Bubbles in inkjet printheads: analytical and numerical models

R.J.M. Jeurissen

Abstract

The phenomenon of nozzle failure of an inkjet printhead due to entrainment of air bubbles was studies using analytical and numerical models. The studied inkjet printheads consist of many channels in which an acoustic field is generated to eject a droplet. When an air bubble is entrained, it disrupts the droplet formation process. This phenomenon is called nozzle failure. A very simple analytical model of a bubble in a nozzle was shown to qualitatively capture the dependence of the droplet velocity on the bubble volume. A more advanced model in which the two-way coupling between the channel acoustics and the bubble volume oscillations is taken into account, is shown to quantitatively agree with experimental data. The two-way coupling between bubble volume oscillations and channel acoustics is essential in this case. To determine when two-way coupling can be neglected, a complete set of dimensionless groups is derived. This set of dimensionless groups yields sharp criteria for the significance of two-wat coupling and for nonlinearity in the volume oscillations. A fully nonlinear numerical model is developed to test the predictions from the dimensionless groups. The predictions are confirmed by the results from the numerical model. This model is extended to also calculate the translational motion of the bubble and its growth by rectified diffusion. The effects that cause air entrainment were also studied. The outside of the printhead is coated by a thin ink film. This ink film flows whenever the printhead is actuated due to Marangoni stress. This flow is the first link in a chain of events that causes air entrainment. A careful analysis of the governing equations shows that these thin Marangoni flows satisfy potential flow. This result is used to analytically calculate the evolution of a moving droplet and a fingering instability, and the theoretical predictions are confirmed by the observations.
Original languageUndefined
Awarding Institution
  • University of Twente
Supervisors/Advisors
  • Lohse, Detlef , Supervisor
Date of Award23 Oct 2009
Place of PublicationEnschede
Publisher
Print ISBNs9789036529211
DOIs
StatePublished - 23 Oct 2009

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bubbles
entrainment
nozzles
air
inks
oscillations
acoustics
predictions
potential flow
translational motion
causes
nonlinearity

Keywords

  • IR-68237
  • METIS-260004

Cite this

Jeurissen, R.J.M.. / Bubbles in inkjet printheads: analytical and numerical models. Enschede : GildePrint, 2009. 149 p.
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abstract = "The phenomenon of nozzle failure of an inkjet printhead due to entrainment of air bubbles was studies using analytical and numerical models. The studied inkjet printheads consist of many channels in which an acoustic field is generated to eject a droplet. When an air bubble is entrained, it disrupts the droplet formation process. This phenomenon is called nozzle failure. A very simple analytical model of a bubble in a nozzle was shown to qualitatively capture the dependence of the droplet velocity on the bubble volume. A more advanced model in which the two-way coupling between the channel acoustics and the bubble volume oscillations is taken into account, is shown to quantitatively agree with experimental data. The two-way coupling between bubble volume oscillations and channel acoustics is essential in this case. To determine when two-way coupling can be neglected, a complete set of dimensionless groups is derived. This set of dimensionless groups yields sharp criteria for the significance of two-wat coupling and for nonlinearity in the volume oscillations. A fully nonlinear numerical model is developed to test the predictions from the dimensionless groups. The predictions are confirmed by the results from the numerical model. This model is extended to also calculate the translational motion of the bubble and its growth by rectified diffusion. The effects that cause air entrainment were also studied. The outside of the printhead is coated by a thin ink film. This ink film flows whenever the printhead is actuated due to Marangoni stress. This flow is the first link in a chain of events that causes air entrainment. A careful analysis of the governing equations shows that these thin Marangoni flows satisfy potential flow. This result is used to analytically calculate the evolution of a moving droplet and a fingering instability, and the theoretical predictions are confirmed by the observations.",
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Jeurissen, RJM 2009, 'Bubbles in inkjet printheads: analytical and numerical models', University of Twente, Enschede. DOI: 10.3990/1.9789036529211

Bubbles in inkjet printheads: analytical and numerical models. / Jeurissen, R.J.M.

Enschede : GildePrint, 2009. 149 p.

Research output: ScientificPhD Thesis - Research UT, graduation UT

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T1 - Bubbles in inkjet printheads: analytical and numerical models

AU - Jeurissen,R.J.M.

PY - 2009/10/23

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N2 - The phenomenon of nozzle failure of an inkjet printhead due to entrainment of air bubbles was studies using analytical and numerical models. The studied inkjet printheads consist of many channels in which an acoustic field is generated to eject a droplet. When an air bubble is entrained, it disrupts the droplet formation process. This phenomenon is called nozzle failure. A very simple analytical model of a bubble in a nozzle was shown to qualitatively capture the dependence of the droplet velocity on the bubble volume. A more advanced model in which the two-way coupling between the channel acoustics and the bubble volume oscillations is taken into account, is shown to quantitatively agree with experimental data. The two-way coupling between bubble volume oscillations and channel acoustics is essential in this case. To determine when two-way coupling can be neglected, a complete set of dimensionless groups is derived. This set of dimensionless groups yields sharp criteria for the significance of two-wat coupling and for nonlinearity in the volume oscillations. A fully nonlinear numerical model is developed to test the predictions from the dimensionless groups. The predictions are confirmed by the results from the numerical model. This model is extended to also calculate the translational motion of the bubble and its growth by rectified diffusion. The effects that cause air entrainment were also studied. The outside of the printhead is coated by a thin ink film. This ink film flows whenever the printhead is actuated due to Marangoni stress. This flow is the first link in a chain of events that causes air entrainment. A careful analysis of the governing equations shows that these thin Marangoni flows satisfy potential flow. This result is used to analytically calculate the evolution of a moving droplet and a fingering instability, and the theoretical predictions are confirmed by the observations.

AB - The phenomenon of nozzle failure of an inkjet printhead due to entrainment of air bubbles was studies using analytical and numerical models. The studied inkjet printheads consist of many channels in which an acoustic field is generated to eject a droplet. When an air bubble is entrained, it disrupts the droplet formation process. This phenomenon is called nozzle failure. A very simple analytical model of a bubble in a nozzle was shown to qualitatively capture the dependence of the droplet velocity on the bubble volume. A more advanced model in which the two-way coupling between the channel acoustics and the bubble volume oscillations is taken into account, is shown to quantitatively agree with experimental data. The two-way coupling between bubble volume oscillations and channel acoustics is essential in this case. To determine when two-way coupling can be neglected, a complete set of dimensionless groups is derived. This set of dimensionless groups yields sharp criteria for the significance of two-wat coupling and for nonlinearity in the volume oscillations. A fully nonlinear numerical model is developed to test the predictions from the dimensionless groups. The predictions are confirmed by the results from the numerical model. This model is extended to also calculate the translational motion of the bubble and its growth by rectified diffusion. The effects that cause air entrainment were also studied. The outside of the printhead is coated by a thin ink film. This ink film flows whenever the printhead is actuated due to Marangoni stress. This flow is the first link in a chain of events that causes air entrainment. A careful analysis of the governing equations shows that these thin Marangoni flows satisfy potential flow. This result is used to analytically calculate the evolution of a moving droplet and a fingering instability, and the theoretical predictions are confirmed by the observations.

KW - IR-68237

KW - METIS-260004

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M3 - PhD Thesis - Research UT, graduation UT

SN - 9789036529211

PB - GildePrint

ER -

Jeurissen RJM. Bubbles in inkjet printheads: analytical and numerical models. Enschede: GildePrint, 2009. 149 p. Available from, DOI: 10.3990/1.9789036529211