Research Papers

A Dynamical Model of Drop Spreading in Electrohydrodynamic Jet Printing

[+] Author and Article Information
Christopher P. Pannier

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: pannier@umich.edu

Mamadou Diagne

Department of Mechanical, Aerospace, and
Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180

Isaac A. Spiegel, Kira Barton

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

David J. Hoelzle

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

1Corresponding author.

Manuscript received May 18, 2017; final manuscript received July 13, 2017; published online September 13, 2017. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 139(11), 111008 (Sep 13, 2017) (6 pages) Paper No: MANU-17-1329; doi: 10.1115/1.4037436 History: Received May 18, 2017; Revised July 13, 2017

Electrohydrodynamic jet (e-jet) printing is a microscale additive manufacturing technique used to print microscale constructs, including next-generation biological and optical sensors. Despite the many advantages to e-jet over competing microscale additive manufacturing techniques, there do not exist validated models of build material drop formation in e-jet, relegating process design and control to be heuristic and ad hoc. This work provides a model to map deposited drop volume to final spread topography and validates this model over the drop volume range of 0.68–13.4 pL. The model couples a spherical cap volume conservation law to a molecular kinetic relationship for contact line velocity and assumes an initial contact angle of 180 deg to predict the drop shape dynamics of dynamic contact angle and dynamic base radius. For validation, the spreading of e-jet-printed drops of a viscous adhesive is captured by high-speed microscopy. Our model is validated to have a relative error less than 3% in dynamic contact angle and 1% in dynamic base radius.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Park, J.-U. , Hardy, M. , Kang, S. J. , Barton, K. , Adair, K. , Mukhopadhyay, D. K. , Lee, C. Y. , Strano, M. S. , Alleyne, A. G. , Georgiadis, J. G. , Ferreira, P. M. , and Rogers, J. A. , 2007, “ High-Resolution Electrohydrodynamic Jet Printing,” Nat. Mater., 6(10), pp. 782–789. [CrossRef] [PubMed]
Sutanto, E. , and Alleyne, A. , 2015, “ A Semi-Continuous Roll-to-Roll (R2R) Electrohydrodynamic Jet Printing System,” Mechatronics, 31, pp. 243–254. [CrossRef]
Sutanto, E. , Shigeta, K. , Kim, Y. K. , Graf, P. G. , Hoelzle, D. J. , Barton, K. L. , Alleyne, A. G. , Ferreira, P. M. , and Rogers, J. A. , 2012, “ A Multimaterial Electrohydrodynamic Jet (E-Jet) Printing System,” J. Micromech. Microeng., 22(4), p. 045008. [CrossRef]
Onses, M. S. , Sutanto, E. , Ferreira, P. M. , Alleyne, A. G. , and Rogers, J. A. , 2015, “ Mechanisms, Capabilities, and Applications of High-Resolution Electrohydrodynamic Jet Printing,” Small, 11(34), pp. 4237–4266. [CrossRef] [PubMed]
Wang, Z. , Pannier, C. , Ojeda, L. , Barton, K. , and Hoelzle, D. J. , 2016, “ An Application of Spatial Iterative Learning Control to Micro-Additive Manufacturing,” American Control Conference (ACC), Boston, MA, July 6–8, pp. 354–359.
Onses, M. S. , Song, C. , Williamson, L. , Sutanto, E. , Ferreira, P. M. , Alleyne, A. G. , Nealey, P. F. , Ahn, H. , and Rogers, J. A. , 2013, “ Hierarchical Patterns of Three-Dimensional Block-Copolymer Films Formed by Electrohydrodynamic Jet Printing and Self-Assembly,” Nat. Nanotechnol., 8(9), pp. 667–675. [CrossRef] [PubMed]
Park, J. U. , Lee, J. H. , Paik, U. , Lu, Y. , and Rogers, J. A. , 2008, “ Nanoscale Patterns of Oligonucleotides Formed by Electrohydrodynamic Jet Printing With Applications in Biosensing and Nanomaterials Assembly,” Nano Lett., 8(12), pp. 4210–4216. [CrossRef] [PubMed]
Kim, B. H. , Onses, M. S. , Lim, J. B. , Nam, S. , Oh, N. , Kim, H. , Yu, K. J. , Lee, J. W. , Kim, J.-H. , Kang, S.-K. , Lee, C. H. , Lee, J. , Shin, J. H. , Kim, N. H. , Leal, C. , Shim, M. , and Rogers, J. A. , 2015, “ High-Resolution Patterns of Quantum Dots Formed by Electrohydrodynamic Jet Printing for Light-Emitting Diodes,” Nano Lett., 15(2), pp. 969–973. [CrossRef] [PubMed]
Kim, K. , Kim, G. , Lee, B. R. , Ji, S. , Kim, S.-Y. , An, B. W. , Song, M. H. , and Park, J.-U. , 2015, “ High-Resolution Electrohydrodynamic Jet Printing of Small-Molecule Organic Light-Emitting Diodes,” Nanoscale, 7(32), pp. 13410–13415. [CrossRef] [PubMed]
Kim, C.-Y. , Jung, H. , Choi, H. , and Choi, D.-k. , 2016, “ Synthesis of One-Dimensional SnO2 Lines by Using Electrohydrodynamic Jet Printing for a NO Gas Sensor,” J. Korean Phys. Soc., 68(2), pp. 357–362. [CrossRef]
An, B. W. , Kim, K. , Kim, M. , Kim, S. Y. , Hur, S. H. , and Park, J. U. , 2015, “ Direct Printing of Reduced Graphene Oxide on Planar or Highly Curved Surfaces With High Resolutions Using Electrohydrodynamics,” Small, 11(19), pp. 2263–2268. [CrossRef] [PubMed]
Qin, H. , Cai, Y. , Dong, J. , and Lee, Y.-S. , 2016, “ Direct Printing of Capacitive Touch Sensors on Flexible Substrates by Additive E-Jet Printing With Silver Nanoinks,” ASME J. Manuf. Sci. Eng., 139(3), p. 031011. [CrossRef]
Park, J.-U. , Lee, S. , Unarunotai, S. , Sun, Y. , Dunham, S. , Song, T. , Ferreira, P. M. , Alleyene, A. G. , Paik, U. , and Rogers, J. A. , 2010, “ Nanoscale, Electrified Liquid Jets for High-Resolution Printing of Charge,” Nano Lett., 10(2), pp. 584–591. [CrossRef] [PubMed]
Mishra, S. , Barton, K. L. , Alleyne, A. G. , Ferreira, P. M. , and Rogers, J. A. , 2010, “ High-Speed and Drop-on-Demand Printing With a Pulsed Electrohydrodynamic Jet,” J. Micromech. Microeng., 20(9), p. 095026. [CrossRef]
Carter, W. , Popell, G. C. , Samuel, J. , and Mishra, S. , 2014, “ A Fundamental Study and Modeling of the Micro-Droplet Formation Process in Near-Field Electrohydrodynamic Jet Printing,” ASME J. Micro Nano-Manuf., 2(2), p. 021005. [CrossRef]
Pannier, C. , Wang, Z. , Hoelzle, D. , and Barton, K. , 2015, “ A Model of Liquid Drop Spreading for Electrohydrodynamic Jet Printing,” ASME Paper No. DSCC2015-9995.
De Ruijter, M. J. , Charlot, M. , Voué, M. , and De Coninck, J. , 2000, “ Experimental Evidence of Several Time Scales in Drop Spreading,” Langmuir, 16(5), pp. 2363–2368. [CrossRef]
Blake, T. D. , Clarke, A. , De Coninck, J. , and de Ruijter, M. J. , 1997, “ Contact Angle Relaxation During Droplet Spreading: Comparison Between Molecular Kinetic Theory and Molecular Dynamics,” Langmuir, 13(7), pp. 2164–2166. [CrossRef]
Harris, J. , and Stocker, H. , 1998, “ Spherical Segment (Spherical Cap),” Handbook of Mathematics and Computational Science, Springer-Verlag, New York, p. 107.
Duvivier, D. , Blake, T. D. , and De Coninck, J. , 2013, “ Toward a Predictive Theory of Wetting Dynamics,” Langmuir, 29(32), pp. 10132–10140. [CrossRef] [PubMed]
Duvivier, D. , Seveno, D. , Rioboo, R. , Blake, T. D. , and De Coninck, J. , 2011, “ Experimental Evidence of the Role of Viscosity in the Molecular Kinetic Theory of Dynamic Wetting,” Langmuir, 27(21), pp. 13015–13021. [CrossRef] [PubMed]
Gennes, P. D. , 1985, “ Wetting: Statics and Dynamics,” Rev. Mod. Phys., 57(3), pp. 827–863.
Thomas, S. M. , and Chan, Y. T. , 1989, “ A Simple Approach for the Estimation of Circular Arc Center and Its Radius,” Comput. Vision, Graphics Image Process., 45(3), pp. 362–370. [CrossRef]
MathWorks, 2017, Statistics and Machine Learning Toolbox User's Guide, The MathWorks Inc., Natick, MA.
Shampine, L. F. , and Reichelt, M. W. , 1997, “ The MATLAB ODE Suite,” SIAM J. Sci. Comput., 18(1), pp. 1–22. [CrossRef]
De Coninck, J. , and Blake, T. , 2008, “ Wetting and Molecular Dynamics Simulations of Simple Liquids,” Annu. Rev. Mater. Res., 38(1), pp. 1–22. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic of an e-jet printing system actuated by a pulsed voltage, with images of build material meniscus, jet, and drop

Grahic Jump Location
Fig. 2

At left: cropped high-speed images of a drop of volume Ω=7.5 pL and printing parameters Vh=1200 V, Tp=2.4 ms with automatically identified θ(t) and R(t) at two different time points. At right: renderings of spherical caps describing the drops, with a 1/3 section cutaway.

Grahic Jump Location
Fig. 3

The e-jet printer with a dashed white line showing a reflection axis and white rays showing the light path. Brightness and contrast have been enhanced around the nozzle.

Grahic Jump Location
Fig. 4

Each of 45 shaded bins indicates a 20-drop data set collected with the plotted Vh and Tp e-jet printing inputs. Inset at top right: drop volume versus printing inputs.

Grahic Jump Location
Fig. 5

Equation (5) is fitted to the collected data to obtain model parameters κ and λ using robust nonlinear least squares regression

Grahic Jump Location
Fig. 6

Measured R¯(t) and simulated R*(t) are plotted for three (Vh, Tp) pairs

Grahic Jump Location
Fig. 7

Relative error in the simulated θ*(t) and R*(t) is plotted for each (Vh, Tp) pair, with i = 1. Inset is the relative error averaged over all 45 (Vh, Tp) pairs with the average e(θ*) (filled circles) and the average e(R*) (filled squares) plotted for varying number of excluded initial frames i.



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