Partial persistence of memory in bubble breakup: Incomplete universality acquired by broken symmetry

When a water drop falls from a faucet, the drop is created with the formation of an axisymmetric constriction region, which thins down to breakup. Such formation of a fluid drop has been extensively studied as a representative of the singular dynamics widely observed in nature. The singular dynamics is often self-similar, i.e., shapes at different times collapsing onto a master curve after rescaling, and the self-similar dynamics has been categorized as either “universal” or “nonuniversal”: The master curve is or the length scales that set the initial boundary conditions, as if memory is or . Here, we focus on the post-breakup dynamics and confine the system to break the axisymmetry, introducing three length scales, which leads to a third category: “incomplete universality” where memory is : The master curve could be dependent on the smallest scale but independent of the other two scales. The fact that only the smallest length scale can affect the shape of the master curve suggests that scale separation is deeply related to the emergence of universality. The present study suggests a promising direction for the study on the singular dynamics by exploring the symmetry.