📝 SummarXiv

Abstract

Self-similarity in partial differential equations has been widely exploited to study many phenomena in physical sciences. We have studied the interfacial dynamics when air is entrained into viscous liquid by a disk in a confined geometry. In a previous study using an original experimental system, we found the sheet- and corn-forming regimes, in which a sheet and cone of air are respectively formed before air detaches from the disk. The sheet eventually breaks up but the corn, which appears when a bit more confined, does not. Here, we find a third regime, in which a corn eventually breaks up, by investigating different ranges of confining parameters: the transition from breakup to non-breakup can occur within the corn regime. Furthermore, with the data obtained in the third regime we deeply explore analogy with critical phenomena to find out that the counterpart of the critical exponents dependent on a length scale. Since the scale is a number not discrete but continuous, the present hydrodynamic analog suggests the existence of an uncountably infinite number of universality classes. The rich physics revealed in our study suggests a promising direction of the study of the self-similar dynamics: exploring analogy with critical phenomena, focusing on confined geometries in many natural and industrial phenomena.