The Role of a Two-Phase Region in Directional Crystallization of Binary Liquids

Motivated by the widespread occurrence of directional crystallization in nature, laboratory experiments and industrial facilities, we consider how a two-phase (mushy) region filled simultaneously with liquid and solid material influences the process and changes the solute concentration in both the phases. A mushy layer arising as a result of constitutional supercooling in binary liquids drastically changes all process parameters in comparison with the frequently used approximation of a macroscopically planar phase interface. The heat and mass transfer problem with a moving mushy region is replaced by the equivalent model with a discontinuity interface that divides the liquid and solid phases and inherits the properties of a mushy layer. Analytical solutions that describe both crystallization modes with a planar phase interface and discontinuity interface (representing a mushy layer) are constructed for the steady-state and self-similar conditions. The switching time of the crystallization model with a planar phase interface to the model with a two-phase layer is determined. Our calculations, based on analytical solutions, show that the presence of a mushy layer can change the solute concentration in liquid and solid phases to a few tens of percent as compared to the planar interface model. This explains the importance of accounting for the two-phase region when describing the crystallization of supercooled binary liquids.