= Marginal equilibrium at a mush-liquid boundary
{title2=$T_z=-mC_z$}
At a sharp mush–liquid edge with linear <liquidus> $T_L=T_m-mC$, marginal equilibrium makes the liquid <temperature gradient> tangent to the local <liquidus>: $T_z=-mC_z$. Together with $T=T_L$ at the edge and $T\ge T_L$ in the exterior liquid, it supplies the usual absence-of-<constitutional supercooling> closure. When solute <diffusion> is neglected inside the <mushy layer> but retained outside it, interfacial solute conservation can require a small <solid fraction> jump; imposing unit <porosity> as an additional finite-diffusivity condition generally overdetermines this sharp-edge reduction.
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