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A cloud of rigid fibres sedimenting in a viscous fluid

Published online by Cambridge University Press:  07 April 2010

JOONTAEK PARK ,
BLOEN METZGER ,
ÉLISABETH GUAZZELLI  and
JASON E. BUTLER
JOONTAEK PARK
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
BLOEN METZGER*
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
JASON E. BUTLER
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: [email protected]
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Abstract

Experiments and numerical simulations have been performed to investigate the deformation and break-up of a cloud of rigid fibres falling under gravity through a viscous fluid in the absence of inertia and interfacial tension. The cloud of fibres is observed to evolve into a torus that subsequently becomes unstable and breaks up into secondary droplets which themselves deform into tori in a repeating cascade. This behaviour is similar to that of clouds of spherical particles, though the evolution of the cloud of fibres occurs more rapidly. The simulations, which use two different levels of approximation of the far-field hydrodynamic interactions, capture the evolution of the cloud and demonstrate that the coupling between the self-motion and hydrodynamically induced fluctuations are responsible for the faster break-up time of the cloud. The dynamics of the cloud are controlled by a single parameter which is related to the self-motion of the anisotropic particles. The experiments confirm these findings.

JFM classification

Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 351 - 362
Copyright
Copyright © Cambridge University Press 2010

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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
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419–440.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.CrossRefGoogle Scholar
Butler, J. E. & Shaqfeh, E. S. G. 2002 Dynamic simulations of the inhomogeneous sedimentation of rigid fibres. J. Fluid Mech. 468, 205–237.CrossRefGoogle Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791–810.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
Harlen, O. G., Sundararajakumar, R. R. & Koch, D. L. 1999 Numerical simulation of a sphere settling through a suspension of neutrally buoyant fibres. J. Fluid Mech. 388, 355–388.CrossRefGoogle Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317–328.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.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
Mackaplow, M. B. & Shaqfeh, E. S. G. 1998 A numerical study of the sedimentation of fibre suspensions. J. Fluid Mech. 376, 149–182.CrossRefGoogle Scholar
Metzger, B., Nicolas, M. & Guazzelli, É. 2007 Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283–301.CrossRefGoogle Scholar
Moran, J. P. 1963 Line source distributions and slender-body theory. J. Fluid Mech. 17, 285–304.CrossRefGoogle Scholar
Nitsche, J. M. & Batchelor, G. K. 1997 Breakup of a falling drop containing dispersed particles. J. Fluid Mech. 340, 161–175.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1994 Numerical Recipes in Fortran, The Art of Scientific Computing. 2nd edn., pp. 719–725. Cambridge University Press.Google Scholar
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation. J. Fluid Mech. 553, 347–388.CrossRefGoogle Scholar
Schaflinger, U. & Machu, G. 1999 Interfacial phenomena in suspensions. Chem. Engng Technol. 22, 617–619.3.0.CO;2-1>CrossRefGoogle Scholar

Park et al. supplementary movie

Movie 1. Fiblet simulation of the sedimentation of a cloud of fibres for c=40 and N_0=1000. (left) side view, (right) bottom view.

Download Park et al. supplementary movie(Video)
Video 289.2 KB

Park et al. supplementary movie

Movie 1. Fiblet simulation of the sedimentation of a cloud of fibres for c=40 and N_0=1000. (left) side view, (right) bottom view.

Download Park et al. supplementary movie(Video)
Video 23.4 MB

Park et al. supplementary movie

Movie 2. Sedimentation of a cloud of copper fibres in a viscous fluid. The movie starts just prior the break-up. The fibre length is typically 1.3 mm.

Download Park et al. supplementary movie(Video)
Video 4.4 MB

Park et al. supplementary movie

Movie 2. Sedimentation of a cloud of copper fibres in a viscous fluid. The movie starts just prior the break-up. The fibre length is typically 1.3 mm.

Download Park et al. supplementary movie(Video)
Video 45.6 MB