Hostname: page-component-89b8bd64d-mmrw7 Total loading time: 0 Render date: 2026-05-09T12:53:05.168Z Has data issue: false hasContentIssue false
  • English
  • Français

Air entrapment of a neutral drop impacting onto a flat solid surface in electric fields

Published online by Cambridge University Press:  04 August 2022

Yu Tian Open the ORCID record for Yu Tian [Opens in a new window] ,
Yanchu Liu Open the ORCID record for Yanchu Liu [Opens in a new window] ,
Zihan Peng Open the ORCID record for Zihan Peng [Opens in a new window] ,
Chenghao Xu Open the ORCID record for Chenghao Xu [Opens in a new window] ,
Dong Ye Open the ORCID record for Dong Ye [Opens in a new window] ,
Yin Guan Open the ORCID record for Yin Guan [Opens in a new window] ,
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window] ,
Weiwei Deng Open the ORCID record for Weiwei Deng [Opens in a new window]  and
YongAn Huang Open the ORCID record for YongAn Huang [Opens in a new window]
Yu Tian
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Yanchu Liu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
Zihan Peng
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Chenghao Xu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
Dong Ye
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Yin Guan
Affiliation:
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Xinping Zhou
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Weiwei Deng*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
YongAn Huang*
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
*
†Email addresses for correspondence: yahuang@hust.edu.cn, dengww@sustech.edu.cn
†Email addresses for correspondence: yahuang@hust.edu.cn, dengww@sustech.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

When a charge neutral drop impacts on a flat solid substrate, a small air bubble is always trapped underneath due to the lubrication pressure coming from the viscous stress in the squeezed air film. Herein we find experimentally and numerically that the process of the air entrapment and the initial contact state of the drop with the substrate can be profoundly altered via an external electric field. In an electric field, the induced electric stresses at the bottom of the drop increase drastically right before the drop contacts the substrate, which acts against the lubrication pressure, resulting in reduced initial contact radius and air bubble size. When the external electric field reaches a critical value, the electrical stress accelerates the flow near the bottom of the drop and generates a conical tip quickly instead of a dimple, resulting in a centre contact and eliminating the air bubble entrapment. Based on the dipole mirror charge model, we find the dimensionless strength of critical electric field scales with the square root of capillary number based on the air viscosity. This scaling law of the critical electric field for eliminating the air bubble entrapment is verified experimentally and numerically. This work may offer a new way to mitigate defects caused by air bubble entrapment for inkjet printing and droplet-based additive manufacturing.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Bubble dynamics Drops and Bubbles: Electrohydrodynamic effects

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A21
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Antonini, C., Lee, J.B., Maitra, T., Irvine, S., Derome, D., Tiwari, M.K., Carmeliet, J. & Poulikakos, D. 2014 Unraveling wetting transition through surface textures with x-rays: liquid meniscus penetration phenomena. Sci. Rep. 4 (1), 4055.CrossRefGoogle ScholarPubMed
Basaran, O.A. & Scriven, L.E. 1989 Axisymmetric shapes and stability of charged drops in an external electric-field. Phys. Fluids A 1 (5), 799–809.10.1063/1.857377CrossRefGoogle Scholar
Bouwhuis, W., van der Veen, R.C.A., Tuan, T., Keij, D.L., Winkels, K.G., Peters, I.R., van der Meer, D., Sun, C., Snoeijer, J.H. & Lohse, D. 2012 Maximal air bubble entrainment at liquid-drop impact. Phys. Rev. Lett. 109 (26), 264501.10.1103/PhysRevLett.109.264501CrossRefGoogle ScholarPubMed
Chan, D.Y.C., Klaseboer, E. & Manica, R. 2011 Film drainage and coalescence between deformable drops and bubbles. Soft Matt. 7 (6), 2235–2264.10.1039/C0SM00812ECrossRefGoogle Scholar
Collins, R.T., Sambath, K., Harris, M.T. & Basaran, O.A. 2013 Universal scaling laws for the disintegration of electrified drops. Proc. Natl Acad. Sci. USA 110 (13), 4905–4910.10.1073/pnas.1213708110CrossRefGoogle ScholarPubMed
van Dam, D.B. & Clerc, C.L. 2004 Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys. Fluids 16 (9), 3403–3414.10.1063/1.1773551CrossRefGoogle Scholar
Derby, B. 2010 Inkjet printing of functional and structural materials: fluid property requirements, feature stability, and resolution. Annu. Rev. Mater. Res. 40, 395–414.10.1146/annurev-matsci-070909-104502CrossRefGoogle Scholar
Gao, F., Yi, H., Qi, L., Qiao, R. & Deng, W. 2019 Weakly charged droplets fundamentally change impact dynamics on flat surfaces. Soft Matt. 15 (28), 5548–5553.10.1039/C9SM00895KCrossRefGoogle ScholarPubMed
García-Geijo, P., Riboux, G. & Gordillo, J.M. 2020 Inclined impact of drops. J. Fluid Mech. 897, A12.10.1017/jfm.2020.373CrossRefGoogle Scholar
Gawande, N., Mayya, Y.S. & Thaokar, R. 2020 Jet and progeny formation in the rayleigh breakup of a charged viscous drop. J. Fluid Mech. 884, A31.10.1017/jfm.2019.970CrossRefGoogle Scholar
Grimm, R.L. & Beauchamp, J.L. 2005 Dynamics of field-induced droplet ionization: time-resolved studies of distortion, jetting, and progeny formation from charged and neutral methanol droplets exposed to strong electric fields. J. Phys. Chem. B 109 (16), 8244–8250.10.1021/jp0450540CrossRefGoogle ScholarPubMed
Ha, J.W. & Yang, S.M. 2000 Deformation and breakup of newtonian and non-newtonian conducting drops in an electric field. J. Fluid Mech. 405, 131–156.CrossRefGoogle Scholar
Herrada, M.A., Lopez-Herrera, J.M., Ganan-Calvo, A.M., Vega, E.J., Montanero, J.M. & Popinet, S. 2012 Numerical simulation of electrospray in the cone-jet mode. Phys. Rev. E 86 (2 Pt 2), 026305.10.1103/PhysRevE.86.026305CrossRefGoogle ScholarPubMed
Hicks, P.D., Ermanyuk, E.V., Gavrilov, N.V. & Purvis, R. 2012 Air trapping at impact of a rigid sphere onto a liquid. J. Fluid Mech. 695, 310–320.10.1017/jfm.2012.20CrossRefGoogle Scholar
Hicks, P.D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135–163.10.1017/S0022112009994009CrossRefGoogle Scholar
Huang, Y., Wu, H., Xiao, L., Duan, Y., Zhu, H., Bian, J., Ye, D. & Yin, Z. 2019 Assembly and applications of 3d conformal electronics on curvilinear surfaces. Mater. Horizons 6 (4), 642–683.10.1039/C8MH01450GCrossRefGoogle Scholar
Jian, Z., Channa, M.A., Kherbeche, A., Chizari, H., Thoroddsen, S.T. & Thoraval, M.J. 2020 To split or not to split: dynamics of an air disk formed under a drop impacting on a pool. Phys. Rev. Lett. 124 (18), 184501.10.1103/PhysRevLett.124.184501CrossRefGoogle ScholarPubMed
Josserand, C. & Thoroddsen, S.T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365–391.10.1146/annurev-fluid-122414-034401CrossRefGoogle Scholar
Klaseboer, E., Manica, R. & Chan, D.Y. 2014 Universal behavior of the initial stage of drop impact. Phys. Rev. Lett. 113 (19), 194501.10.1103/PhysRevLett.113.194501CrossRefGoogle ScholarPubMed
Kumar, R., Shukla, R.K., Kumar, A. & Kumar, A. 2020 A computational study on air entrapment and its effect on convective heat transfer during droplet impact on a substrate. Intl J. Therm. Sci. 153, 106363.CrossRefGoogle Scholar
Langley, K.R., Castrejon-Pita, A.A. & Thoroddsen, S.T. 2020 Droplet impacts onto soft solids entrap more air. Soft Matt. 16 (24), 5702–5710.10.1039/D0SM00713GCrossRefGoogle ScholarPubMed
Lee, J.S., Weon, B.M., Je, J.H. & Fezzaa, K. 2012 How does an air film evolve into a bubble during drop impact? Phys. Rev. Lett. 109 (20), 204501.10.1103/PhysRevLett.109.204501CrossRefGoogle ScholarPubMed
Li, E.Q., Langley, K.R., Tian, Y.S., Hicks, P.D. & Thoroddsen, S.T. 2017 b Double contact during drop impact on a solid under reduced air pressure. Phys. Rev. Lett. 119 (21), 214502.CrossRefGoogle ScholarPubMed
Li, E.Q. & Thoroddsen, S.T. 2015 Time-resolved imaging of a compressible air disc under a drop impacting on a solid surface. J. Fluid Mech. 780, 636–648.10.1017/jfm.2015.466CrossRefGoogle Scholar
Li, E.Q., Vakarelski, I.U. & Thoroddsen, S.T. 2015 Probing the nanoscale: the first contact of an impacting drop. J. Fluid Mech. 785, R2.CrossRefGoogle Scholar
Li, D., Zhang, D., Zheng, Z. & Tian, X. 2017 a Numerical analysis on air entrapment during a droplet impacts on a dry flat surface. Intl J. Heat Mass Transfer 115, 186–193.CrossRefGoogle Scholar
Ligon, S.C., Liska, R., Stampfl, J., Gurr, M. & Mulhaupt, R. 2017 Polymers for 3d printing and customized additive manufacturing. Chem. Rev. 117 (15), 10212–10290.10.1021/acs.chemrev.7b00074CrossRefGoogle ScholarPubMed
Liu, Y., Tan, P. & Xu, L. 2013 Compressible air entrapment in high-speed drop impacts on solid surfaces. J. Fluid Mech. 716, R9.CrossRefGoogle Scholar
Liu, Y., Tan, P. & Xu, L. 2015 Kelvin–Helmholtz instability in an ultrathin air film causes drop splashing on smooth surfaces. Proc. Natl Acad. Sci. USA 112 (11), 3280–3284.CrossRefGoogle Scholar
Mandre, S., Mani, M. & Brenner, M.P. 2009 Precursors to splashing of liquid droplets on a solid surface. Phys. Rev. Lett. 102 (13), 134502.CrossRefGoogle ScholarPubMed
Mehdi-Nejad, V., Mostaghimi, J. & Chandra, S. 2003 Air bubble entrapment under an impacting droplet. Phys. Fluids 15 (1), 173–183.CrossRefGoogle Scholar
Minemawari, H., Yamada, T., Matsui, H., Tsutsumi, J., Haas, S., Chiba, R., Kumai, R. & Hasegawa, T. 2011 Inkjet printing of single-crystal films. Nature 475 (7356), 364–367.CrossRefGoogle ScholarPubMed
Oratis, A.T., Bush, J.W.M., Stone, H.A. & Bird, J.C. 2020 A new wrinkle on liquid sheets: turning the mechanism of viscous bubble collapse upside down. Science 369 (6504), 685–688.CrossRefGoogle ScholarPubMed
Papadopoulos, M. 1963 Classical electrodynamics (JD Jackson). SIAM Rev. 5 (1), 82.CrossRefGoogle Scholar
Roghair, I., Musterd, M., van den Ende, D., Kleijn, C., Kreutzer, M. & Mugele, F. 2015 A numerical technique to simulate display pixels based on electrowetting. Microfluid. Nanofluid. 19 (2), 465–482.CrossRefGoogle Scholar
Santra, S., Mandal, S. & Chakraborty, S. 2018 Electrohydrodynamics of confined two-dimensional liquid droplets in uniform electric field. Phys. Fluids 30 (6), 062003.CrossRefGoogle Scholar
Saville, D.A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 27–64.CrossRefGoogle Scholar
Sengupta, R., Walker, L.M. & Khair, A.S. 2017 The role of surface charge convection in the electrohydrodynamics and breakup of prolate drops. J. Fluid Mech. 833, 29–53.CrossRefGoogle Scholar
Shen, D., Zou, G., Liu, L., Duley, W.W. & Zhou, Y.N. 2016 Investigation of splashing phenomena during the impact of molten sub-micron gold droplets on solid surfaces. Soft Matt. 12 (1), 295–301.CrossRefGoogle ScholarPubMed
Shukla, R.K., Kumar, A., Kumar, R., Singh, D. & Kumar, A. 2019 Numerical study of pore formation in thermal spray coating process by investigating dynamics of air entrapment. Surf. Coat. Technol. 378, 124972.CrossRefGoogle Scholar
Singh, M., Haverinen, H.M., Dhagat, P. & Jabbour, G.E. 2010 Inkjet printing-process and its applications. Adv. Mater. 22 (6), 673–685.CrossRefGoogle ScholarPubMed
Snoeijer, J.H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45 (1), 269–292.CrossRefGoogle Scholar
Stringer, J., et al. 2016 Integration of additive manufacturing and inkjet printed electronics: a potential route to parts with embedded multifunctionality. Manuf. Rev. 3 (12), 2265–4224.Google Scholar
Taylor, G.I. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. Math. Phys. Engng Sci. 291 (1425), 159–166.Google Scholar
Thoraval, M.J., Takehara, K., Etoh, T.G. & Thoroddsen, S.T. 2013 Drop impact entrapment of bubble rings. J. Fluid Mech. 724, 234–258.CrossRefGoogle Scholar
Thoroddsen, S.T., Etoh, T.G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125–134.CrossRefGoogle Scholar
Thoroddsen, S.T., Etoh, T.G. & Takehara, K. 2008 High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 40 (1), 257–285.CrossRefGoogle Scholar
Thoroddsen, S.T., Etoh, T.G., Takehara, K., Ootsuka, N. & Hatsuki, Y. 2005 The air bubble entrapped under a drop impacting on a solid surface. J. Fluid Mech. 545 (-1), 203–212.CrossRefGoogle Scholar
van der Veen, R.C.A., Tuan, T., Lohse, D. & Sun, C. 2012 Direct measurements of air layer profiles under impacting droplets using high-speed color interferometry. Phys. Rev. E 85 (2), 026315.CrossRefGoogle ScholarPubMed
Vlahovska, P.M. 2019 Electrohydrodynamics of drops and vesicles. Annu. Rev. Fluid Mech. 51 (1), 305–330.CrossRefGoogle Scholar
Vo, Q. & Tran, T. 2021 Mediation of lubricated air films using spatially periodic dielectrophoretic effect. Nat. Commun. 12 (1), 4289.CrossRefGoogle ScholarPubMed
Wagoner, B.W., Vlahovska, P.M., Harris, M.T. & Basaran, O.A. 2020 Electric-field-induced transitions from spherical to discocyte and lens-shaped drops. J. Fluid Mech. 904, R4.CrossRefGoogle Scholar
Wang, Z., Tian, Y., Zhang, C., Wang, Y. & Deng, W. 2021 Massively multiplexed electrohydrodynamic tip streaming from a thin disc. Phys. Rev. Lett. 126 (6), 064502.CrossRefGoogle ScholarPubMed
Wu, H., Tian, Y., Luo, H., Zhu, H., Duan, Y. & Huang, Y. 2020 Fabrication techniques for curved electronics on arbitrary surfaces. Adv. Mater. Technol. 5 (8), 2000093.CrossRefGoogle Scholar
Xiong, W. & Cheng, P. 2018 Numerical investigation of air entrapment in a molten droplet impacting and solidifying on a cold smooth substrate by 3d lattice Boltzmann method. Intl J. Heat Mass Transfer 124, 1262–1274.CrossRefGoogle Scholar
Yang, W., Duan, H., Li, C. & Deng, W. 2014 Crossover of varicose and whipping instabilities in electrified microjets. Phys. Rev. Lett. 112 (5), 054501.CrossRefGoogle ScholarPubMed
Yarin, A.L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Yi, H.H., Qi, L., Luo, J., Jiang, Y. & Deng, W. 2016 Pinhole formation from liquid metal microdroplets impact on solid surfaces. Appl. Phys. Lett. 108 (4), 041601.CrossRefGoogle Scholar
Zhang, J., Zahn, J.D. & Lin, H. 2013 Transient solution for droplet deformation under electric fields. Phys. Rev. E 87 (4), 043008.CrossRefGoogle ScholarPubMed

Tian et al. supplementary movie 1

See pdf file for movie caption

Download Tian et al. supplementary movie 1(Video)
Video 9.7 MB

Tian et al. supplementary movie 2

See pdf file for movie caption

Download Tian et al. supplementary movie 2(Video)
Video 10 MB

Tian et al. supplementary movie 3

See pdf file for movie caption

Download Tian et al. supplementary movie 3(Video)
Video 8.1 MB

Tian et al. supplementary movie 4

See pdf file for movie caption

Download Tian et al. supplementary movie 4(Video)
Video 9.4 MB

Tian et al. supplementary movie 5

See pdf file for movie caption

Download Tian et al. supplementary movie 5(Video)
Video 7.8 MB

Tian et al. supplementary movie 6

See pdf file for movie caption

Download Tian et al. supplementary movie 6(Video)
Video 9.9 MB
Supplementary material: PDF

Tian et al. supplementary material

Captions for movies 1-6

Download Tian et al. supplementary material(PDF)
PDF 101 KB
Supplementary material: PDF

Tian et al. supplementary material

Supplementary data

Download Tian et al. supplementary material(PDF)
PDF 2.3 MB