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Modeling and analysis of electrohydrodynamic printing under various pulsed voltage waveforms

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Abstract

Electrohydrodynamic (EHD) printing is a very promising approach for micro/nanoscopic additive manufacturing but suffers from printing stability problems due to the insufficient knowledge of its controlling techniques. Here, we conduct a numerical study on EHD printing under six unconventional pulsed voltage waveforms and investigate the influences of upward/downward voltage time and waveform shape on liquid behaviors and printing outcomes. With the assistance of the clear snapshots, voltage distribution, and interface charge density obtained from the numerical results, it is discovered that the three upward voltage waveforms only alter the duration of Taylor cone formation with very minor impact on the printing process and deposited droplet volume. On the other hand, all three downward voltage waveforms exert a significant influence on liquid behaviors. The printing processes under the trapezoidal down waveform are the most stable ones owing to the continuous and smooth voltage reduction. The processes under the two steps down waveform are similar to the trapezoidal down waveform but become unstable when the downward time is too long. Due to the two drastic voltage drops, the processes under the one step down waveform are the least stable and produce more satellite droplets than the other two waveforms. The volume of deposited droplet generally decreases with increasing downward time for all three waveforms, and the droplets produced under the one step down waveform are smaller than the other two waveforms, resulting from the rapidly reduced electric force after the voltage switches. To our best knowledge, this is the first numerical work on EHD printing under various unconventional waveforms. The results obtained in this paper provide useful addition to the understanding of its complicated mechanisms.

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Data availability

The data that support the findings of this study are available within the article.

Abbreviations

\(\overrightarrow{U}\) :

Liquid velocity

\(\rho\) :

Liquid density

\(\mu\) :

Liquid dynamic viscosity

\(\gamma\) :

Liquid surface tension coefficient

\(\varepsilon\) :

Liquid permittivity

\(K\) :

Liquid electrical conductivity

\(\overrightarrow{{F}_{\gamma }}\) :

Surface tension force

\(\kappa\) :

Mean curvature of liquid–gas interface

\(\widehat{n}\) :

Unit normal of gas–liquid interface

\(F\) :

VOF function

\(\Phi\) :

Electric voltage

\(\overrightarrow{E}\) :

Electric field

\(\overrightarrow{{F}_{e}}\) :

Electrostatic force

\({\rho }_{e}\) :

Liquid–gas interface charge density

\({t}_{u}\) :

Upward voltage time

\({t}_{d}\) :

Downward voltage time

\({t}_{f}\) :

Taylor cone formation time

\({t}_{j}\) :

Jetting time

\({t}_{o}\) :

Meniscus oscillation time

\({t}_{deta}\) :

Jet detachment time

\({V}_{d}\) :

Deposited droplet volume

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Acknowledgements

This work was supported by the National Key R&D Program of China (2021YFB3200701), and the National Natural Science Foundation of China (Nos. 51906073 and 52188102). The authors would also like to thank the Flexible Electronics Manufacturing Laboratory at the Comprehensive Experiment Center for access to advanced manufacturing and equipment technology. The computation is completed in the HPC Platform of Huazhong University of Science and Technology.

Funding

This work was supported by the National Key R&D Program of China (Grant number 2021YFB3200701), and the National Natural Science Foundation of China (Grant numbers 51906073 and 52188102).

Author information

Authors and Affiliations

  1. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Yin Guan, Mengduo Wang & Shuang Wu

  2. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Yu Tian, Dong Ye & YongAn Huang

Authors
  1. Yin Guan
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  4. Yu Tian
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  5. Dong Ye
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Contributions

Conceptualization: YG; methodology: YG, MW; formal analysis and investigation: YG, MW, SW, YT; writing—original draft preparation: YG, DY; writing—review and editing: DY, YAH; funding acquisition: YG, YAH; supervision: YAH.

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Correspondence to Dong Ye or YongAn Huang.

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Guan, Y., Wang, M., Wu, S. et al. Modeling and analysis of electrohydrodynamic printing under various pulsed voltage waveforms. Microfluid Nanofluid 27, 10 (2023). https://doi.org/10.1007/s10404-022-02621-4

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