= No-flux constraint in a fixed-temperature mush
{title2=$J_C=-D(1-\phi)C_z$}
For nonzero imposed thermal gradient and linear <liquidus> equilibrium, $C_z=-G/m\ne0$ 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 $1-\phi=0$, 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.
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