Effective transport rates and transport-induced melting and solidification in mushy layers

Abstract

Mushy layers are known to occur in magma chambers, sea-ice, and metal castings. They are often modeled as a porous layer in which a fluid and solid matrix exist in thermal and compositional equilibria. In nonreactive porous media, both advective and diffusive transport rates for heat and solute differ. In mushy layers, however, the temperature and composition of the fluid phase are constrained by the liquidus relationship giving rise to effective transport rates that are intermediate between those for heat and solute in passive porous layers. The transport of heat and solute, even if the invading fluid is itself in equilibrium, is also accompanied by a degree of solidification or melting due to the difference in the transport rates for these two quantities. In this paper, analytical expressions for the effective velocity and diffusivity in a mushy layer and for the degree of melting or solidification accompanying the passage of a front with a different temperature and composition are derived and compared with the predictions of a numerical model and found to be in very good agreement. Characteristic parameters for a few mushy systems are calculated and appropriate transport and melting/freezing regimes are indicated.