Abstract
Long-range hydrodynamic interactions of the particles sedimenting in the fluid under gravity force with small Reynolds numbers lead to the large-scale velocity disturbances. Behaviour of the disturbances of the fluid velocity due to fluctuations of particle concentration is described commonly on the basis of solution of the steady Stokes equations. A stability problem for a dilute homogeneous suspension of spherical particles was considered by Koch & Shaqfeh (1989). The orientation of a particle pair are affected by a fluid shear field induced by particle density disturbances. The coupling between the pairs’ velocities and their relative position was suggested as the possible mechanism of the instability. However the linear-stability analysis based on the steady Stokes equations indicated that the suspension is neutrally stable. Nevertheless Segre et al. (1997) in their recent experiments observed the structures in a sedimenting suspension which prove that the instability still occurs.
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References
Asmolov, E. S. 2001 Instability of a suspension of sedimenting spherical particles. Submitted to Eur. J. Mech. B/Fluids.
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.
Batchelor, G. K. & Green, J. T. 1972 The hydrodynamic interactions of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375–400.
Hussain, A. K. M. F. 1983 Coherent structures — reality and myth. Physics of Fluids 26, 2816–2850.
Koch, D. L. & Shaqfeh, E. S. G. 1989 The instability of a dispersion of sedimenting spheroids. J. Fluid Mech. 209, 521–542.
Saffman, P. G. 1973 On the settling speed of free and fixed suspensions. Stud. Appl. Math. 52, 115–127.
Segre, P. N., Herbolzheimer, E. & Chaikin, P. M. 1997 Long ranged correlations in sedimentation. Phys. Rev. Lett. 79, 2574–2577.
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© 2003 Springer Science+Business Media Dordrecht
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Asmolov, E.S. (2003). Numerical Simulation of the Coherent Structures in a Homogeneous Sedimenting Suspension. In: Gyr, A., Kinzelbach, W. (eds) Sedimentation and Sediment Transport. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0347-5_25
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DOI: https://doi.org/10.1007/978-94-017-0347-5_25
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6282-6
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