Oscillatory Incompressible Fluid Flow in a Tapered Tube With a Free Surface in an Inkjet Print Head

[+] Author and Article Information
Dong-Youn Shin

104-1 Munji-dong, Yoosung-ku, Taejon, South Korea

Telephone: +82-42-870-6057 Fax: +82-42-861-2585

e-mail: wonwhale@lgehem.com

Paul Grassia

School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, Sackville Street, Manchester M60 1QD, United Kingdom

Telephone: +44-161-306-8851 Fax +44-161-306-4399

e-mail: paul.grassia@manchester.ac.uk

Brian Derby

Manchester Materials Science Center, The University of Manchester, Grosvenor Street, Manchester M1 7HS, United Kingdom

Telephone: +44-161-200-3569 Fax: +44-161-200-8877

e-mail: brian.derby@manchester.ac.uk

J. Fluids Eng 127(1), 98-109 (Mar 22, 2005) (12 pages) doi:10.1115/1.1852474 History: Received September 23, 2002; Revised August 31, 2004; Online March 22, 2005
Copyright © 2005 by ASME
Your Session has timed out. Please sign back in to continue.


Antohe,  B. V., and Wallace,  D. B., 2002, “Acoustic Phenomena in a Demand Mode Piezoelectric Ink Jet Printer,” J. Imaging Sci. Technol., 46(5), pp. 409–414.
Khaskia, A. M., 2002, “Static and Dynamic Modeling of Piezoelectric Drivers in Drop on Demand Printing,” FEMCI Workshop, Maryland, USA.
Yeh, J. T., 2000, “Simulation and Industrial Applications of Inkjet,” Proceedings of the 7th National Computational Fluid Dynamics Conference, Kenting, Taiwan.
Yeh, J. T., 2001, “A VOF-FEM and Coupled Inkjet Simulation,” Proceedings of ASME Fluids Engineering Division Summer Meeting, The American Society of Mechanical Engineers, New York, USA.
Pan,  F., Kubby,  J., and Chen,  J., 2002, “Numerical Simulation of Fluid–Structure Interaction in a MEMS Diaphragm Drop Ejector,” J. Micromech. Microeng., 12, pp. 70–76.
Fromm,  J. E., 1984, “Numerical Calculation of the Fluid Dynamics of Drop-On-Demand Jets,” IBM J. Res. Dev., 28(3), pp. 322–333.
Shield,  T. W., Bogy,  D. B., and Talke,  F. E., 1986, “A Numerical Comparison of One-Dimensional Fluid Jet Models Applied to Drop-On-Demand Printing,” J. Comput. Phys., 67, pp. 327–347.
Shield,  T. W., Bogy,  D. B., and Talke,  F. E., 1987, “Drop Formation by DOD Ink-Jet Nozzles—A Comparison of Experiment and Numerical Simulation,” IBM J. Res. Dev., 31(1), pp. 96–110.
Adams,  R. L., and Roy,  J., 1986, “A One-Dimensional Numerical Model of a Drop-On-Demand Ink Jet,” ASME J. Appl. Mech., 53, pp. 193–197.
Liou,  T. M., Shih,  K. C., Chau,  S. W., and Chen,  S. C., 2002, “Three-Dimensional Simulations of the Droplet Formation During the Inkjet Printing Process,” Int. Commun. Heat Mass Transfer, 29(8), pp. 1109–1118.
Kyser,  E. L., Collins,  L. F., and Herbert,  N., 1981, “Design of an Impulse Ink Jet,” J. Appl. Photogr. Eng., 7(3), pp. 73–79.
Wallace, D. B., 1989, “A Method of Characteristics Model of a Drop-on-Demand Ink-Jet Device Using an Integral Method Drop Formation Model,” Proc. ASME Winter Ann. Meeting, San Francisco, CA, USA.
Chen,  P. H., Peng,  H. Y., Liu,  H. Y., Chang,  S. L., Wu,  T. I., and Cheng,  C. H., 1999, “Pressure Response and Droplet Ejection of a Piezoelectric Inkjet Printhead,” Int. J. Mech. Sci., 41(2), pp. 235–248.
Wilkes,  E. D., Phillips,  S. D., and Basaran,  O. A., 1999, “Computational and Experimental Analysis of Dynamics of Drop Formation,” Phys. Fluids, 11(12), pp. 3577–3598.
Teng,  K. F., 1988, “A Mathematical Model of Impulse Jet Mechanism,” Math. Comput. Modell., 11, pp. 751–753.
Koltay, P., Moosmann, C., Litterst, C., Streule, W., Birkenmeier, B., and Zengerle, R., 2002, “Modelling Free Jet Ejection on a System Level—an Approach for Microfluidics,” Technical Proceedings of the 2002 International Conference on Modeling and Simulation of Microsystems, San Juan, Puerto Rico, pp. 112–115.
Koltay, P., Moosmann, C., Litterst, C., Streule, W., and Zengerle, R., 2002, “Simulation of a Micro Dispenser Using Lumped Models,” Technical Proceedings of the 2002 International Conference on Modeling and Simulation of Microsystems, San Juan, Puerto Rico, pp. 170–173.
Dijksman,  J. F., 1984, “Hydrodynamics of Small Tubular Pumps,” J. Fluid Mech., 139, pp. 173–191.
Baek,  S. H., Jeong,  E. S., and Jeong,  S., 2000, “Two-Dimensional Model for Tapered Pulse Tubes. Part 1: Theoretical Modeling and Net Enthalpy Flow,” Cryogenics, 40, pp. 379–385.
Rembe,  C., Wiesche,  S., and Hofer,  E. P., 2000, “Thermal Ink Jet Dynamics: Modeling, Simulation, and Testing,” Microelectron. Reliab., 40, pp. 525–532.
Hart,  V. G., and Shi,  J., 1995, “Governing Equations for Wave Propagation in Prestressed Joined Dissimilar Elastic Tubes Containing Fluid Flow: With an Example for a Tapered Section,” Int. J. Eng. Sci., 33(8), pp. 1121–1138.
Chakravarty,  S., and Mandal,  P. K., 2000, “Two-Dimensional Blood Flow Through Tapered Arteries Under Stenotic Conditions,” Int. J. Non-Linear Mech., 35, pp. 779–793.
Bogy,  D. B., and Talke,  F. E., 1984, “Experimental and Theoretical Study of Wave Propagation Phenomena in Drop-On-Demand Ink Jet Devices,” IBM J. Res. Dev., 28(3), pp. 314–321.
Meinhart,  C. D., and Zhang,  H., 2000, “The Flow Structure Inside a Microfabricated Inkjet Printhead,” J. Microelectromech. Syst., 9(1), pp. 67–75.
Pierce, A. D., 1989, Acoustics: An Introduction to Its Physical Principles and Applications, The Acoustical Society of America, New York, USA, p. 348.
Rossing, T. D., and Fletcher, N. H., 1998, The Physics of Musical Instruments, 2nd ed., Springer, New York, USA, p. 200.
Shin,  D. Y., Grassia,  P., and Derby,  B., 2003, “Oscillatory Limited Compressible Fluid Flow Induced by the Radial Motion of a Thick-Walled Piezoelectric Tube,” J. Acoust. Soc. Am., 114(3), pp. 1314–1321.
Benjamin,  T. B., and Ursell,  F., 1954, “The Stability of the Plane Free Surface of a Liquid in Vertical Periodic Motion,” Proc. R. Soc. London, Ser. A, 225, pp. 505–515.
Valha,  J., and Kubie,  J., 1996, “Stability of a Gas–Liquid Interface in a Periodic Vertical Motion,” Chem. Eng. Sci., 51(22), pp. 4997–5006.
Technical Publication TP-226: Properties of Piezoelectricity Ceramics, Morgan Electro Ceramics, http://www.morganelectroceramics.com/pdfs/tp226.pdf
Chen,  A. U., and Basaran,  O. A., 2002, “A New Method for Significantly Reducing Drop Radius Without Reducing Nozzle Radius in Drop-On-Demand Drop Production,” Phys. Fluids, 14(1), pp. L1–L4.


Grahic Jump Location
Nozzle sectioning. (a) A set of discrete cylinders. (b) A set of continuous tapered nozzle sections
Grahic Jump Location
Schematic of the drop formation stages illustrated by FLOW 3D simulations. (a) Meniscus motion without deformation. (b) Meniscus deformation. (c) Inception of necking. (d) Break-off. The different intensity of shading represents different axial velocities.
Grahic Jump Location
Schematic drawing of the meniscus cross-section at the nozzle tip
Grahic Jump Location
Print head dimensions (Provided by MicroFab Inc.)
Grahic Jump Location
Voltage waveforms. (a) Three voltage waveforms for cases A–C. (b) Fourier series approximated voltage waveform for case C with 50 Fourier terms.
Grahic Jump Location
Comparison of F3(z) and its series function approximation T1(z) with four nozzle sections and four terms per section, and eight nozzle sections and eight terms per section. (a) Real part of these functions. (b) Imaginary part of these functions. (c) Overall error of series approximations.
Grahic Jump Location
Comparison of pressure results from numerical and analytical computations at 400 μm before the nozzle orifice on the axis. (a) Case A. (b) Case B. (c) Case C.
Grahic Jump Location
Computational domain of the last 400 μm of the nozzle for numerical simulations with FLOW 3D
Grahic Jump Location
Pressure and axial velocity comparisons. (a) Case A. (b) Case B. (c) Case C.
Grahic Jump Location
Volumetric flow rate comparisons. (a) Case A. (b) Case B. (c) Case C.
Grahic Jump Location
Schematic based on experimental observations of meniscus inversion by local deformation and extra mass transport. (a) Meniscus retreat. (b) Meniscus advance without window model (conventional assumption). (c) Meniscus advance with window model (present model). Retreat and advance are clearly asymmetric in time.
Grahic Jump Location
Elapsed time, Δt, from the moment of maximum meniscus retreat to the moment when an emerging jet reaches a hemispherical volume. (a) Against voltage at 5 kHz. (b) Against frequency at 60 V.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In