Microbubbles entrained in a piezo-driven drop-on-demand printhead disturb the acoustics of the microfluidic ink channel and, thereby, the jetting behavior. Here, the resonance behavior of an ink channel as a function of the microbubble size and number of bubbles is studied through theoretical modeling and experiments. The system is modeled as a set of two coupled harmonic oscillators: one corresponds to the compliant ink channel and the other corresponds to the microbubble. The predicted and measured eigenfrequencies are in excellent agreement. It was found that the resonance frequency is independent of the bubble size as long as the compliance of the bubble dominates over that of the piezo actuator. An accurate description of the eigenfrequency of the coupled system requires the inclusion of the increased inertance of the entrained microbubble due to confinement. It is shown that the inertance of a confined bubble can be accurately obtained by using a simple potential flow approach. The model is further validated by the excellent agreement between the modeled and measured microbubble resonance curves. The present work, therefore, provides physical insight into the coupled dynamics of a compliant ink channel with an entrained microbubble.
References
1.
B.
Derby
, “Inkjet printing of functional and structural materials: Fluid property requirements, feature stability, and resolution
,” Annu. Rev. Mater. Res.
40
, 395
–414
(2010
).2.
H.
Wijshoff
, “The dynamics of the piezo inkjet printhead operation
,” Phys. Rep.
491
, 77
–177
(2010
).3.
R.
Daly
, T.
Harrington
, G.
Martin
, and I.
Hutchings
, “Inkjet printing for pharmaceutics—A review of research and manufacturing
,” Int. J. Pharm.
494
(2
), 554
–567
(2015
).4.
D.
Lohse
, “Fundamental fluid dynamics challenges in inkjet printing
,” Ann. Rev. Fluid Mech.
54
, 349
–382
(2022
).5.
S. D.
Hoath
, Fundamentals of Inkjet Printing: The Science of Inkjet and Droplets
(Wiley-VCH
, Weinheim, Germany
, 2015
).6.
J. F.
Dijksman
, Design of Piezo Inkjet Print Heads: From Acoustics to Applications
(Wiley
, New York
, 2019
).7.
S.
Majee
, M.
Song
, S.-L.
Zhang
, and Z.-B.
Zhang
, “Scalable inkjet printing of shear-exfoliated graphene transparent conductive films
,” Carbon
102
, 51
–57
(2016
).8.
S.
Majee
, C.
Liu
, B.
Wu
, S.-L.
Zhang
, and Z.-B.
Zhang
, “Ink-jet printed highly conductive pristine graphene patterns achieved with water-based ink and aqueous doping processing
,” Carbon
114
, 77
–83
(2017
).9.
S.
Eshkalak
, A.
Cinnappan
, W.
Jayathilaka
, M.
Khatibzadeh
, E.
Kowsari
, and S.
Ramakrishna
, “A review on inkjet printing of CNT composites for smart applications
,” Appl. Mater. Today
9
, 372
–386
(2017
).10.
M.
Vilardell
, X.
Granados
, S.
Ricart
, I. V.
Driessche
, A.
Palau
, T.
Puig
, and X.
Obradors
, “Flexible manufacturing of functional ceramic coatings by inkjet printing
,” Thin Solid Films
548
, 489
–497
(2013
).11.
A.
Moya
, G.
Gabriel
, R.
Villa
, and F. J.
del Campo
, “Inkjet-printed electrochemical sensors
,” Curr. Opin. Electrochem.
3
(1
), 29
–39
(2017
).12.
T.
Eggenhuisen
, Y.
Galagan
, E.
Coenen
, W.
Voorthuijzen
, M.
Slaats
, S.
Kommeren
, S.
Shanmuganam
, M.
Coenen
, R.
Andriessen
, and W.
Groen
, “Digital fabrication of organic solar cells by inkjet printing using non-halogenated solvents
,” Sol. Energy Mater. Sol. Cells
134
, 364
–372
(2015
).13.
S.
Hashmi
, M.
Ozkan
, J.
Halme
, K.
Misic
, S.
Zakeeruddin
, J.
Paltakari
, M.
Grätzel
, and P.
Lund
, “High performance dye-sensitized solar cells with inkjet printed ionic liquid electrolyte
,” Nano Energy
17
, 206
–215
(2015
).14.
T.
Shimoda
, K.
Morii
, S.
Seki
, and H.
Kiguchi
, “Inkjet printing of light-emitting polymer displays
,” Inkjet Print. Funct. Mater.
28
(11
), 821
–827
(2003
).15.
C.
Jiang
, L.
Mu
, J.
Zou
, Z.
He
, Z.
Zhong
, L.
Wang
, M.
Xu
, J.
Wang
, J.
Peng
, and Y.
Cao
, “Full-color quantum dots active matrix display fabricated by ink-jet printing
,” Sci. China Chem.
60
(10
), 1349
–1355
(2017
).16.
B.
Derby
, “Additive manufacture of ceramic components by inkjet printing
,” Engineering
1
(1
), 113
–123
(2015
).17.
A.
Simaite
, F.
Mesnilgrente
, B.
Tondu
, P.
Souères
, and C.
Bergaud
, “Towards inkjet printable conducting polymer artifical muscles
,” Sens. Actuators B: Chem.
229
, 425
–433
(2016
).18.
S.
Hewes
, A.
Wong
, and P.
Searson
, “Bioprinting microvessels using and inkjet printer
,” Bioprinting
7
, 14
–18
(2017
).19.
M.
Nakamura
, A.
Kobayashi
, F.
Takagi
, A.
Watanabe
, Y.
Hiruma
, K.
Ohuchi
, Y.
Iwasaki
, M.
Horie
, I.
Morita
, and S.
Takatani
, “Biocompatible inkjet printing technique for designed seeding of individual living cells
,” Tissue Eng.
11
(11-12
), 1658
–1666
(2005
).20.
G.
Villar
, A.
Graham
, and H.
Bayley
, “A tissue-like printed material
,” Science
340
(6128
), 48
–52
(2013
).21.
A.
Fraters
, M.
van den Berg
, Y.
de Loore
, H.
Reinten
, H.
Wijshoff
, D.
Lohse
, M.
Versluis
, and T.
Segers
, “Inkjet nozzle failure by heterogeneous nucleation: Bubble entrainment, cavitation, and diffusive growth
,” Phys. Rev. Appl.
12
(6
), 064019
(2019
).22.
J.
de Jong
, G.
de Bruin
, H.
Reinten
, M.
van den Berg
, H.
Wijshoff
, M.
Versluis
, and D.
Lohse
, “Air entrapment in piezo-driven inkjet printheads
,” J. Acoust. Soc. Am.
120
(3
), 1257
–1265
(2006
).23.
J.
de Jong
, R.
Jeurissen
, H.
Borel
, M.
van den Berg
, H.
Wijshoff
, H.
Reinten
, M.
Versluis
, A.
Prosperetti
, and D.
Lohse
, “Entrapped air bubbles in piezo-driven inkjet printing: Their effect on the droplet velocity
,” Phys. Fluids
18
(12
), 121511
(2006
).24.
R.
Jeurissen
, J.
de Jong
, H.
Reinten
, M.
van den Berg
, H.
Wijshoff
, M.
Versluis
, and D.
Lohse
, “Effect of an entrained air bubble on the acoustics of an ink channel
,” J. Acoust. Soc. Am.
123
(5
), 2496
–2505
(2008
).25.
R.
Jeurissen
, A.
van der Bos
, H.
Reinten
, M.
van den Berg
, H.
Wijshoff
, J.
de Jong
, M.
Versluis
, and D.
Lohse
, “Acoustic measurement of bubble size in an inkjet printhead
,” J. Acoust. Soc. Am.
126
(5
), 2184
–2190
(2009
).26.
S.
Lee
, D.
Kwon
, and Y.
Choi
, “Dynamics of entrained air bubbles inside a piezodriven inkjet printhead
,” Appl. Phys. Lett.
95
(22
), 221902
(2009
).27.
B.-H.
Kim
, T.-G.
Kim
, T.-K.
Lee
, S.
Kim
, S.-J.
Shin
, S.-J.
Kim
, and S.-J.
Lee
, “Effects of trapped air bubbles on frequency responses of the piezo-driven inkjet printheads and visualization of the bubbles using synchrotron X-ray
,” Sens. Actuators A: Phys.
154
(1
), 132
–139
(2009
).28.
R.
Jeurissen
, H.
Wijshoff
, M.
van den Berg
, H.
Reinten
, and D.
Lohse
, “Regimes of bubble volume oscillations in a pipe
,” J. Acoust. Soc. Am.
130
(5
), 3220
–3232
(2011
).29.
A.
van der Bos
, T.
Segers
, R.
Jeurissen
, M.
van den Berg
, H.
Reinten
, H.
Wijshoff
, M.
Versluis
, and D.
Lohse
, “Infrared imaging and acoustic sizing of a bubble inside a micro-electro-mechanical system piezo ink channel
,” J. Appl. Phys.
110
(3
), 034503
(2011
).30.
A.
Fraters
, T.
Segers
, M.
van den Berg
, H.
Reinten
, H.
Wijshoff
, D.
Lohse
, and M.
Versluis
, “Shortwave infrared imaging setup to study entrained air bubble dynamics in a MEMS-based piezo-acoustic inkjet printhead
,” Exp. Fluids
60
(8
), 123
(2019
).31.
32.
A.
Fraters
, R.
Jeurissen
, M.
van den Berg
, Y.
de Loore
, H.
Reinten
, H.
Wijshoff
, D.
van der Meer
, D.
Lohse
, M.
Versluis
, and T.
Segers
, “Meniscus oscillations driven by flow-focusing lead to bubble pinch-off and entrainment in a piezo acoustic inkjet nozzle
,” Phys. Rev. Appl.
16
(4
), 044052
(2021
).33.
M.-J.
van der Meulen
, H.
Reinten
, H.
Wijshoff
, M.
Versluis
, D.
Lohse
, and P.
Steen
, “Nonaxisymmetric effects in drop-on-demand piezoacoustic inkjet printing
,” Phys. Rev. Appl.
13
(5
), 054071
(2020
).34.
L. A.
Crum
, “Bjerknes forces on bubbles in a stationary sound field
,” J. Acoust. Soc. Am.
57
(6
), 1363
–1370
(1975
).35.
L.
Crum
, “Rectified diffusion
,” Ultrasonics
22
(5
), 215
–223
(1984
).36.
37.
M.
Brenner
, S.
Hilgenfeldt
, and D.
Lohse
, “Single-bubble sonoluminescence
,” Rev. Mod. Phys.
74
(2
), 425
–484
(2002
).38.
N. P.
Hine
, “Deaeration system for a high-performance drop-on-demand ink jet
,” J. Imaging Technol.
17
(5
), 223
–227
(1991
).39.
J.
Brock
, I.
Cohen
, I.
Ivanov
, H.
Le
, and J.
Roy
, “Oscillations of an air bubble in an ink jet
,” J. Appl. Photogr. Eng.
10
(3
), 127
–129
(1984
).40.
J.
De Jong
, H.
Reinten
, H.
Wijshoff
, M.
Van Den Berg
, K.
Delescen
, R.
Van Dongen
, F.
Mugele
, M.
Versluis
, and D.
Lohse
, “Marangoni flow on an inkjet nozzle plate
,” Appl. Phys. Lett.
91
(20
), 204102
(2007
).41.
W.
Lauterborn
, “Numerical investigation of nonlinear oscillations of gas bubbles in liquids
,” J. Acoust. Soc. Am.
59
(2
), 283
–293
(1976
).42.
43.
M.
Versluis
, E.
Stride
, G.
Lajoinie
, B.
Dollet
, and T.
Segers
, “Ultrasound contrast agents modeling
,” Ultrasound Med. Biol.
46
, 2117
–2144
(2020
).44.
M.
Minnaert
, “On musical air-bubbles and the sound of running water
,” Philos. Mag.
16
(104
), 235
–248
(1933
).45.
K.-S.
Kwon
and W.
Kim
, “A waveform design method for high-speed inkjet printing based on self-sensing measurement
,” Sens. Actuators A: Phys.
140
(1
), 75
–83
(2007
).46.
K.-S.
Kwon
, “Methods for detecting air bubble in piezo inkjet dispensers
,” Sens. Actuators A: Phys.
153
(1
), 50
–56
(2009
).47.
B.-H.
Kim
, H.-S.
Lee
, S.-W.
Kim
, P.
Kang
, and Y.-S.
Park
, “Hydrodynamic responses of a piezoelectric driven MEMS inkjet print-head
,” Sens. Actuators A: Phys.
210
, 131
–140
(2014
).48.
J.
Dijksman
, “Hydro-acoustics of piezoelectrically driven ink-jet print heads
,” Flow, Turbul. Combust.
61
, 211
–237
(1998
).49.
50.
U.
Ingard
, “On the theory and design of acoustic resonators
,” J. Acoust. Soc. Am.
25
(6
), 1037
–1061
(1953
).51.
L. D.
Landau
, J.
Bell
, M.
Kearsley
, L.
Pitaevskii
, E.
Lifshitz
, and J.
Sykes
, Electrodynamics of Continuous Media
(Elsevier
, New York
, 2013
), Vol. 8
.52.
T.
Segers
and M.
Versluis
, “Acoustic bubble sorting for ultrasound contrast agent enrichment
,” Lab. Chip
14
(10
), 1705
–1714
(2014
).53.
H.
Oguz
and A.
Prosperetti
, “The natural frequency of oscillation of gas bubbles in tubes
,” J. Acoust. Soc. Am.
103
(6
), 3301
–3308
(1998
).54.
V.
Garbin
, D.
Cojoc
, E.
Ferrari
, E.
Di Fabrizio
, M.
Overvelde
, S.
Van Der Meer
, N.
De Jong
, D.
Lohse
, and M.
Versluis
, “Changes in microbubble dynamics near a boundary revealed by combined optical micromanipulation and high-speed imaging
,” Appl. Phys. Lett.
90
(11
), 114103
(2007
).55.
C.
Devin
, “Survey of thermal, radiation, and viscous damping of pulsating air bubbles in water
,” J. Acoust. Soc. Am.
31
(12
), 1654
–1667
(1959
).56.
J.
Sijl
, M.
Overvelde
, B.
Dollet
, V.
Garbin
, N.
de Jong
, D.
Lohse
, and M.
Versluis
, “‘Compression-only’ behavior: A second-order nonlinear response of ultrasound contrast agent microbubbles
,” J. Acoust. Soc. Am.
129
(4
), 1729
–1739
(2011
).57.
A.
Prosperetti
, “Nonlinear oscillations of gas bubbles in liquids: Steady-state solutions
,” J. Acoust. Soc. Am.
56
, 878
–885
(1974
).58.
C.
Church
, “The effects of an elastic solid surface layer on the radial pulsations of gas bubbles
,” J. Acoust. Soc. Am.
97
(3
), 1510
–1521
(1995
).© 2022 Acoustical Society of America.
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