Manifold Death and the breakup of bags in atomizing flows

The breakup of liquid masses by high speed air flow, or atomization, involves the formation of thin sheets or bags, that perforate at so-called weak spots, followed by a rapid expansion of holes as the Taylor-Culick rim advances. Similar hole formation is observed in floating bubbles, where it leads to bubble death and droplet impact. In some situations, large numbers of holes are observed to coexist, while in other situations a single hole rapidly expands before other holes can form. The numerical procedure we propose to handle hole formation is Manifold Death. We describe this procedure and also give simple statistical estimates for the number of holes that can be observed during the breakup of a single bag, that is the number of coexisting holes. Two models are discussed, one in which breakup is triggered by external random events such as the impact of a microdroplet on the sheet, and one in which breakup is triggered by a distribution of impurities, such as bubbles or oil droplets, immersed inside the sheet. A dimensionless number involving the typical sheet or bag thickness at breakup h_c and the local strain rate γ predicts the number of coexisting holes. This prediction is compared to experiments.