Emergence of foams from the breakdown of the phase field crystal model

TL;DR

This paper investigates foam-like behaviors emerging from the phase field crystal model at high undercooling, proposing a modified model that captures foam dynamics and reproduces known foam coarsening rules.

Contribution

It introduces a modified PFC model capable of simulating foam behaviors and reproduces key foam coarsening phenomena.

Findings

The foam phase of the PFC model is characterized at large undercooling.

The modified PFC model reproduces von Neumann's rule and Lifshitz-Slyozov coarsening.

Coordination number distribution's second moment exceeds previous experimental and theoretical values.

Abstract

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams, and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously-reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.