The failure of two-dimensional particle raft under tension

We study particle rafts, which are submillimeter particles aggregated at an air-liquid interface, as they are pulled apart from their opposing sides. There is a distinct failure morphology which depends on the pulling velocity, V_pull. When V_pull is high, there are many microcracks that are distributed throughout the entire system. As V_pull is decreased, the cluster size, that is the number of particles between adjacent cracks, increases until it becomes comparable to the length of the raft. A one-dimensional linear instability analysis reveals that there is a healing velocity V_heal(k) for clusters to rearrange which decreases with the wavevector, k. That is, the time it takes for a cluster to heal (i.e., rearrange and find new neighbors) increases as the length of the cluster increases. This accounts for the rate dependence in the failure morphology: the pulling speed selects the length scale at which the clusters can relax effectively.  We further explore this raft failure under different parameters, such as changing the viscosity and surface tension of the  underlying liquid, the boundary conditions (using either repulsive or attractive interactions with the puller) and system size.