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Early azimuthal instability during drop impact

  • E. Q. Li (a1) (a2), M.-J. Thoraval (a1) (a3), J. O. Marston (a1) (a4) and S. T. Thoroddsen (a1)
Abstract

When a drop impacts on a liquid surface its bottom is deformed by lubrication pressure and it entraps a thin disc of air, thereby making contact along a ring at a finite distance from the centreline. The outer edge of this contact moves radially at high speed, governed by the impact velocity and bottom radius of the drop. Then at a certain radial location an ejecta sheet emerges from the neck connecting the two liquid masses. Herein, we show the formation of an azimuthal instability at the base of this ejecta, in the sharp corners at the two sides of the ejecta. They promote regular radial vorticity, thereby breaking the axisymmetry of the motions on the finest scales. The azimuthal wavenumber grows with the impact Weber number, based on the bottom curvature of the drop, reaching over 400 streamwise streaks around the periphery. This instability occurs first at Reynolds numbers ( $Re$ ) of ${\sim}7000$ , but for larger $Re$ is overtaken by the subsequent axisymmetric vortex shedding and their interactions can form intricate tangles, loops or chains.

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Corresponding author
Email address for correspondence: Sigurdur.Thoroddsen@KAUST.edu.sa
References
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Agbaglah, G., Josserand, C. & Zaleski, S. 2013 Longitudinal instability of a liquid rim. Phys. Fluids 25, 022103.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bouwhuis, W., van der Veen, R. C. A., Tran, 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, 264501.
Castrejon-Pita, A. A., Castrejon-Pita, J. R. & Hutchings, I. M. 2012 Experimental observation of von Karman vortices during drop impact. Phys. Rev. E 86, 045301(R).
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 11311198.
Crooks, J., Marsh, B., Turchetta, R., Taylor, K., Chan, W., Lahav, A. & Fenigstein, A. 2013 Kirana: a solid-state megapixel uCMOS image sensor for ultrahigh speed imaging. Proc. SPIE 8659, 865903.
Deegan, R. D., Brunet, P. & Eggers, J. 2008 Complexities of splashing. Nonlinearity 21, C1C11.
Etoh, T. G. et al. 2003 An image sensor which captures 100 consecutive frames at 1000000 frames/s. IEEE Trans. Electron Devices 50, 144151.
Gordillo, J. M., Lhuissier, H. & Villermaux, E. 2014 On the cusps bordering liquid sheets. J. Fluid Mech. 754, R1.
Hendrix, M. H. W., Bouwhuis, W., Van Der Meer, D., Lohse, D. & Snoeijer, J. H. 2016 Universal mechanism for air entrainment during liquid impact. J. Fluid Mech. 789, 708725.
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, 310320.
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649, 135163.
Howison, S. D., Ockendon, J. R., Oliver, J. M., Purvis, R. & Smith, F. T. 2005 Droplet impact on a thin fluid layer. J. Fluid Mech. 542, 123.
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365391.
Josserand, C. & Zaleski, S. 2003 Droplet splashing on a thin liquid film. Phys. Fluids 15, 16501657.
Korobkin, A. A. 2007 Second-order Wagner theory of wave impact. J. Engng Maths 58, 121139.
Korobkin, A. A., Ellis, A. S. & Smith, F. T. 2008 Trapping of air in impact between a body and shallow water. J. Fluid Mech. 611, 365394.
Korobkin, A. A. & Scolan, Y. M. 2006 Three-dimensional theory of water impact. Part 2. Linearized Wagner problem. J. Fluid Mech. 549, 343373.
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, 636648.
Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2011 Bubble entrapment during sphere impact onto quiescent liquid surfaces. J. Fluid Mech. 680, 660670.
Moore, M. R., Ockendon, H., Ockendon, J. R. & Oliver, J. M. 2014 Capillary and viscous perturbations to Helmholtz flows. J. Fluid Mech. 742, R1.
Oliver, J. M.2002 Water entry and related problems. PhD thesis, Oxford University.
Peck, B. & Sigurdson, L. 1998 On the kinematics at a free surface. IMA J. Appl. Maths 61, 113.
Philippi, J., Lagrée, P.-Y. & Antkowiak, A. 2016 Drop impact on a solid surface: short-time self-similarity. J. Fluid Mech. 795, 96135.
Prosperetti, A., Crum, L. A. & Pumphrey, H. C. 1989 The underwater noise of rain. J. Geophys. Res. 94 (C3), 32553259.
Reyssat, E. & Quéré, D. 2006 Bursting of a fluid film in a viscous environment. Europhys. Lett. 76 (2), 236242.
Riboux, G. & Gordillo, J. M. 2014 Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing. Phys. Rev. Lett. 113, 024507.
Rioboo, R., Marengo, M. & Tropea, C. 2002 Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33, 112124.
Scolan, Y. M. & Korobkin, A. A. 2001 Three-dimensional theory of water impact. Part 1. Inverse Wagner problem. J. Fluid Mech. 440, 293326.
Semenov, Y. A., Wu, G. X. & Korobkin, A. A. 2015 Impact of liquids with different densities. J. Fluid Mech. 766, 527.
Thoraval, M.-J., Takehara, K., Etoh, T. G., Popinet, S., Ray, P., Josserand, C., Zaleski, S. & Thoroddsen, S. T. 2012 Von Kármán vortex street within an impacting drop. Phys. Rev. Lett. 108, 264506.
Thoraval, M.-J., Takehara, K., Etoh, T. G. & Thoroddsen, S. T. 2013 Drop impact entrapment of bubble rings. J. Fluid Mech. 724, 234258.
Thoroddsen, S. T. 2002 The ejecta sheet generated by the impact of a drop. J. Fluid Mech. 451, 373381.
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2008 High-speed imaging of drops and bubble. Annu. Rev. Fluid Mech. 40, 257285.
Thoroddsen, S. T., Takehara, K. & Etoh, T. G. 2012a Micro-splashing by drop impacts. J. Fluid Mech. 706, 560570.
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2003 Air entrapment under an impacting drop. J. Fluid Mech. 478, 125134.
Thoroddsen, S. T., Thoraval, M.-J., Takehara, K. & Etoh, T. G. 2012b Micro-bubble morphologies following drop impacts onto a pool surface. J. Fluid Mech. 708, 469479.
Tran, T., De Maleprade, H., Sun, C. & Lohse, D. 2013 Air entrainment during impact of droplets on liquid surfaces. J. Fluid Mech. 726, R3.
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419446.
Wagner, H. 1932 Uber Stoss- und Gleitvorgange an der Oberflache von Flussigkeiten. Z. Angew. Math. Mech. 12, 193215.
Weiss, D. A. & Yarin, A. L. 1999 Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation. J. Fluid Mech. 385, 229254.
Worthington, A. M. 1908 A Study of Splashes. Longmans, Green and Co.
Zhang, L. V., Brunet, P., Eggers, J. & Deegan, R. D. 2010 Wavelength selection in the crown splash. Phys. Fluids 22, 122105.
Zhang, L. V., Toole, J., Fezzaa, K. & Deegan, R. D. 2012 Evolution of the ejecta sheet from the impact of a drop with a deep pool. J. Fluid Mech. 690, 515.
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Li et al. supplementary movie 1
Movie 1: Video corresponding to Figure 4(a). The frame rate is 500 kfps.

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Li et al. supplementary material
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Li et al. supplementary movie 2
Movie 2: Video corresponding to Figure 4(b). The frame rate is 2 million fps.

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Li et al. supplementary movie 3
Movie 3: Video corresponding to Figure 5(a). The frame rate is 2 million fps.

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Li et al. supplementary movie 4
Movie 4: Video corresponding to Figure 5(b). The frame rate is 2 million fps.

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Li et al. supplementary movie 5
Movie 5: Video corresponding to Figure 8(a). The frame rate is 1 million fps.

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Li et al. supplementary movie 6
Movie 6: Video showing close-up of radial and axial vortices, with entrapment of bubble rings. Impact height is 59 cm and pixel resolution is 1 micron/px. The frame rate is 1 million fps.

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