Directional crystallization of a two-phase region with a mixed conductive–convective heat and mass transport

Here we consider the influence of simultaneous operation of convective and conductive heat and mass fluxes in a binary liquid on directional crystallization processes with a two-phase region. We consider two possible crystallization scenarios with constant and unsteady growth velocities and construct the corresponding analytical solutions in a parametric form. These solutions enable us to find such process characteristics as temperature, impurity concentration, solid-phase fraction, the laws of motion for the two-phase region boundaries dependent on material parameters and crystallization driving force, i.e. the specified system cooling conditions. The solutions obtained enable us to describe the material microstructure by means of two-phase region permeability and primary interdendritic spacing dependent on the solid-phase fraction of a solidified material. The theory under consideration also enables us to find the unfrozen liquid phase fraction of a two-phase material released in ice and permafrost melting processes, which defines the biophysical significance of the issue under study.