Ivantsov parabolic solution for two combined moving interfaces

TL;DR

This paper derives an exact steady-state solution for a liquid layer with two moving parabolic interfaces during melting and solidification, revealing conditions for convex and concave interface solutions.

Contribution

It introduces a novel analytical solution for two moving interfaces with parabolic shapes in solidification processes, expanding understanding of interface dynamics.

Findings

Existence of solutions with two convex or two concave parabolas

Conditions where steady-state with two planar interfaces is impossible

Relations between Peclet numbers and control parameters

Abstract

We demonstrate that for a migration of a liquid layer between the melting and the solidification front an exact steady-state solution with two parabolic fronts can be found. A necessary condition hereby is that the temperature of the solidification front exceeds the temperature of the melting front (both temperatures are supposed to be constant). It is shown that in pure materials and alloys there exist two types of solutions with two convex and with two concave parabolas respectively. While a steady-state process with two planar interfaces is only possible for a single point, the processes with two parabolas are possible inside a region of control parameters. The relations between the Peclet numbers and the control parameters are obtained.