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Oblique impact of microspheres on the surface of quiescent liquid

Published online by Cambridge University Press:  06 August 2020

Bingqiang Ji ,
Qiang Song Open the ORCID record for Qiang Song [Opens in a new window] ,
Kai Shi ,
Jiaheng Liu  and
Qiang Yao
Bingqiang Ji
Affiliation:
Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
Qiang Song*
Affiliation:
Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
Kai Shi
Affiliation:
Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
Jiaheng Liu
Affiliation:
Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
Qiang Yao
Affiliation:
Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
*
†Email address for correspondence: qsong@tsinghua.edu.cn
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Abstract

Impact of microspheres on liquid surfaces is a universal phenomenon in nature and in industrial processes. However, most relevant studies have mainly focused on the sphere's vertical impact. Herein, we present the first observation on the oblique impact of microspheres on the surface of quiescent liquid using high-speed microphotography. The sphere motion and liquid surface distortion after the oblique impact are basically different from those after a vertical impact. The sphere rotates and its trajectory deviates from the impact direction during the oblique impact process, while the non-axisymmetric liquid surface distortion experiences an evolution from half-cavity to full-cavity patterns. The dependence of motions of the sphere and the three-phase contact line on the impact angle $\alpha$ and Weber number are investigated, and the scaling laws for the sphere's penetration time and penetration depth are given. We provide a phase diagram with respect to the Weber number and impact angle that describes the observed impact modes of submergence and oscillation, which shows that the critical Weber number between two impact modes increases when the impact angle decreases. Additionally, a scaling model is established based on energy balance to distinguish different impact modes. The model indicates that the critical Weber number for the microsphere's oblique impact is equal to $1/{\rm sin}\,\alpha$ times that for vertical impact, agreeing well with the experimental results.

JFM classification

Interfacial Flows (free surface): Contact lines Waves/Free-surface Flows: Capillary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Ji et al. supplementary movie 1

A 249 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 2.74 m/s (We = 34, Re = 894) and impact angle of 13.3°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 1(Video)
Video 360.6 KB

Ji et al. supplementary movie 2

A 240 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 2.89 m/s (We = 16, Re = 529) and impact angle of 29.5°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 2(Video)
Video 385.9 KB

Ji et al. supplementary movie 3

A 220.7 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 3.36 m/s (We = 34, Re = 740) and impact angle of 29.5°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 3(Video)
Video 247.2 KB

Ji et al. supplementary movie 4

A 284.9 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 3.59 m/s (We = 50, Re = 1021) and impact angle of 29.5°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 4(Video)
Video 347.1 KB

Ji et al. supplementary movie 5

A 306 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 2.84 m/s (We = 34, Re = 867) and impact angle of 43.8°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 5(Video)
Video 610.9 KB

Ji et al. supplementary movie 6

A 246.3 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 3.15 m/s (We = 34, Re = 774) and impact angle of 56°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 6(Video)
Video 294.7 KB

Ji et al. supplementary movie 7

A 295 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 2.89 m/s (We = 34, Re = 851) and impact angle of 72.8°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 7(Video)
Video 323.5 KB

Ji et al. supplementary movie 8

A 327 μm diameter PMMA sphere impacts a quiescent water surface with velocity u0 = 2.74 m/s (We = 34, Re = 894) and impact angle of 89°exhibiting an oscillation mode. The movie is played back at 1/2800 of real speed.

Download Ji et al. supplementary movie 8(Video)
Video 534.3 KB