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\chapter*{Notations}
\addcontentsline{toc}{chapter}{Notations}
\markboth{Notations}{Notations}
\renewcommand{\arraystretch}{1.4}
\setlength{\tabcolsep}{6pt}
\begin{xltabular}{\linewidth}{@{}l X l@{}}
\multicolumn{3}{@{}l}{\textit{\textbf{Latin symbols}}} \\
\midrule
\endfirsthead
\multicolumn{3}{@{}l}{\textit{\textbf{(continued)}}} \\
\midrule
\endhead
\midrule
\multicolumn{3}{r@{}}{\textit{continued on next page}} \\
\endfoot
\endlastfoot
$A$ & Tank (column) base area & m$^2$ \\
$a$ & Specific interfacial area & m$^{-1}$ \\
$c_{T_2}$ & Tritium concentration in liquid & mol\,m$^{-3}$ \\
$d_b$ & Sauter mean bubble diameter & m \\
\dnoz & Sparger nozzle diameter & m \\
$d_t$ & Tank (column) diameter & m \\
$D_l$ & Tritium diffusivity in liquid & m$^2$\,s$^{-1}$ \\
$E_\alpha$ & Axial dispersion coeff. of phase $\alpha$ & m$^2$\,s$^{-1}$ \\
$g$ & Gravitational acceleration & m\,s$^{-2}$ \\
$h_l$ & Liquid-side mass transfer coeff. & m\,s$^{-1}$ \\
$H$ & Liquid column height & m \\
$J_{T_2}$ & Interfacial tritium flux & mol\,m$^{-2}$\,s$^{-1}$ \\
$k_e$ & Isotopic exchange coeff. at the sweep surface & m$^4$\,s$^{-1}$ \\
$k_\mathrm{eff}$ & Effective salt-to-wall mass transfer coeff., $k_m/\mathrm{PRF}$ & m\,s$^{-1}$ \\
$k_m$ & Salt-to-wall mass transfer coeff. & m\,s$^{-1}$ \\
$k_r$ & Recombination coeff. at the sweep surface & m$^4$\,s$^{-1}$ \\
$K_s$ & Solubility (Henry) constant & mol\,m$^{-3}$\,Pa$^{-1}$ \\
$m_k$ & Multiplier of unit cell $k$ at vessel scale & -- \\
$M_{\mathrm{He}}$ & Molar mass of helium & kg\,mol$^{-1}$ \\
$\dot n_g$ & Molar gas flow rate & mol\,s$^{-1}$ \\
$n_{T_2}$ & Tritium inventory & mol \\
$N_\alpha$ & Total tritium inventory in phase $\alpha$ & mol \\
\Nnoz & Number of sparger nozzles & -- \\
$P$ & Pressure & Pa \\
$P_{\mathrm{top}}$ & Pressure at column top & Pa \\
$P_{\mathrm{bot}}$ & Hydrostatic pressure at column bottom & Pa \\
$P_{T_2}$ & Tritium partial pressure in gas & Pa \\
$Q_\mathrm{T_2}$ & Integral tritium source & mol\,s$^{-1}$ \\
$R$ & Ideal gas constant & J\,mol$^{-1}$\,K$^{-1}$ \\
$S_\mathrm{T_2}$ & Volumetric tritium source & mol\,s$^{-1}$\,m$^{-3}$ \\
$t$ & Time & s \\
$T$ & Temperature & K or $^\circ$C \\
$u_g$ & Superficial gas velocity & m\,s$^{-1}$ \\
$v_{g0}$ & Bubble true (interstitial) terminal velocity & m\,s$^{-1}$ \\
$V_\alpha$ & Volume of phase $\alpha$ & m$^3$ \\
$\dot V_g$ & Volumetric gas flow rate & m$^3$\,s$^{-1}$ \\
$y_{T_2}$ & Tritium molar fraction in gas & -- \\
$z$ & Axial coordinate & m \\
\addlinespace[1em]
\multicolumn{3}{@{}l}{\textit{\textbf{Greek symbols}}} \\
\midrule
$\varepsilon_\alpha$ & Volumetric fraction of phase $\alpha$ & -- \\
$\mu_l$ & Liquid dynamic viscosity & Pa\,s \\
$\nu_l$ & Liquid kinematic viscosity & m$^2$\,s$^{-1}$ \\
$\rho_g$ & Gas-phase density & kg\,m$^{-3}$ \\
$\rho_l$ & Liquid-phase density & kg\,m$^{-3}$ \\
$\Delta\rho$ & Liquid--gas density difference & kg\,m$^{-3}$ \\
$\sigma_l$ & Liquid surface tension & N\,m$^{-1}$ \\
$\tau$ & Tritium extraction time (e-folding) & s \\
$\chi_i$ & Contact ratio of unit cell $i$, $A_\mathrm{contact}/A_\mathrm{total}$ & -- \\
\addlinespace[1em]
\multicolumn{3}{@{}l}{\textit{\textbf{Timescales}}} \\
\midrule
\Tana & Analytical extraction time, \cref{eq:tau_ana} & s \\
\Tnum & Extraction time fitted on the numerical solution & s \\
$\tau_\mathrm{SPP}$ & Extraction time in the small partial pressure limit, \cref{eq:tau_SPP} & s \\
$\tau_\mathrm{MTL}$ & Extraction time in the mass transfer limited regime & s \\
$\tau_\mathrm{PPL}$ & Extraction time in the partial pressure limited regime & s \\
$\tau_{99}$ & Time to extract 99\% of the tritium inventory & s \\
$\tau_\mathrm{sat}$ & Bubble saturation time, $1/(a_b h_l R T K_s)$ & s \\
$\tau_\mathrm{mix}$ & Liquid mixing time, $H^2/E_l$ & s \\
\addlinespace[1em]
\multicolumn{3}{@{}l}{\textit{\textbf{Dimensionless groups}}} \\
\midrule
\PI & Saturation number: bubble saturation at the outlet, \cref{eq:Pi_def_macro} & -- \\
\Gmix & Mixing number: $\tau_\mathrm{mix}/\tau$, liquid uniformity & -- \\
\Gp & Hydrostatic number: $\rho_l g H/P_\mathrm{top}$, pressure variation along the column & -- \\
$\mathrm{Bo}$ & Bodenstein number: gas advection over gas dispersion & -- \\
$\mathrm{Pe}$ & P\'eclet number & -- \\
$\mathrm{Sh}$ & Sherwood number & -- \\
$\mathrm{Sc}$ & Schmidt number & -- \\
$\mathrm{Re}$ & Reynolds number & -- \\
$\mathrm{Eo}$ & E\"otv\"os number & -- \\
$\mathrm{Mo}$ & Morton number & -- \\
$\mathrm{TBR}$ & Tritium breeding ratio & -- \\
$\mathrm{PRF}$ & Permeation reduction factor of the salt-metal interface & -- \\
\addlinespace[1em]
\multicolumn{3}{@{}l}{\textit{\textbf{Subscripts and superscripts}}} \\
\midrule
$0$ & Evaluated at the tank bottom (gas inlet) & \\
$\alpha$ & Any phase, liquid or gas & \\
$b$ & Bubble & \\
$g$ & Gas phase & \\
$l$ & Liquid phase & \\
$i$ & Liquid--gas interface & \\
noz & Sparger nozzle & \\
$t$ & Tank & \\
$\langle\,\cdot\,\rangle$ & Average over the column height & \\
$\langle\,\cdot\,\rangle^\alpha$ & Intrinsic average over phase $\alpha$ & \\
\addlinespace[1em]
\multicolumn{3}{@{}l}{\textit{\textbf{Acronyms}}} \\
\midrule
ARD & Advection--reaction--dispersion & \\
CANDU & CANada Deuterium Uranium reactor & \\
FHR & Fluoride-salt-cooled high-temperature reactor & \\
FLiBe & Molten salt Li$_2$BeF$_4$ & \\
FPP & Fusion power plant & \\
HEX & Structured hexahedral mesh & \\
ITER & International Thermonuclear Experimental Reactor & \\
IV, OV & Inner vessel, outer vessel & \\
LIBRA & Liquid Immersion Blanket: Robust Accountancy & \\
MSBR & Molten Salt Breeder Reactor & \\
MSRE & Molten Salt Reactor Experiment & \\
MTL & Mass transfer limited regime & \\
PFC & Plug-flow contactor & \\
PHWR & Pressurized heavy water reactor & \\
PPL & Partial pressure limited regime & \\
PRF & Permeation reduction factor & \\
SPP & Small partial pressure limit & \\
TES & Tritium extraction system & \\
TET & Unstructured tetrahedral mesh & \\
\end{xltabular}