Shock driven jamming and periodic fracture of particulate rafts

A tenuous monolayer of hydrophobic particles at the air-water interface often forms a scum or raft. When such a monolayer is disturbed by the localized introduction of a surfactant droplet, a radially divergent surfactant shock front emanates from the surfactant origin and packs the particles into a jammed, compact, annular band with a packing fraction that saturates at a peak packing fraction $\phi^*$. As the resulting two-dimensional, disordered elastic band grows with time and is driven radially outwards by the surfactant, it fractures to form periodic triangular cracks with robust geometrical features. We find the number of cracks $N$ and the compaction band radius $R^*$ at fracture onset vary monotonically with the initial packing fraction ($\phi_{init}$). However, its width $W^*$ is constant for all $\phi_{init}$. A simple geometric theory that treats the compaction band as an elastic annulus, and accounts for mass conservation allows us to deduce that $N \simeq 2\pi R^*/W^* \simeq 4\pi \phi_{RCP}/\phi_{init}$, a result we verify both experimentally and numerically. We show the essential ingredients for this phenomenon are an initially low enough particulate packing fraction that allows surfactant driven advection to cause passive jamming and eventual fracture of the hydrophobic particulate interface.