Cluster Formation and Relaxation in Particle Rafts under Uniform Radial Expansion

TL;DR

This study investigates how particle rafts at an air-liquid interface form clusters and relax under uniform radial expansion, revealing inverse scaling of cluster size with pulling velocity and modeling failure patterns.

Contribution

It introduces a generalized model for failure morphology in radially expanded particle rafts, highlighting the interplay of competing velocities and nonlinear relaxation in two dimensions.

Findings

Cluster size scales inversely with pulling velocity.

A generalized stability model matches observed failure patterns.

Nonlinear relaxation occurs after initial clustering.

Abstract

Particle rafts floating at an air-liquid interface exhibit a variety of behaviors when interfacial flow is introduced. Motivated by previous experimental observations, the failure pattern of particle rafts under uniform radial expansion is reported in this paper. The expansion process is specifically designed to expand the system affinely in the radial direction and to keep the velocity gradient constant throughout. A strong resemblance to the results of particle rafts under uniform uniaxial expansion[1] is found. The size of the cluster emerging as the rafts are pulled apart scales inversely with the pulling velocity. This is a result of two competing velocities: the inter-particle separation speed provided by the flow and a size-dependent relaxation speed for clustering. A model, generalized from a one-dimensional linear (in)stability calculation, is in agreement with the failure morphology found for this radially expanded system. Nonlinear relaxation and particle rearrangement is observed after the initial clustering occurs. This is a feature unique to a two-dimensional system. With its easily accessible particle dynamics at the microscopic level, this system provides insights into the morphology controlled by two competing mechanisms in two or higher dimensions and across different scales.