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

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 ξ/t 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.

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