 No-flux constraint in a fixed-temperature mush

For nonzero imposed thermal gradient and linear liquidus equilibrium, $C_z=-G/m\ne 0$ wherever a mixture of crystals and pore liquid persists. A sealed boundary requires zero solute flux, so a local-equilibrium mush trace there would require $1-\varphi =0$, not a zero-solid-fraction roof. In particular a pure-liquid trace with the equilibrium concentration gradient has nonzero diffusive flux. A sealed column must develop a nonequilibrium-in-the-liquid temperature/composition relation, a separate liquid cap, or an appropriate phase-fraction jump; simply transporting the initial zero-fraction level violates the boundary condition.