# Thin interface limit for phase-field models of solidification with local mobility correction

## TL;DR

This paper introduces a novel method for deriving mobility corrections in phase-field models of solidification, utilizing local interface information to improve accuracy across a wider range of diffusivity conditions.

## Contribution

It presents a new approach that removes systematic errors in phase-field kinetics without relying on small interface Peclet number approximations.

## Key findings

- Broader applicability for higher interface Peclet numbers.
- Elimination of systematic errors in phase-field kinetics.
- Analytical form for mobility corrections derived from local interface data.

## Abstract

A new approach is developed to derive an analytical form for mobility corrections in phase-field models for pure material solidification. Similar to the thin interface limit approach (Karma and Rappel, 1996) it seeks to remove systematic errors in the kinetics of phase-field models that arise due to the diffusivity of the interface. The new approach harnesses local information within the diffuse interface instead of an expansion within the interface peclet number $p_e=\eta/\delta$, the ratio of diffuse interface thickness to diffusion length. Therefore it has no need for an approximation of $p_e$ being small. This results in a broader range of applicability of the approach for higher $p_e$.