Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Air bubbles entrapped in the ink channel are a major problem in piezo-driven inkjet printing. They grow by rectified diffusion and eventually counteract the pressure buildup at the nozzle, leading to a breakdown of the jetting process. Experimental results on the droplet velocity u drop as a function of the equilibrium radius R 0 of the entrained bubble are presented. Surprisingly, u drop ͑R 0 ͒ shows a pronounced maximum around R 0 =17 m before it sharply drops to zero around R 0 =19 m. A simple one-dimensional model is introduced to describe this counterintuitive behavior which turns out to be a resonance effect of the entrained bubble.

The volume of a bubble in a piezoinkjet printhead is measured acoustically. The method is based on a numerical model of the investigated system. The piezo not only drives the system but it is also used as a sensor by measuring the current it generates. The numerical model is used to predict this current for a given bubble volume. The inverse problem is to infer the bubble volume from an experimentally obtained piezocurrent. By solving this inverse problem, the size and position of the bubble can thus be measured acoustically. The method is experimentally validated with an inkjet printhead that is augmented with a glass connection channel, through which the bubble was observed optically, while at the same time the piezocurrent was measured. The results from the acoustical measurement method correspond closely to the results from the optical measurement.

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The stability of high-end piezoacoustic drop-on-demand (DOD) inkjet printing is sometimes compromised by the entrainment of an air bubble inside the ink channel. Here, bubble pinch-off from an oscillating meniscus is studied in an optically transparent DOD printhead as a function of the driving waveform. We show that bubble pinch-off follows from low-amplitude high-frequency meniscus oscillations on top of the global high-amplitude low-frequency meniscus motion that drives droplet formation. In a certain window of control parameters, phase inversion between the low-and high-frequency components leads to the enclosure of an air cavity and bubble pinch-off. Although phenomenologically similar, bubble pinch-off is not a result of capillary-wave interaction such as observed in drop impact on a liquid pool. Instead, we reveal geometrical-flow focusing as the mechanism through which, at first, an outward jet is formed on the retracted concave meniscus. The subsequent high-frequency velocity oscillation acts on the now toroidal-shaped meniscus and it accelerates the toroidal ring outward, resulting in the formation of an air cavity that can pinch off. Through incompressible boundary-integral simulations, we reveal that bubble pinch-off requires an unbalance between the capillary and inertial time scales and that it does not require acoustics. The critical control parameters for pinch-off are the pulse timing and amplitude. To cure the bubble entrainment problem, the threshold for bubble pinch-off can be increased by suppressing the highfrequency driving through appropriate waveform design. The present work therefore aids the improvement of the stability of inkjet printers through a physical understanding of meniscus instabilities.

Piezo-driven inkjet systems are very sensitive to air entrapment. The entrapped air bubbles grow by rectified diffusion in the ink channel and finally result in nozzle failure. Experimental results on the dynamics of fully grown air bubbles are presented. It is found that the bubble counteracts the pressure buildup necessary for the droplet formation. The channel acoustics and the air bubble dynamics are modeled. For good agreement with the experimental data it is crucial to include the confined geometry into the model: The air bubble acts back on the acoustic field in the channel and thus on its own dynamics. This two-way coupling limits further bubble growth and thus determines the saturation size of the bubble.