Onsager approach to 1D solidification problem and its relation to phase field description

TL;DR

This paper presents a phenomenological Onsager-based framework for 1D solidification, linking it to phase field models, and explains complex velocity-concentration behaviors in alloys and pure materials.

Contribution

It introduces a general Onsager approach to steady-state 1D solidification, connecting it with phase field models and explaining non-single-value velocity behaviors.

Findings

Positive-definite Onsager matrix allows arbitrary slope signs.

The approach explains non-single-value velocity-concentration phenomena.

Relation established between Onsager approach and phase field models.

Abstract

We give a general phenomenological description of the steady state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two component dilute alloys. The solidification of a pure material is controlled by the heat transport in the bulk and the interface kinetics. The isothermal solidification of two component alloys is controlled by the diffusion in the bulk and the interface kinetics. We find that the condition of positive-definiteness of the symmetric Onsager matrix of interface kinetic coefficients still allows an arbitrary sign of the slope of the velocity-concentration line near the solidus in the alloy problem or of the velocity-temperature line in the case of solidification of a pure material. This result offers a very simple and elegant way to describe the interesting phenomenon of a possible non-single-value behavior of velocity versus concentration which has previously been discussed by different approaches. We also discuss the relation of this Onsager approach to the thin interface limit of the phase field description.