Abstract
Drop generation from an axially vibrating nozzle exhibits a transition in drop diameter when varying the vibration amplitude. Below a threshold amplitude, forcing has essentially no effect on drop size and drops form in dripping mode. Above the threshold, drop size is controlled by forcing: drops detach at resonance, i.e., when the first eigenfrequency of the growing drop coincides with the forcing frequency. We experimentally study the impact of the nozzle inner diameter, dispersed phase flow rate, interfacial tension, and dispersed phase viscosity on this transition. Drop diameter is well correlated to the mode 1 eigenfrequency of Strani and Sabetta for a drop in partial contact with a spherical bowl. We propose a transient model to describe drop dynamics until detachment. The drop is modelled as a linearly forced harmonic oscillator, with the eigenfrequency of Strani and Sabetta. Since the dispersed phase does not wet the nozzle tip, an additional damping coefficient is introduced to account for the viscous dissipation in the film of continuous phase between the drop and nozzle surface. The model adequately reproduces the effect of the different parameters on the threshold amplitude.
Highlights
Inducing vibration to jets or drops can be used to control breakup, drop size
We found that at a set forcing frequency, smaller drops were generated above a threshold forcing amplitude: a growing drop detached prematurely when its first resonance frequency and the forcing frequency coincided
We examine the effect of these parameters on (i) the threshold amplitude for the stretching mode and (ii) the resulting drop diameters
Summary
Inducing vibration to jets or drops can be used to control breakup, drop size. Vibration is applied for example in ink jet printing, spray coating or vibrating cross-flow membrane emulsification, the latter having motivated our research. Smithwick and Boulet[9] studied the first resonance frequency of mercury drops on glass (pinned contact line) under partial vacuum and compared their data to the calculations of S&S.7. Noblin et al.[13] studied bound drop oscillations with mobile instead of pinned contact lines: a decrease in resonance frequency was found. Wilkes and Basaran[14] (hereafter denoted W&B) used computational fluid dynamics (CFD) to study large-amplitude axisymmetric oscillations of a viscous bound drop on a rod (pinned contact line). They found that the drop resonance frequency varies slightly with amplitude at high Ohnesorge numbers (Oh, expressed in section V.B.) but decreases significantly with amplitude at low Oh, Oh being the ratio of a viscocapillary to an inertial-capillary timescale.
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