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Falling clouds of particles in viscous fluids

Published online by Cambridge University Press:  21 May 2007

BLOEN METZGER ,
MAXIME NICOLAS  and
ÉLISABETH GUAZZELLI
BLOEN METZGER
Affiliation:
IUSTI – CNRS UMR 6595, Polytech-Marseille, Technopôle de Château-Gombert, 13453 Marseille cedex 13, France
MAXIME NICOLAS
Affiliation:
IUSTI – CNRS UMR 6595, Polytech-Marseille, Technopôle de Château-Gombert, 13453 Marseille cedex 13, France
ÉLISABETH GUAZZELLI
Affiliation:
IUSTI – CNRS UMR 6595, Polytech-Marseille, Technopôle de Château-Gombert, 13453 Marseille cedex 13, France
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Abstract

We have investigated both experimentally and numerically the time evolution of clouds of particles settling under the action of gravity in an otherwise pure liquid at low Reynolds numbers. We have found that an initially spherical cloud containing enough particles is unstable. It slowly evolves into a torus which breaks up into secondary droplets which deform into tori themselves in a repeating cascade. Owing to the fluctuations in velocity of the interacting particles, some particles escape from the cloud toroidal circulation and form a vertical tail. This creates a particle deficit near the vertical axis of the cloud and helps in producing the torus which eventually expands. The rate at which particles leak from the cloud is influenced by this change of shape. The evolution toward the torus shape and the subsequent evolution is a robust feature. The nature of the breakup of the torus is found to be intrinsic to the flow created by the particles when the torus aspect ratio reaches a critical value. Movies are available with the online version of the paper.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 580 , 10 June 2007 , pp. 283 - 301
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Adachi, K., Kiriyama, S. & Yoshioka, N. 1978 The behavior of a swarm of particles moving in a viscous fluid. Chem. Engng Sci. 33, 115–121.CrossRefGoogle Scholar
Bosse, T., Kleiser, L., Härtel, C. & Meiburg, E. 2005 Numerical simulation of finite Reynolds number suspension drops settling under gravity. Phys. Fluids 17, 037101.Google Scholar
Brinkman, H. C. 1947 A calculation of the viscous fluid on a dense swarm of particles. Appl. Sci. Res. A1, 27–34.Google Scholar
Ekiel-Jeżewska, M. L., Metzger, B. & Guazzelli, É. 2006 Spherical cloud of point particles falling in a viscous fluid. Phys. Fluids 18, 038104.CrossRefGoogle Scholar
Hadamard, J. S. 1911 Mouvement permanent lent d'une sphère liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. (Paris) 152, 1735–1738.Google Scholar
Jánosi, I. M., Tél, T., Wolf, D. E., Gallas, J. A. C. 1997 Chaotic particle dynamics in viscous flows: the three-particle Stokeslet problem. Phys. Rev. E 56, 2858–2868.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Machu, G., Meile, W., Nitsche, L. C. & Schaflinger, U. 2001 Coalescence, torus formation and break-up of sedimenting clouds: experiments and computer simulations. J. Fluid Mech. 447, 299–336.CrossRefGoogle Scholar
Nicolas, M. 2002 Experimental study of gravity-driven dense suspension jets. Phys. Fluids 14, 3570–3576.CrossRefGoogle Scholar
Nitsche, J. M. & Batchelor, G. K. 1997 Break-up of a falling cloud containing dispersed particles. J. Fluid Mech. 340, 161–175.CrossRefGoogle Scholar
Pozrikidis, C. 1989 The instability of a moving viscous drop. J. Fluid Mech. 210, 1–21.CrossRefGoogle Scholar
Rybczyński, W. 1911 Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium. Bull. Acad. Sci. Cracovie A, 40–46.Google Scholar

Metzger et al. supplementary movie

Illustration of the leakage mechanism. The particle positions are integrated over the whole range of the azimuthal angle. All the particles which have escaped from the cloud at t*=100 are colored in red.

Download Metzger et al. supplementary movie(Video)
Video 4 MB

Metzger et al. supplementary movie

Side and bottom view of a simulation of a sedimenting cloud of point particles in an infinit fluid. The initial number of particles is 3000 but only half of them are plotted.

Download Metzger et al. supplementary movie(Video)
Video 8.3 MB

Metzger et al. supplementary movie

Bottom view of a cloud of colored glass particles settling in silicon oil. The particle radius is 400 microns and the fluid viscosity is 1000 cP.

Download Metzger et al. supplementary movie(Video)
Video 8.4 MB