Scaling of critical velocity for bubble raft fracture under tension

Abstract

The behavior of materials under tension is a rich area of both fluid and solid mechanics. For simple fluids, the breakup of a liquid as it is pulled apart generally exhibits an instability driven, pinch-off type behavior. In contrast, solid materials typically exhibit various forms of fracture under tension. The interaction of these two distinct failure modes is of particular interest for complex fluids, such as foams, pastes, slurries, etc. The rheological properties of complex fluids are well-known to combine features of solid and fluid behaviors, and it is unclear how this translates to their failure under tension. In this paper, we present experimental results for a model complex fluid, a bubble raft. As expected, the system exhibits both pinch-off and fracture when subjected to elongation under constant velocity. We report on the critical velocity vc below which pinch-off occurs and above which fracture occurs as a function of initial system width W, length L, bubble size R, and fluid viscosity for both monodisperse and polydisperse systems. Though both exhibit a transition from pinch-off to fracture, the behavior as a function of L/W is qualitatively different for the two systems. For the polydisperse systems, the results for the critical velocity are consistent with a simple scaling law vcτ/R∼L/W, where the fluid viscosity sets the typical time for bubble rearrangements τ. We show that this scaling can be understood in terms of the dynamics of local bubble rearrangements (T1 events). For the monodisperse systems, we observe a critical value for L/W below which the system only exhibits fracture.