Breakup of diminutive Rayleigh jets

TL;DR

This study combines ultra high-speed imaging and numerical modeling to analyze the breakup of micron-sized liquid jets, identifying conditions that suppress satellite droplet formation and comparing model predictions with experimental data.

Contribution

It provides a detailed comparison between lubrication approximation models and experiments for micron-sized jet breakup, highlighting the effects of velocity and viscosity.

Findings

Satellite droplet formation can be suppressed in certain parameter regimes.

Lubrication model predictions agree with experiments on pinch-off times and droplet velocities.

Deviations occur between models and experiments at the final pinch-off shape.

Abstract

Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $\tau_\mathrm{c} = \sqrt{\rho r^3 / \gamma}$ of the order of 100\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Shi, Brenner, and Nagel, Science 265, 219 (1994)]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off between the lubrication approximation model and a boundary integral (BI) calculation, showing deviations at the final moment of the pinch-off. Inspite of this discrepancy, the results on pinch-off times and droplet and satellite droplet velocity obtained from the lubrication approximation agree with the high-speed imaging results.