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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)

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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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 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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