Sharp-Interface Limit of a Fluctuating Phase-Field Model

TL;DR

This paper derives a sharp-interface limit for a fluctuating phase-field model of solidification, incorporating noise in the diffusion and boundary conditions, applicable to both variational and non-variational formulations.

Contribution

It introduces a noise-inclusive sharp-interface projection method that does not depend on the fluctuation-dissipation theorem, applicable to various phase-field models.

Findings

Derived a noise-inclusive sharp-interface limit for phase-field models.

Applicable to both variational and non-variational formulations.

Enables more accurate and flexible simulations of crystal growth with fluctuations.

Abstract

We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuation-dissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or non-variational phase-field formulations. In particular, it can be used to introduce thermodynamical fluctuations in non-variational formulations of the phase-field model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phase-field simulations in crystal growth while accounting for the proper fluctuations of the system.