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 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. Copyright c © EPLA, 2011 The behavior of hydrophobic particles at interfaces presents interesting phenomena of fundamental significance at the intersection of interfacial physics, chemistry, and continuum mechanics [1,2], as well as being relevant in a variety of applications as particles at interfaces can stabilize drops and emulsions via jamming [3]. Recent experiments [4,5] have demonstrated the two-dimensional elastic properties of jammed hydrophobic particulate monolayers at interfaces and aspects of their deformation via buckling and random cracking. These particulate rafts also afford a nice system to study dynamics of the formation of a jammed solid, and its failure via fracture and flow, both phenomena that are hard to analyze in bulk granular media. Here we study both these phenomena at an interface using a combination of experiments and computations and show how a tenuous particulate monolayer driven by Marangoni stresses induced by localized surfactant introduction leads to formation of a jammed solid and its eventual failure via a regular cracking pattern. Figure 1(a) shows a schematic of the experimental setup. A clean glass Petri dish (diameter 0.14m) filled (a)E-mail: [email protected] 1See the Supplementary Material: S1.mov —experimental movie of the formation and failure of an annular solid. with distilled water to a height of 0.01m is placed atop a light tablet. Teflon-coated hollow glass particles (diameter d= 50± 10μm, specific gravity 0.25) are introduced at the air-water interface to form a particulate monolayer with an initial areal packing fraction φinit (defined as ratio of total initial particulate area to total interfacial area) that varies in the range 0.1± 0.01 φinit 0.64± 0.01. Owing to the protocol followed for particle introduction, φinit cannot be controlled, but can be measured (please see Methods section below). When a clean steel needle wetted with oleic acid is dipped into the water surface at the dish center at time t= 0 s, the spreading surfactant pushes the hydrophobic particles radially outwards and packs them along an annulus around the growing particle-free hole as shown in fig. 1(b) and in S1.mov. The compaction dynamics are imaged with a high-speed digital camera (Phantom v5) at 600 frames per second and analyzed to measure the packing fraction (see Methods section). This allows us to follow the compaction band’s evolution in terms of the azimuthally averaged radial packing fraction φθ(r, t) = 1 2π ∫ 2π 0 φ(r, θ, t)dθ. Immediately following the surfactant introduction, the particles move slower relative to the surfactant front due to subphase drag. After a short time, the particle dynamics