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 $(1-\phi )C=C_0$. If $\theta =(T-T_0)/\Delta T$, $\mathcal{C}=m{C}_0/\Delta T$, and the liquidus is $T-T_0=-m(C-C_0)$, then