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Center for Nonlinear Studies |
A monolayer of hydrophobic particles at the air-water interface exhibits properties of a two-dimensional solid under compression. Localized surfactant introduction on such monolayers causes dynamical fracture due to stresses exerted by the advancing surfactant. Here we experimentally demonstrate a radially divergent particulate shock emerges from the point of surfactant introduction. Using similarity solutions that predict $t^{3/4}$ scaling for an advancing surfactant on the surface of a deep fluid, we experimentally show the particulate shock travels with the Thoreau-Reynolds ridge. The shock induces particulate compaction in its wake which increases until the particles jam into a disordered,two-dimensional solid. Fracture occurs when the compaction band\'s packing fraction saturates at random close packed density $\\phi_{RCP}$ and gives rise to nearly regular, triangle shaped cracks with robust geometrical features. The number of cracks $N$ varies monotonically with the initial particulate packing fraction $\\phi_{init}$. Whereas the compaction band\'s radius $R^*$ at fracture onset also exhibits similar monotonic dependence on $\\phi_{init}$, its width $W^*$ shows no such dependence. By treating the compaction band as a rigid, elastic annulus, and invoking mass conservation, we show $N \\sim R^*/W^* = 2\\phi_{RCP}/\\phi_{init}$ and verify it experimentally over a range of initial packing fractions ($0.1 \\le \\phi_{init} \\le 0.64$
Host: Robert Ecke