Sedimentation of small particles: how can such a simple problem be so difficult?

Élisabeth Guazzelli

doi:10.1016/j.crme.2006.07.009

Sedimentation of small particles: how can such a simple problem be so difficult?
[Sédimentation de petites particules : comment un problème si simple peut-il être si compliqué ?]

Élisabeth Guazzelli ¹

¹ IUSTI CNRS UMR 6595, polytech'Marseille, technopôle de château-Gombert, 13453 Marseille cedex 13, France

Comptes Rendus. Mécanique, Volume 334 (2006) no. 8-9, pp. 539-544.

Résumé
Abstract

La sédimentation de particules à bas nombre de Reynolds peut être considérée comme un des exemples les plus simples d'écoulement de suspension. Et pourtant ce problème est compliqué à cause de la dominance des interactions hydrodynamiques multicorps à longues portées. Trois situations illustreront cette difficulté : la sédimentation d'une suspension de sphères, de particules anisotropes (des fibres) et d'un nuage sphérique de particules.

Although sedimentation can be considered as one of the simplest examples of suspension flow, much remains unknown about the fundamental properties of sedimenting suspensions. The problem that one encounters lies in the long range nature of the multibody hydrodynamic interactions between particles. This will be illustrated for sedimenting suspensions of spheres, of non-spherical particles such as fibers, and for sedimenting clouds of particles.

Publié le : 2006-08-01

DOI : 10.1016/j.crme.2006.07.009

Keywords: Fluid mechanics, Sedimentation, Multibody hydrodynamic interactions, Low Reynolds number
Mot clés : Mécanique des fluides, Sédimentation, Interactions hydrodynamiques multicorps, Bas nombre de Reynolds

Affiliations des auteurs :

Élisabeth Guazzelli ¹

¹ IUSTI CNRS UMR 6595, polytech'Marseille, technopôle de château-Gombert, 13453 Marseille cedex 13, France

@article{CRMECA_2006__334_8-9_539_0,
     author = {\'Elisabeth Guazzelli},
     title = {Sedimentation of small particles: how can such a simple problem be so difficult?},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {539--544},
     publisher = {Elsevier},
     volume = {334},
     number = {8-9},
     year = {2006},
     doi = {10.1016/j.crme.2006.07.009},
     language = {en},
}

TY  - JOUR
AU  - Élisabeth Guazzelli
TI  - Sedimentation of small particles: how can such a simple problem be so difficult?
JO  - Comptes Rendus. Mécanique
PY  - 2006
SP  - 539
EP  - 544
VL  - 334
IS  - 8-9
PB  - Elsevier
DO  - 10.1016/j.crme.2006.07.009
LA  - en
ID  - CRMECA_2006__334_8-9_539_0
ER  -

%0 Journal Article
%A Élisabeth Guazzelli
%T Sedimentation of small particles: how can such a simple problem be so difficult?
%J Comptes Rendus. Mécanique
%D 2006
%P 539-544
%V 334
%N 8-9
%I Elsevier
%R 10.1016/j.crme.2006.07.009
%G en
%F CRMECA_2006__334_8-9_539_0

Élisabeth Guazzelli. Sedimentation of small particles: how can such a simple problem be so difficult?. Comptes Rendus. Mécanique, Volume 334 (2006) no. 8-9, pp. 539-544. doi : 10.1016/j.crme.2006.07.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.07.009/

Bibliographie
Cité par

[1] G.K. Batchelor Sedimentation in a dilute dispersion of spheres, J. Fluid Mech., Volume 52 (1972), pp. 245-268

[2] J.M. Ham; G.M. Homsy Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspension, Int. J. Multiphase Flow, Volume 14 (1988), pp. 533-546

[3] H. Nicolai; B. Herzhaft; E.J. Hinch; L. Oger; E. Guazzelli Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres, Phys. Fluids, Volume 7 (1995), pp. 12-23

[4] R.E. Caflisch; J.H.C. Luke Variance in the sedimenting speed of a suspension, Phys. Fluids, Volume 28 (1985), pp. 759-760

[5] E.J. Hinch Sedimentation of small particles (E. Guyon; J.-P. Nadal; Y. Pomeau, eds.), Disorder and Mixing, Kluwer Academic, Dordrecht, 1988, pp. 153-161

[6] H. Nicolai; E. Guazzelli Effect of the vessel size on the hydrodynamic diffusion of sedimenting spheres, Phys. Fluids, Volume 7 (1995), pp. 3-5

[7] P.N. Segrè; E. Helbolzheimer; P.M. Chaikin Long-range correlations in sedimentation, Phys. Rev. Lett., Volume 79 (1997), pp. 2574-2577

[8] É. Guazzelli Evolution of particle-velocity correlations in sedimentation, Phys. Fluids, Volume 13 (2001), pp. 1537-1540

[9] D.L. Koch; E.S.G. Shaqfeh Screening mechanisms in sedimenting suspension, J. Fluid Mech., Volume 224 (1991), pp. 275-303

[10] A. Levine; S. Ramaswamy; E. Frey; R. Bruinsma Screened and unscreened phases in sedimenting suspensions, Phys. Rev. Lett., Volume 81 (1998), pp. 5944-5947

[11] P. Tong; B.J. Ackerson Analogies between colloidal sedimentation and turbulent convection at high Prandtl numbers, Phys. Rev. E, Volume 58 (1998), p. R6931

[12] M.P. Brenner Screening mechanisms in sedimentation, Phys. Fluids, Volume 11 (1999), pp. 754-772

[13] J.H.C. Luke Decay of velocity fluctuations in a stably stratified suspension, Phys. Fluids, Volume 12 (2000), pp. 1619-1621

[14] A.J.C. Ladd Effect of container walls on the velocity fluctuations of sedimenting spheres, Phys. Rev. Lett., Volume 88 (2002), p. 048301

[15] S.-Y. Tee; P.J. Mucha; L. Cipelletti; S. Manley; M.P. Brenner; P.N. Segrè; D.A. Weitz Nonuniversal velocity fluctuations of sedimenting particles, Phys. Rev. Lett., Volume 89 (2002), p. 054501

[16] P.J. Mucha; S.-Y. Tee; D.A. Weitz; B.I. Shraiman; M.P. Brenner; P.N. Segrè; D.A. Weitz A model for velocity fluctuations in sedimentation, J. Fluid Mech., Volume 501 (2004), pp. 71-104

[17] E.S. Asmolov Evolution of fluctuations in a suspension sedimenting in a container bounded by horizontal walls, Phys. Fluids, Volume 16 (2004), pp. 3086-3093

[18] N.-Q. Nguyen; A.J.C. Ladd Microstructure in a settling suspension of hard spheres, Phys. Rev. Lett. E, Volume 69 (2004), p. 050401

[19] N.-Q. Nguyen; A.J.C. Ladd Sedimentation of hard-sphere suspensions at low Reynolds number, J. Fluid Mech., Volume 525 (2005), pp. 73-104

[20] L. Bergougnoux; S. Ghicini; É. Guazzelli; E.J. Hinch Spreading fronts and fluctuations in sedimentation, Phys. Fluids, Volume 15 (2003), pp. 1875-1887

[21] D. Chehata, L. Bergougnoux, É. Guazzelli, E.J. Hinch, in preparation

[22] D.L. Koch; E.S.G. Shaqfeh The instability of a dispersion of sedimenting spheroids, J. Fluid Mech., Volume 209 (1989), pp. 521-542

[23] B. Herzhaft; É. Guazzelli; M.B. Mackaplow; E.S.G. Shaqfeh Experimental investigation of the sedimentation of a dilute fiber suspension, Phys. Rev. Lett., Volume 77 (1996), pp. 290-293

[24] B. Herzhaft; É. Guazzelli Experimental study of the sedimentation of dilute and semi-dilute suspensions of fibres, J. Fluid Mech., Volume 384 (1999), pp. 133-158

[25] B. Metzger; É. Guazzelli; J.E. Butler Large-scale streamers in the sedimentation of a dilute fiber suspension, Phys. Rev. Lett., Volume 95 (2005), p. 164506

[26] M.B. Mackaplow; E.S.G. Shaqfeh A numerical study of the sedimentation of fibre suspension, J. Fluid Mech., Volume 376 (1998), pp. 149-182

[27] J.E. Butler; E.S.G. Shaqfeh Dynamic simulations of the inhomogeneous sedimentation of rigid fibres, J. Fluid Mech., Volume 468 (2002), pp. 205-237

[28] D. Saintillan; E. Darve; E.S.G. Shaqfeh A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers, Phys. Fluids, Volume 17 (2005), p. 033301

[29] D. Saintillan; E.S.G. Shaqfeh; E. Darve The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation, J. Fluid Mech., Volume 553 (2006), pp. 347-388

[30] J.M. Nitsche; G.K. Batchelor Break-up of a falling drop containing dispersed particles, J. Fluid Mech., Volume 340 (1997), pp. 161-175

[31] B. Metzger; M.L. Ekiel-Jeżewska; É. Guazzelli Spherical cloud of point particles falling in a viscous fluid, Phys. Fluids, Volume 18 (2006), p. 038104

[32] G. Machu; W. Meile; L.C. Nitsche; U. Schaflinger Coalescence, torus formation and breakup of sedimenting drops: experiments and computer simulations, J. Fluid Mech., Volume 447 (2001), pp. 299-336

Cité par Sources :

Commentaires - Politique