A Soluble Phase Field Model

TL;DR

This paper introduces a generalized phase field model for solid-liquid phase transitions, analyzing its dynamics, solutions, and comparison with standard models, revealing relaxation towards mixed phases with large fluctuations.

Contribution

It develops a soluble, generalized phase field model coupling non-conserved and conserved fields, with analytical solutions and validation against simulations and standard models.

Findings

The model's solutions agree reasonably with simulations.

System relaxes to a mixed phase depending on initial conditions.

Large fluctuations occur in the phase field during relaxation.

Abstract

The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to a conserved field (e.g. thermal field). After obtaining the rules governing the evolution process, by means of analytical arguments, we present a discussion of the asymptotic time-dependent solutions. The full solutions of the exact self-consistent equations for the model are also obtained and compared with computer simulation results. In addition, in order to check the validity of the present model we confronted its predictions against those of the standard Phase field model and found reasonable agreement. Interestingly, we find that the system relaxes towards a mixed phase, depending on the average value of the conserved field, i.e. on the initial condition. Such a phase is characterized by large fluctuations of the phi field.