A particle raft floating on an expanding liquid substrate provides a macroscopic analog for studying material failure. The time scales in this system allow both particle-relaxation dynamics and rift formation...

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.

The failure of materials is often considered as a quasi-static process in classical fracture mechanics. No dynamics can be allowed because the speed of sound is much greater than any other velocity. In this paper, we introduce a macroscopic system where the dynamics of particle relaxation and rift formation can be resolved: a particle aggregate is stretched uniaxially by the expansion of the air-fluid interface on which it floats. The failure morphology of these rafts change continuously with pulling velocity. This can be understood by the competition between two velocities: the speed of particle relaxation towards the nearest low energy configuration (i.e., re-aggregation), which is determined by viscous and capillary forces, and the velocity difference between neighboring particles, which is caused by the expanding underlying fluid. This crossover behavior selects the cluster length scales, i.e., the distance between adjacent rifts, and is consistent with the the experimental failure patterns.

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 (To and Nagel [2022]) 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.