Influence of Disorder Strength on Phase Field Models of Interfacial Growth

TL;DR

This study examines how varying disorder strength affects interface roughening in phase-field models with conserved dynamics, revealing different scaling behaviors and nucleation phenomena under weak and strong disorder conditions.

Contribution

It compares one-sided and two-sided phase-field models, showing how disorder strength influences interface scaling and nucleation processes.

Findings

Weak disorder leads to super-rough scaling in both models.

Strong disorder causes intrinsic anomalous scaling.

Nucleation occurs in the two-sided model under strong disorder.

Abstract

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.