Solute conservation in a steadily pulled mush
= Solute conservation in a steadily pulled mush
With pure solid crystals, negligible solute diffusion, and the <density-change flow in a pulled mushy layer>, steady solute balance gives $(1-\varphi)C=C_0$. If $\theta=(T-T_0)/\Delta T$, $\mathcal C=mC_0/\Delta T$, and the <liquidus> is $T-T_0=-m(C-C_0)$, then
$$
\varphi=-\frac{\theta}{\mathcal C-\theta}.
$$