The 145th R-CCS Cafe

Hydrophobic particles at a liquid-air interface tend to aggregate and form a monolayer, known as a particulate raft. These particles, otherwise non-cohesive, deform the liquid surface and interact through capillary bridges, enabling the monolayer to withstand tensile and shear deformations. The study of particulate monolayers is of great interest to scientists and engineers due to their potential for stabilizing liquid drops and emulsions via jamming. Experiments show that when a certain particle density is achieved, the raft can be characterized as a two-dimensional elastic solid, the properties of which depend on the liquid layer's surface tension. Consequently, a practical way to further study particle rafts is through the introduction of a controlled quantity of surfactant into the system. Injected at a particular point, the surfactant decreases the surface tension and generates a front, fracturing the monolayer. The goal of this work is to determine the critical physics underlying the surfactant-driven fracture of particulate rafts. We propose a continuum approach based on a phase-field model to describe the damaged zones in the system. In the model, the fracture evolves as a result of the interplay between the pressure exerted by the surfactant and the elastic response of the monolayer. We model the monolayer behavior, accounting for the fracture toughness, the solid rigid nature of the particles, and their initial distribution. The pressure is proportional to the surface tension difference between the surfactant and the liquid layer. A comparison between the experimental observations and the numerical results indicates a qualitative match in both the fracture patterns and temporal scaling of the process. We explore the influence of particle distribution on secondary features (e.g., crack bending). Importantly, we find a dimensionless parameter that characterizes the number of cracks in the final configuration, separating different fracture regimes. We support our findings with new experimental results that confirm the trends inferred from the simulations.