On physical mechanisms of mushy zone formation in solidification of pure semitransparent materials

Two different models, the isothermal mushy zone model and the non-equilibrium planar interface model, are employed to solve the solidification problem of a one-dimensional semitransparent slab subject to radiative and convective cooling at the surface. The mushy zone model is based on the assumption of local equilibrium and predicts the formation of a mushy zone as soon as the temperature of the slab surface reaches the equilibrium melting temperature. The non-equilibrium planar interface model, on the other hand, assumes a stable planar solid/liquid interface during solidification. It allows the existence of melt undercooling at the interface and in the bulk melt. The stability of the planar interface is then examined approximately using the linear stability criterion derived for an opaque material. It is found that a planar interface would be stable even if a large undercooling is generated in the bulk melt in front of the interface. If the rate of external heat transfer is small, however, the planar interface will break down and develop into thermal cells or dendrites. In addition, a transition from a mushy zone to a planar interface is also observed. Based on these results, the thermodynamics and kinetics of crystalline nucleation and growth are examined to illustrate the physical mechanisms of mushy zone formation during solidification of a semitransparent material. It is suggested that the isothermal mushy model and the planar interface model are valid only under corresponding processing conditions, and more research is needed to provide a complete description of the process.