Multiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowires

TL;DR

This paper introduces a novel phase field model for multiphase mean curvature flows that effectively incorporates mobility contrasts, enabling accurate simulations of complex systems like nanowire growth and droplet wetting.

Contribution

The authors propose a new phase field approach that embeds mobility coefficients into the metric of the gradient flow, improving modeling of systems with high or degenerate mobilities.

Findings

The model is consistent with sharp interface limits.

Numerical simulations demonstrate advantages in nanowire growth and droplet wetting.

Efficient scheme enables practical computations for complex multiphase systems.

Abstract

The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface evolution laws depend also on interface mobility coefficients. Having in mind some applications where highly contrasted or even degenerate mobilities are involved, for which classical phase field models are inapplicable, we propose a new effective phase field approach to approximate multiphase mean curvature flows with mobilities. The key aspect of our model is to incorporate the mobilities not in the phase field energy (which is conventionally the case) but in the metric which determines the gradient flow. We show the consistency of such approach by a formal analysis of the sharp interface limit. We also propose an efficient numerical scheme which allows us to illustrate the advantages of the model on various examples, as the wetting of droplets on solid surfaces or the simulation of nanowires growth generated by the so-called vapor-liquid-solid method.