Speed of fragments ejected by an expanding liquid tin sheet

Abstract

We experimentally investigate the speed of fragments produced by ligament breakup in the laser-induced deformation of tin microdroplets into axisymmetric sheets. The experiments were carried out covering a wide range of droplet diameters and laser-pulse energies. In addition to fragments produced by end-pinching, we also observe fragments shed via Rayleigh-Plateau breakup of long ligaments at late times. A double-frame backlit camera was used to obtain the speeds of the fragments uf and the time of their detachment td. We show that by normalizing uf to the initial expansion speed of the sheet Ṙ0, all data collapse onto a single, universal curve that is a function of the dimensionless time td/τc only, where τc is the capillary time. This universal curve is explicitly independent of the droplet's Weber number. The collapse of uf is supported by energy conservation arguments. Our findings enable the prediction of the instantaneous speed and position of the fragments shed from liquid tin targets used in state-of-the-art extreme ultraviolet nanolithography, facilitating the design of effective mitigation strategies against microparticulate debris.