Rim destabilization and re-formation upon severance from its expanding sheet

TL;DR

This study investigates the destabilization, fragmentation, and re-formation of rims on radially expanding liquid sheets, revealing how severance affects rim stability and correlating experimental results with theoretical predictions.

Contribution

It introduces an experimental method to study rim behavior before and after severance, and links rim fragmentation to theoretical models originally developed for droplet impact systems.

Findings

Severed rims follow ballistic trajectories with inherited velocities.

Fragmentation occurs at ligament bases and rim corrugation junctions.

Theoretical predictions accurately capture ligament and fragment numbers.

Abstract

Upon radial liquid sheet expansion, a bounding rim forms, with a thickness and stability governed, in part, by the liquid influx from the unsteady connected sheet. We examine how the thickness and fragmentation of such a radially expanding rim change upon its severance from its sheet, absent of liquid influx. To do so, we design an experiment enabling the study of rims pre and post severance by vaporizing the thin neck connecting the rim. We confirm that the severed rim follows a ballistic motion, with a radial velocity inherited from the sheet at severance time. We identify that the severed rim undergoes fragmentation in two types of junctions: the base of inherited, pre-severance, ligaments and the junction between nascent rim corrugations, with no significant distinction between the two associated timescales. The number of ligaments and fragments formed is captured well by the theoretical prediction of rim corrugation and ligament wavenumbers established for unsteady expanding sheets upon droplet impact on surfaces of comparable size to the droplet, and with the sheet thickness profiles in both systems having the same functional form. Our findings are robust to changes in impacting laser energy and initial droplet size. Finally, we report and analyze the re-formation of the rim on the expanding sheet and propose a prediction for its characteristic corrugation timescale. Our findings highlight the fundamental mechanisms governing interfacial destabilization of connected fluid-fed expanding rims that become severed, thereby clarifying destabilization of freely radially expanding toroidal fluid structures absent of fluid influx.