Breakup of diminutive Rayleigh jets

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 τc=ρr3/γ of the order of 100 ns, and requires imaging at 14×106 frames/s. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [J. Eggers and T. F. Dupont, J. Fluid Mech. 262, 205 (1994); X. D. Shi, M. P. Brenner, and S. R. 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 calculation, showing deviations at the final moment of the pinch-off. In spite 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.