Characterizing Interface Topology in Multiphase Flows using Skeletons*

The unsteady motion of a gas-liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here we explore the use of skeletonization to identify the minimum amount of information needed to describe their geometry. We skeletonize a periodic liquid jet by a modification of a recently introduced approach to coarsen multiphase flows while retaining a sharp interface. The process consists of diffusing an index function and at the same time moving the interfaces with it, until they "collapse" into each other and form skeletons. The skeleton represents the basic topology of the jet and we also keep track of how much the interface is moved (or how much volume is "accumulated") during the process, which can be used to approximately reconstruct the jet. We explore various quantitative measures to characterize and distinguish the skeletons. Those include standard morphometrics such as branch length distribution, after segmenting the skeletons into branches, and a more sophisticated representation of the skeleton structures called Topology Morphology Descriptor (TMD), to obtain an "equivalent" description of the skeletons by retaining information about the topology in a compact way.