= Finite-inventory directional salt rejection
{title2=$C_I=VN/D$}
For pure solid rejecting all solute, pulling speed $V>0$, solutal diffusivity $D$ and finite solute inventory per unit area $N$, a stationary planar front has $C(z)=C_Ie^{-Vz/D}$ in its liquid half-space. The <advection-diffusion equation> gives this profile, and $\int_0^\infty C\,dz=N$ fixes $C_I=VN/D$. A <liquidus> $T_I=-mC_I$ fixes its position in an imposed <temperature gradient>. The pure-solid branch requires $C_I<C_E$, where $C_E$ is the <eutectic composition>.
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