} \hline
**Pb-Li** & \(D_{\infty}\) & \(E_{d}\) & \(S_{\infty}\) & \(E_{s}\) \\
**(\(D_{2}\))** & **(m\({}^{2}\)/s)** & **(k)/k mol** & **(mol/m\({}^{3}\cdot 1/\sqrt{\mathbf{r_{d}}}\))** & **(k/k mol)** \\ \hline
**max** & \(1.72\times 10^{-4}\)[18] & 41.83 [19] & \(5.40\times 10^{0}\)[23] & 54.44 [23] \\
**avg** & \(2.49\times 10^{-7}\) (all) & 24.05 (all) & \(4.71\times 10^{-2}\) (all) & 16.65 (all) \\
**min** & \(3.21\times 10^{-9}\)[10] & 6.63 [10] & \(1.24\times 10^{-3}\)[22] & \(-0.93\)[30] \\ \hline \end{tabular}
\end{table} 
Table 3: Average and extreme values of dissolution parameters for deuterium in Pb-Li [11; 18; 20; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. The concentration at the Pb-Li side of the interface rises with time. Due to the different diffusivities in each medium, deuterium arrives at the interface quicker than it transfers into steel, even if steel presents a higher affinity for the deuterium atoms. This leads to an accumulation in Pb-Li, which rises the interface concentration. This difference in diffusivities can also be seen by how much the 18 h profile in Pb-Li (Figure 11a) is closer to reaching its pseudo-steady-state than its counterpart in steel (Figure 11b). Figure 11: Simulation of concentration profiles evolution during 18 h in Pb-Li and BASE steel media, using **avg** dissolution parameters (_vide_ Tables 1 and 3). Initial gas pressure set at 780 mbar, heater temperature set at 450 \({}^{\circ}\)C. (**a**) Concentration profile evolution in Pb-Li. Concentration maximum in the order of \(8\times 10^{-1}\) mol/m\({}^{3}\). Medium thickness of 18 mm. (**b**) Concentration profile evolution in BASE. Concentration maximum in the order of 5 mol/m\({}^{3}\). Notice the difference in concentration scale in comparison to Figure 6b. Figure 10: Schematic of the VST’s Upper Chamber as modelled using the quasi-2D modelling approach for simulations that include Pb-Li. No radial diffusion is assumed for the WALL surface covered by Pb-Li. The lower vertical diffusion channel is extended to double metallic barrier channel, with a set of Co-Dependent BCs at the metal-metal interface (in _orange_). Still focusing on the 18 h profiles, it should also be noted that the leftmost concentration in the BASE:  
* is approximately 20 mol/m\({}^{3}\) in the simulation _without_ Pb-Li (_vide_ Figure 6b);
* but is only approximately 5 mol/m\({}^{3}\) in the simulation _with_ Pb-Li (_vide_ (Figure 11b); under the same temperature and pressure conditions. This difference is again explained by the one order of magnitude difference between Sieverts' constants assumed for steel and Pb-Li. It leads to a temporarily bounded concentration in Pb-Li that limits the maximum BC that steel can experience. This implies that Pb-Li acts as a _permeation barrier_ to steel.