Shock driven jamming and periodic fracture of particulate rafts
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Abstract
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 φ
∗
. 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 that the number of cracks N and the compaction band
radius R
∗
at fracture onset vary monotonically with the initial packing fraction (φinit). However,
the compaction band’s width W∗
is constant for all φinit. A simple geometric theory that treats
the compaction band as an elastic annulus, and accounts for mass conservation allows us to deduce
that N ≃ 2πR∗
/W∗ ≃ 4πφRCP /φinit, a result we verify both experimentally and numerically. We
show that 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.