Elimination of surface diffusion in the non-diagonal phase field model

TL;DR

This paper introduces a non-diagonal phase field model that effectively eliminates artificial surface diffusion effects in phase transformations with unequal diffusivities, improving boundary condition accuracy.

Contribution

The paper develops a novel non-diagonal phase field model incorporating kinetic cross coupling to remove artificial surface diffusion effects.

Findings

Successfully recovers desired boundary conditions at interfaces.

Numerical tests show elimination of artificial surface diffusion.

Model accurately describes interface relaxation dynamics.

Abstract

We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of the artificial surface diffusion effect. The model is non-diagonal since it incorporates the kinetic cross coupling between the non-conserved and the conserved fields that was recently introduced [{Phys. Rev. E {\bf 86}, 060601(R), (2012)}]. We test numerically this model for the two-dimensional relaxation of a weakly perturbed interface toward its flat equilibrium.