## 5 Simulation of Future VST Experiments with Pb-Li Using Literature-Averaged Dissolution Parameters
This also supports neglecting fluxes through the lower, wet sections of the WALL surfaces while Pb-Li is not saturated, as it was assumed for the developed model. The consequences of different evolution speeds in each medium can also be visualized by spacial integration of the concentration profiles, which provides the total amount of gas dissolved in each medium. The evolution of these values simulated for 288 h (12-days experiment) can be seen in Figure 12a, given in molecular form--the gas is dissolved in atomic form, but values in molecular form allow for easier comparison with injection amounts to determine how much deuterium gas is lost from the chamber. Notice how in this period Pb-Li reaches a relatively stable amount of dissolved gas, while the curves for the LID and the BASE still present positive, non-negligible derivatives in time at the end of the simulation. The same cannot be said about the WALL, that reaches medium saturation much more quickly, ultimately attributed to its thinner dimension. Figure 12: Evolution of number of moles dissolved in, and fluxes through, each UC part for a simulation of 288 h, using avg dissolution parameters (_vide_ Tables 1 and 3). Values given in molecular amounts, instead of atomic, for easier comparison with the amount of gas injected in the chamber. Initial gas pressure set to 780 mbar and BASE temperature set to 450 \({}^{\circ}\)C. (**a**) Evolution of the equivalent molecular number of moles of deuterium dissolved, in logarithmic scale. (**b**) Evolution of the equivalent molecular fluxes of deuterium, in logarithmic scale. Fluxes into Pb-Li and into BASE tend to the same value as the system tends to an equilibrium state. Figure 12a also shows that the amount of deuterium trapped in the BASE is significantly smaller than in the LID for the initial period of evolution. This is true in spite of their temperature difference, that favors diffusion into the former (temperatures were assumed similar to the ones in experiments without Pb-Li; e.g., LID at \(\approx\)362 \({}^{\circ}\)C when the BASE is at 450 \({}^{\circ}\)C). This is attributed to the permeation barrier effect brought by Pb-Li, that considerably reduces the fluxes entering the BASE in the beginning of the process. Such fluxes can be derived using Fick's Law (_vide_ Section 2). Figure 12b shows the fluxes entering each metal by their innermost surface in respect to the center of the UC. The curves displayed confirm that fluxes through the inner surface of the WALL reach equilibrium conditions much faster than for other UC parts. However, although one can verify that fluxes into the Pb-Li and BASE approach the same value (as expected) as the complete system tends to equilibrium, these curves do not display negligible derivatives in time after 288 h. This implies that the system is close to equilibrium but the Pb-Li is not saturated, which is confirmed by Figure 13, shown in its respective profile of a longer simulation run in Figure 13a. Additionally, Figure 13b also supports the permeation barrier interpretation, since the BASE Co-Dependent BC after 288 h is still lower than the BASE Coupled BC in the simulation without Pb-Li after only 18 h of evolution (_vide_ Figure 6b). Figure 13: Simulation of concentration profiles evolution during 288 hours 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. Coupled BC (left) visibly decreases because the continued diffusion eventually reduces the amount of gas available in the UC in meaningful quantities. (**b**) Concentration profile evolution in BASE. Concentration maximum in the order of 13 mol/m3. Notice how this value is lower than the maximum in Figure 6b, even after a much longer period of system evolution.