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Published in: Experiments in Fluids 4/2014

01-04-2014 | Research Article

High-speed monodisperse droplet generation by ultrasonically controlled micro-jet breakup

Authors: Philipp Erhard Frommhold, Alexander Lippert, Frank Ludwig Holsteyns, Robert Mettin

Published in: Experiments in Fluids | Issue 4/2014

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Abstract

A liquid jet that is ejected from a nozzle into air will disintegrate into drops via the well-known Plateau–Rayleigh instability within a certain range of Ohnesorge and Reynolds numbers. With the focus on the micrometer scale, we investigate the control of this process by superimposing a suitable ultrasonic signal, which causes the jet to break up into a very precise train of monodisperse droplets. The jet leaves a pressurized container of liquid via a small orifice of about 20 μm diameter. The break-up process and the emerging droplets are recorded via high-speed imaging. An extended parameter study of exit speed and ultrasonic frequency is carried out for deionized water to evaluate the jet’s state and the subsequent generation of monodisperse droplets. Maximum exit velocities obtained reach almost 120 m s−1, and frequencies have been applied up to 1.8 MHz. Functionality of the method is confirmed for five additional liquids for moderate jet velocities \(\lesssim\)38 m s−1. For the uncontrolled jet disintegration, the drop size spectra revealed broad distributions and downstream drop growth by collision, while the acoustic control generated monodisperse droplets with a standard deviation less than 0.5 %. By adjustment of the acoustic excitation frequency, drop diameters could be tuned continuously from about 30 to 50 μm for all exit speeds. Good agreement to former experiments and theoretical approaches is found for the relation of overpressure and jet exit speed, and for the observed stability regions of monodisperse droplet generation in the parameter plane of jet speed and acoustic excitation frequency. Fitting of two free parameters of the general theory to the liquids and nozzles used is found to yield an even higher precision. Furthermore, the high-velocity instability limit of regular jet breakup described by von Ohnesorge has been superseded by more than a factor of two without entering the wind-induced instability regime, and monodisperse droplet generation was always achievable. Thus, the reliable and robust realization of tunable high-speed monodisperse micro-droplet trains is demonstrated. Some implication for applications is discussed.

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Footnotes
1
Please note the difference between the acoustic wavelength of sound propagation, \(\lambda _{{\mathrm{s}}}=c/f\) with the speed of sound c, and the spatial disturbance wavelength \(\lambda\) that describes the disturbances along the liquid jet.
 
2
The typical time scale on which drop pinch-off occurs can be roughly estimated (Eggers 1997) by \(\tau \sim \sqrt{\rho a^{3}/\sigma }\) and yields \(\tau \approx 4\,\upmu \hbox{s}\) for water and a nozzle of 20 μm in diameter. This shows the demand of short exposure times and high-speed recordings.
 
3
For the disintegration of an unperturbed liquid jet, the location of jet breakup is not constant over time. The error bars in Fig. 10 depict this uncertainty.
 
4
As the recordings for the image processing were not synchronized to the drop separation frequency, the exact position and thus the state of relaxation oscillation to spherical was different for each imaged drop. Although the ellipsoidal contour shape was corrected to axisymmetric volume, the optical resolution limit (\(\sim\)2 μm/pix) together with some motion blurring lead to the observed drop size variations.
 
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Metadata
Title
High-speed monodisperse droplet generation by ultrasonically controlled micro-jet breakup
Authors
Philipp Erhard Frommhold
Alexander Lippert
Frank Ludwig Holsteyns
Robert Mettin
Publication date
01-04-2014
Publisher
Springer Berlin Heidelberg
Published in
Experiments in Fluids / Issue 4/2014
Print ISSN: 0723-4864
Electronic ISSN: 1432-1114
DOI
https://doi.org/10.1007/s00348-014-1716-6

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