Hostname: page-component-669899f699-cf6xr Total loading time: 0 Render date: 2025-04-25T23:41:29.969Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of a liquid lamella during vertical impact of a solid plate

Published online by Cambridge University Press:  24 March 2025

Nayoung Kim Open the ORCID record for Nayoung Kim [Opens in a new window] ,
Yee Li (Ellis) Fan Open the ORCID record for Yee Li (Ellis) Fan [Opens in a new window] ,
Hyungmin Park Open the ORCID record for Hyungmin Park [Opens in a new window]  and
Devaraj van der Meer Open the ORCID record for Devaraj van der Meer [Opens in a new window]
Nayoung Kim*
Affiliation:
Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, University of Twente, 7500 AE, Enschede, The Netherlands
Yee Li (Ellis) Fan
Affiliation:
Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, University of Twente, 7500 AE, Enschede, The Netherlands
Hyungmin Park
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul 08826, Korea Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Korea
Devaraj van der Meer*
Affiliation:
Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, University of Twente, 7500 AE, Enschede, The Netherlands
*
Corresponding authors: Nayoung Kim, [email protected]; Devaraj van der Meer, [email protected]
Corresponding authors: Nayoung Kim, [email protected]; Devaraj van der Meer, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the dynamics of a thin liquid sheet that flows upwards along the sides of a vertically aligned, impacting plate. Upon impact of the vertical solid plate onto a liquid pool, the liquid film is ejected and subsequently continues to flow over the solid surface while the plate enters the water. With increasing impact velocity, the liquid film is observed to rise up faster and higher. We focus on the time evolution of the liquid film height and the thickness of its upper rim and discuss their dynamics in detail. Similar to findings in previous literature on sheet fragmentation during drop impact, we find the rim thickness to be governed by the local instantaneous capillary number based on gravity and the deceleration of the liquid sheet, showing that the retraction of the rim is primarily due to capillarity. In contrast, for the liquid film height, we demonstrate that the viscous dissipation in the thin boundary layer is the dominant factor for the vertical deceleration of the liquid sheet, by modelling the time evolution of the film height and showing that the influences of capillarity, gravity and deceleration due to the air phase are all negligible compared with the viscous term. Finally, we introduce characteristic viscous time and length scales based on the initial rim thickness and show that the maximum height of the film and the corresponding time can be determined from these viscous scales.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Thin films Aerodynamics: Flow-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A69
Check for updates
Copyright
© The Author(s), 2025. 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

Aristoff, J.M. & Bush, J.W. 2009 Water entry of small hydrophobic spheres. J. Fluid Mech. 619, 45–78.CrossRefGoogle Scholar
Bird, J.C., Dhiman, R., Kwon, H.-M. & Varanasi, K.K. 2013 Reducing the contact time of a bouncing drop. Nature 503 (7476), 385–388.CrossRefGoogle ScholarPubMed
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3 (3), 180–183.CrossRefGoogle Scholar
Eggers, J., Fontelos, M.A., Josserand, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22 (6), 062101.CrossRefGoogle Scholar
de Gennes, P.G. 2002 On fluid/wall slippage. Langmuir 18 (9), 3413–3414.CrossRefGoogle Scholar
Kim, N. & Park, H. 2019 Water entry of rounded cylindrical bodies with different aspect ratios and surface conditions. J. Fluid Mech. 863, 757–788.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. 112 (11), 3280–3284.CrossRefGoogle Scholar
Marston, J. & Thoroddsen, S.T. 2014 Ejecta evolution during cone impact. J. Fluid Mech. 752, 410–438.CrossRefGoogle Scholar
Mayer, H.C. & Krechetnikov, R. 2018 Flat plate impact on water. J. Fluid Mech. 850, 1066–1116.CrossRefGoogle Scholar
Okumura, K., Chevy, F., Richard, D., Quéré, D. & Clanet, C. 2003 Water spring: a model for bouncing drops. Europhys. Lett. 62 (2), 237–243.CrossRefGoogle Scholar
Pack, M., Kaneelil, P., Kim, H. & Sun, Y. 2018 Contact line instability caused by air rim formation under nonsplashing droplets. Langmuir 34 (17), 4962–4969.CrossRefGoogle ScholarPubMed
Peters, I.R., van der Meer, D. & Gordillo, J.M. 2013 Splash wave and crown breakup after disc impact on a liquid surface. J. Fluid Mech. 724, 553–580.CrossRefGoogle Scholar
Rayleigh, L. et al. 1879 On the capillary phenomena of jets. Proc. R. Soc. London 29 (196–199), 71–97.Google Scholar
Richard, D., Clanet, C. & Quéré, D. 2002 Contact time of a bouncing drop. Nature 417 (6891), 811–811.CrossRefGoogle ScholarPubMed
Roisman, I.V., Rioboo, R. & Tropea, C. 2002 Normal impact of a liquid drop on a dry surface: model for spreading and receding, Proc. R. Soc. Lond. Series A: Math. Phys. Engng Sci. 458 (2022), 1411–1430.CrossRefGoogle Scholar
Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M. 2002 Impact of water drops on small targets. Phys. Fluids 14 (10), 3485–3501.CrossRefGoogle Scholar
Snoeijer, J.H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45 (1), 269–292.CrossRefGoogle Scholar
Speirs, N.B., Mansoor, M.M., Belden, J. & Truscott, T.T. 2019 Water entry of spheres with various contact angles. J. Fluid Mech. 862, R3.CrossRefGoogle Scholar
Thoroddsen, S., Etoh, T., Takehara, K. & Takano, Y. 2004 Impact jetting by a solid sphere. J. Fluid Mech. 499, 139–148.CrossRefGoogle Scholar
Truscott, T., Epps, B. & Belden, J. 2014 Water entry of projectiles. Annu. Rev. Fluid Mech. 46 (1), 355–378.Google Scholar
Truscott, T.T., Epps, B.P. & Techet, A.H. 2012 Unsteady forces on spheres during free-surface water entry. J. Fluid Mech. 704, 173–210.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2011 Drop fragmentation on impact. J. Fluid Mech. 668, 412–435.Google Scholar
Wang, Y. & Bourouiba, L. 2021 Growth and breakup of ligaments in unsteady fragmentation. J. Fluid Mech. 910, A39.CrossRefGoogle Scholar
Wang, Y., Dandekar, R., Bustos, N., Poulain, S. & Bourouiba, L. 2018 Universal rim thickness in unsteady sheet fragmentation. Phys. Rev. Lett. 120 (20), 204503.Google ScholarPubMed
Worthington, A.M. 1877 Xxviii. on the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. Lond. 25 (171–178), 261–272.Google Scholar
Worthington, A.M. & Cole, R.S. 1897 Reginald Sorrè 1897 V. impact with a liquid surface, studied by the aid of instantaneous photography, Phil. Trans. R. Soc. Lond. Series A Containing Papers of a Mathematical or Physical Character 189, 137–148.Google Scholar
Zhao, M.-H., Chen, X.-P. & Wang, Q. 2014 Wetting failure of hydrophilic surfaces promoted by surface roughness. Sci. Rep.-UK 4 (1), 1–5.Google ScholarPubMed
Supplementary material: File

Kim et al. supplementary movie

The evolution of fingering patterns during the vertical impact of a solid plate at Uo = 1.3 m/s, with Do = 10 mm.
Download Kim et al. supplementary movie(File)
File 22.1 MB