Mushy layer

A mushy layer contains solid crystals and liquid in local phase equilibrium, rather than a single sharp phase boundary. Its solid fraction changes as heat and solute are transported. A concentration-dependent liquidus couples temperature to liquid composition; a connected crystal framework makes the residual liquid behave as a porous-media flow.

The solid fraction is the volume fraction occupied by solid in a solid–liquid mixture. The complementary liquid fraction is $1-\phi$.

The liquid fraction is the volume fraction occupied by liquid in a solid–liquid mixture. For a saturated rigid mushy layer, it is the porosity available to Darcy flux.

For constant phase mass densities ${\rho }_s,{\rho }_l$, a fixed solid framework has mixture density $\bar{\rho }={\rho }_s\phi +{\rho }_l(1-\phi )$. Mass conservation giveswhere $\mathbf{u}$ is Darcy flux. Equal phase densities give a divergence-free flux. Unequal densities require expansion or contraction flow during freezing or melting.