Nonlinear viscous liquid jets from a rotating orifice

Abstract

A liquid jet follows a curved trajectory when the orifice from which the jet emerges is rotating. Surface-tension-driven instabilities cause the jet to lose coherence and break to form droplets. The sizes of the drops formed from such jets are in general not uniform, ranging from drops with diameters of the order of the jet diameter to droplets with diameters which are several orders of magnitude smaller. This presentation details a theoretical investigation of the effects of changing operating parameters on the break-up of curved liquid jets in stagnant air at room temperature and pressure. The Navier–Stokes equations are solved in this system with the usual viscous free-surface boundary conditions, using an asymptotic method based upon a slender-jet assumption, which is clearly appropriate from experimental observations of the jet. Nonlinear temporal simulations of the break-up of the liquid jets using slender theory are also presented. These simulations based upon both a steady-trajectory assumption, and the more general equations which allow for an unsteady trajectory, show all the break-up modes viewed in experiments. Satellite-droplet formation is also considered.