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Dense suspensions in rotating-rod flows: normal stresses and particle migration

Published online by Cambridge University Press:  30 August 2011

François Boyer ,
Olivier Pouliquen  and
Élisabeth Guazzelli
François Boyer*
Affiliation:
IUSTI-CNRS UMR 6596, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille cedex 13, France
Olivier Pouliquen
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: francois.boyer@polytech.univ-mrs.fr
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Abstract

Normal stress differences are measured in dense suspensions of neutrally buoyant non-Brownian spheres dispersed in a Newtonian fluid. Rotating-rod rheometry is used to characterize the suspension normal stresses which are responsible for a rod-dipping phenomenon. These normal stress differences are seen to strongly increase above a volume fraction of approximately 22 %. During the course of the experiments, a new time-dependent behaviour is also observed: the dip is filled with increasing times. This time evolution is found to be related to particle migration from regions of high shear rate to regions of low shear rate. The behaviour is compared with the predictions of a suspension balance model in which the particle migration flux is related to the normal stresses of the suspension.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 5 - 25
Copyright
Copyright © Cambridge University Press 2011

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References

1. Abott, J. R., Tetlow, N. & Graham, A. L. 1991 Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol. 35, 773–795.Google Scholar
2. Barnes, H. A. 1995 A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure. J. Non-Newtonian Fluid Mech. 56, 221–251.Google Scholar
3. Batchelor, G. K. & Green, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401–427.Google Scholar
4. Beavers, G. S. & Joseph, D. D. 1975 The rotating-rod viscometer. J. Fluid Mech. 69, 475–512.Google Scholar
5. Couturier, É., Boyer, F., Pouliquen, O. & Guazzelli, É. 2011 Suspensions in a tilted trough: second normal stress difference. J. Fluid Mech. 10.1017/jfm.2011.315.Google Scholar
6. De Gennes, P.-G. 1979 Conjectures on the transition from Poiseuille to plug flow in suspensions. J. Phys. France 40, 783–787.Google Scholar
7. Gadala-Maria, F. & Acrivos, A. 1980 Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799.Google Scholar
8. Einstein, A. 1905 Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. (4) 17, 549–560 1956, reprinted in Investigations on the Theory of Brownian Movement. Dover Publications.Google Scholar
9. Krieger, I. M. 1963 A dimensional approach to colloid rheology. Trans. Soc. Rheol. 7, 101–109.CrossRefGoogle Scholar
10. Krieger, I. M. 1972 Rheology of monodisperse lattice. Adv. Colloid Interface Sci. 3, 111–136.Google Scholar
11. Leighton, D. T. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.CrossRefGoogle Scholar
12. Lhuillier, D. 2009 Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.Google Scholar
13. Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 1213–1237.CrossRefGoogle Scholar
14. Morris, J. F. 2009 A review of microstructure in concentrated suspensions and its implication for rheology and bulk flow. Rheol. Acta 48, 909–923.CrossRefGoogle Scholar
15. Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209–223.CrossRefGoogle Scholar
16. Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157–199.Google Scholar
17. Nott, P. R., Guazzelli, É. & Pouliquen, O. 2011 The suspension balance revisited. Phys. Fluids 23, 043304.CrossRefGoogle Scholar
18. Ovarlez, G., Bertrand, F. & Rodts, S. 2006 Local determination of the constitutive law of a dense suspension of non-colloidal particles through MRI. J. Rheol. 50, 259–292.CrossRefGoogle Scholar
19. Richardson, J. F. & Zaki, W. N. 1954 Sedimentation and fluidization: part I. Trans. Inst. Chem. Engrs 32, 35–53.Google Scholar
20. Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated non-colloidal suspensions. J. Rheol. 46, 1031–1056.Google Scholar
21. Singh, A. & Nott, P. R. 2000 Normal stresses and microstructure in bounded sheared suspensions via Stokesian dynamics simulations. J. Fluid Mech. 412, 279–301.Google Scholar
22. Singh, A. & Nott, P. R. 2003 Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490, 293–320.Google Scholar
23. Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
24. Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
25. Taylor, J. R. 1982 An introduction to error analysis. In University Science Books. Oxford University Press.Google Scholar
26. Tetlow, N. et al. 1998 Particle migration in a Couette apparatus: experiment and modeling. J. Rheol. 42, 307–328.Google Scholar
27. Wilson, H. J. 2005 An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. J. Fluid Mech. 534, 97–114.Google Scholar
28. Zarraga, I. E., Hill, D. A. & Leighton, D. T. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185–220.Google Scholar