Partial persistence of memory in bubble breakup: incomplete universality acquired by broken symmetry (2408.01793v8)

Abstract: 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 case of the singular dynamics widely observed in nature. The singular dynamics is often self-similar: shape at different times collapsing onto a master curve after rescaling. The self-similar dynamics has been categorized as either universal or non-universal: the master curve is independent from or dependent on the length scales that set the initial boundary conditions, as if memory is erased or retained. In the previously known cases, where the axisymmetry is maintained, only a single length scale is available for the boundary conditions, a tube radius, and, thus, there is no possibility of partial memory. Here, we focus on the post-breakup and confine the system to break the axisymmetry, introducing three length scales, which leads to a third category of incomplete universality, where memory is partially retained: the master curve for the post-breakup is dependent on the smallest scale but independent from the other two scales. Affecting of only the smallest length scale on the master curve underscores the importance of scale separation for the emergence of universality: near the singularity physics at small scales becomes important. The present study suggests a promising direction for the study on the singular dynamics by exploring the symmetry and has implications for bubble/drop generation in confined geometries, encountered in various fields from microfluidics to geology.