Mushy layers are porous media in which the liquid and solid can exchange both mass and heat through melting and freezing. When more than one component is present, the melting and freezing temperatures also become functions of the concentration of a dissolved species and a rich spectrum of sometimes non-intuitive behaviour results. For instance, in an advection dominated system, a hot invading fluid will result in freezing while a cold invading fluid will cause melting. Geophysical examples of mushy layers include magma chambers and sea-ice and mushy layers may exist at the inner-core-outer-core boundary and in the D’’ region of the deep mantle. Continuum equations governing the evolution of mushy layers have been derived and extensively investigated in the literature. Mushy layers in these cases are assumed to be “ideal” in the sense that they remain in local thermodynamic equilibria. In this contribution, we derive a highly simplified pore-scale mushy layer model in which the solid and liquid are treated as separate continua and thermodynamic equilibrium is enforced only on the pore wall. We investigate conditions necessary for the “ideal” mushy layer assumptions to be valid. We show that provided that an appropriately defined Peclet number is less that 0.3 that system is well described by “ideal” mushy layer theory.
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