Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-09T21:53:12.054Z Has data issue: false hasContentIssue false
  • English
  • Français

A falling cloud of particles at a small but finite Reynolds number

Published online by Cambridge University Press:  17 February 2011

FLORENT PIGNATEL ,
MAXIME NICOLAS  and
ÉLISABETH GUAZZELLI
FLORENT PIGNATEL
Affiliation:
IUSTI-CNRS UMR 6596, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
MAXIME NICOLAS
Affiliation:
IUSTI-CNRS UMR 6596, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
ÉLISABETH GUAZZELLI*
Affiliation:
IUSTI-CNRS UMR 6596, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Through a comparison between experiments and numerical simulations, we have examined the dynamics of a cloud of spheres at a small but finite Reynolds number. The cloud is seen to flatten and to transition into a torus, which further widens and eventually breaks up into droplets. While this behaviour bears some similarity to that observed at zero inertia, the underlying physical mechanisms differ. Moreover, the evolution of the cloud deformation is accelerated as inertia is increased. Two inertial regimes in which macro-scale inertia and micro-scale inertia become successively dominant are clearly identified.

JFM classification

Drops and Bubbles: Breakup/coalescence Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 34 - 51
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adachi, K., Kiriyama, S. & Koshioka, N. 1978 The behaviour of a swarm of particles moving in a viscous fluid. Chem. Engng Sci. 33, 115–121.CrossRefGoogle Scholar
Bosse, T., Favre, J., Meiburg, E. & Kleiser, L. 2005 a Settling and breakup of suspension drops. Award-winning video entry to the Gallery of Fluid Motion, 57th APS/DFD Annual Meeting, Nov. 21–23, 2004, Seattle, WA, USA. Phys. Fluids 17, 091107.CrossRefGoogle Scholar
Bosse, T., Kleiser, L., Härtel, C. & Meiburg, E. 2005 b Numerical simulation of finite Reynolds number suspension drops settling under gravity. Phys. Fluids 17, 037101.CrossRefGoogle Scholar
Bush, J. W. M., Thurber, B. A., & Blanchette, F. 2003 Particle clouds in homogeneous and stratified environments. J. Fluid Mech. 489, 29–54.CrossRefGoogle 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
Lamb, H. 1932 Fluid Mechanics, 6th edn. Dover.Google Scholar
Machu, G., Meile, W., Nitsche, L. C. & Schaflinger, U. 2001 Coalescence, torus formation and breakup of sedimenting drops: experiments and computer simulations. J. Fluid Mech. 447, 299–336.CrossRefGoogle Scholar
Metzger, B., Nicolas, M. & Guazzelli, É. 2007 Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283–301.CrossRefGoogle Scholar
Nitsche, J. M. & Batchelor, G. K. 1997 Break-up of a falling drop containing dispersed particles. J. Fluid Mech. 340, 161–175.CrossRefGoogle Scholar
Noh, Y. & Fernando, H. J. S. 1993 The transition in the sedimentation pattern of a particle cloud. Phys. Fluids A 5, 3049–3055.CrossRefGoogle Scholar
Park, J., Metzger, B., Guazzelli, É. & Butler, J. E. 2010 A cloud of rigid fibres sedimenting in a viscous fluid. J. Fluid Mech. 648, 351–362.CrossRefGoogle Scholar
Subramanian, G. & Koch, D. L. 2008 Evolution of clusters of sedimenting low-Reynolds-number particles with Oseen interactions. J. Fluid Mech. 603, 63–100.CrossRefGoogle Scholar

Pignatel et al. supplementary movie

Movie 1. Typical evolution of a cloud in the macro-scale inertia regime: experiment with a cloud Reynolds number of 0.7, an initial number of particles of 16000, an inertial length normalised by the initial radius of the cloud of 179 (a particle Reynolds number of 0.00008, a ratio of cloud to particle radius of 66, a volume fraction of 6 %, and a particle Stokes number of 0.00002)

Download Pignatel et al. supplementary movie(Video)
Video 9.6 MB

Pignatel et al. supplementary movie

Movie 1. Typical evolution of a cloud in the macro-scale inertia regime: experiment with a cloud Reynolds number of 0.7, an initial number of particles of 16000, an inertial length normalised by the initial radius of the cloud of 179 (a particle Reynolds number of 0.00008, a ratio of cloud to particle radius of 66, a volume fraction of 6 %, and a particle Stokes number of 0.00002)

Download Pignatel et al. supplementary movie(Video)
Video 8.7 MB

Pignatel supplementary movie

Movie 2. Typical evolution of the cloud in the micro-scale inertia regime: experiment with a cloud Reynolds number of 15, an initial number of particles of 600, an inertial length normalised by the initial radius of the cloud of 0.65 (a particle Reynolds number of 0.14, an ratio of cloud to particle radius of 11, a volume fraction of 50 %, and a particle Stokes number of 0.077)

Download Pignatel supplementary movie(Video)
Video 7.9 MB

Pignatel supplementary movie

Movie 2. Typical evolution of the cloud in the micro-scale inertia regime: experiment with a cloud Reynolds number of 15, an initial number of particles of 600, an inertial length normalised by the initial radius of the cloud of 0.65 (a particle Reynolds number of 0.14, an ratio of cloud to particle radius of 11, a volume fraction of 50 %, and a particle Stokes number of 0.077)

Download Pignatel supplementary movie(Video)
Video 9.5 MB

Pignatel supplementary movie

Movie 3. Typical evolution of the cloud in the micro-scale inertia regime: experiment with a cloud Reynolds number of 3.5, an initial number of particles of 7000, an inertial length normalised by the initial radius of the cloud of 21 (a particle Reynolds number of 0.002, an ratio of cloud to particle radius of 24, a volume fraction of 50 %, and a particle Stokes number of 0.0005)

Download Pignatel supplementary movie(Video)
Video 1.8 MB

Pignatel supplementary movie

Movie 3. Typical evolution of the cloud in the micro-scale inertia regime: experiment with a cloud Reynolds number of 3.5, an initial number of particles of 7000, an inertial length normalised by the initial radius of the cloud of 21 (a particle Reynolds number of 0.002, an ratio of cloud to particle radius of 24, a volume fraction of 50 %, and a particle Stokes number of 0.0005)

Download Pignatel supplementary movie(Video)
Video 3.6 MB

Pignatel supplementary movie

Movie 4. Flow field at succesive times in the vertical plane through the vertical axis of symmetry in the cloud reference frame. Oseenlet simulation with an initial number of particles of 2000 and an inertial length normalised by the initial radius of the cloud of 1. High (low) velocity is indicated in white (dark).

Download Pignatel supplementary movie(Video)
Video 20.6 MB

Pignatel supplementary movie

Movie 4. Flow field at succesive times in the vertical plane through the vertical axis of symmetry in the cloud reference frame. Oseenlet simulation with an initial number of particles of 2000 and an inertial length normalised by the initial radius of the cloud of 1. High (low) velocity is indicated in white (dark).

Download Pignatel supplementary movie(Video)
Video 9.8 MB

Pignatel supllementary movie

Movie 5. Same as movie 4 but with an inertial length normalised by the initial radius of the cloud of 20.

Download Pignatel supllementary movie(Video)
Video 24.6 MB

Pignatel supllementary movie

Movie 5. Same as movie 4 but with an inertial length normalised by the initial radius of the cloud of 20.

Download Pignatel supllementary movie(Video)
Video 10 MB