This paper is devoted to the mathematical modeling of a combined effect
of directional and bulk crystallization in a phase transition layer with
allowance for nucleation and evolution of newly born particles. We
consider two models with and without fluctuations in crystal growth
velocities, which are analytically solved using the saddle-point
technique. The particle-size distribution function, solid-phase fraction
in a supercooled two-phase layer, its thickness and permeability,
solidification velocity, and desupercooling kinetics are defined. This
solution enables us to characterize the mushy layer composition. We show
that the region adjacent to the liquid phase is almost free of crystals
and has a constant temperature gradient. Crystals undergo intense growth
leading to fast mushy layer desupercooling in the middle of a two-phase
region. The mushy region adjacent to the solid material is filled with
the growing solid phase structures and is almost desupercooled.
Mathematical modeling of bulk and directional crystallization with the moving phase transition layer
