On the theory of self-similar phase transitions with a mushy layer

D V Alexandrov,I V Alexandrova,A A Ivanov

doi:10.1088/1757-899x/192/1/012017

Abstract

It is well-known that directional crystallization processes frequently occur in unsteady-state manner. One of such time-dependent crystallization regimes is the self-similar process characterizing by the scaled combination between the spatial coordinate ξ (directed along the solidification axis) and time t. Such scaling relation usually establishes when the crystallization process is far from its initial stage t = 0. In this paper, we consider some approximate heuristic relations describing the self-similar solidification mode.

Highlights

A mathematical description of directional crystallization plays a very important role in different applications such as the crystal growth, engineering, geophysical and metallurgical process [1,2,3,4,5,6,7,8,9]
The solidification process occurs in accordance with the classical thermodiffusion model with a planar front
This means that the solidification process may occur in accordance with two scenarios

Summary

Introduction

A mathematical description of directional crystallization plays a very important role in different applications such as the crystal growth, engineering, geophysical and metallurgical process [1,2,3,4,5,6,7,8,9]. When the impurity displacement is rather large, the constitutional supercooling originates ahead of the planar solid-liquid interface [10] and, generally speaking, the two-phase zone (mushy layer) appears.

Results

Conclusion