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Viscosity of a dense suspension in Couette flow

Published online by Cambridge University Press:  15 October 2007

NICOLAS HUANG  and
DANIEL BONN
NICOLAS HUANG
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
DANIEL BONN
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlandsdaniel.bonn@lps.ens.fr
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Abstract

We study the rheology of a granular paste, i.e. a dense suspension of non-Brownian particles, quantitatively at steady state, in a cylindrical Couette cell. Previous studies have shown a discrepancy between local and global measurements of the viscosity for these materials, making it impossible to predict their resistance to flow. Using both MRI investigation techniques and classical rheology studies, we show that agreement between local and global measurements can be obtained, provided the migration of particles inside the gap is taken into account. As found by Leighton & Acrivos (J. Fluid Mech. vol. 181, 1987, p. 415), the migration leads to a particle density gradient in the flow, the highly sheared regions being less dense in particles. Here, by comparing the local viscosity and particle density measurements from MRI with the macroscopic relation between viscosity and the volume fraction, it is shown that global and local measurements agree with each other. This consequently allows us to define a viscosity for dense suspensions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 497 - 507
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Abbott, J. R., Tetlow, N., Graham, A. L., Altobelli, S. A., Fushima, E., Mondy, L. A. & Stephens, T. S. 1991 A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration: Couette flow. J. Rheol. 35.CrossRefGoogle Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a newtonian fluid under shear. Proc. R. Soc. Lond. 225, 49–63.Google Scholar
Barentin, C., Azanza, E. & Pouligny, B. 2004 Flow and segregation in sheared granular slurries. Europhys. Lett. 66, 139–145.CrossRefGoogle Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluid Mech. 17, 103301.CrossRefGoogle Scholar
da Cruz, F. 2004 Écoulement de grains secs: frottement et blocage. PhD thesis, École Nationale des Ponts et Chaussées, Marne-la-Vallée.Google Scholar
Gadala-Maria, F. & Acrivos, A. 1980 The avalanching of granular solids on dune and similar slopes. J. Rheol. 24, 799–814.Google Scholar
GDRMiDi 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.Google Scholar
Herminghaus, S. 2005 Dynamics of wet granular matter. Adv. Phys. 54, 221–261.CrossRefGoogle Scholar
Huang, N., Ovarlez, G., Bertrand, F., Rodts, S., Coussot, P. & Bonn, D. 2005 Flow of wet granular materials. Phys. Rev. Lett. 94, 028301.CrossRefGoogle ScholarPubMed
Hunt, M. L., Zenit, R., Campbell, C. S. & Brennen, C. E. 2002 Revisiting the 1954 suspension experiments of r. a. bagnold. J. Fluid Mech. 452, 1–24.CrossRefGoogle Scholar
Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of side walls for granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167–192.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441, 727–730.CrossRefGoogle ScholarPubMed
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137–152.CrossRefGoogle Scholar
Lagrée, P.-Y. & Lhuillier, D. 2006 The Couette flow of dense and fluid-saturated granular media. Eur. J. Mech. B-Fluids 25, 960–970.CrossRefGoogle Scholar
Larson, R. G. 1999 In The Structure and Rheology of Complex Fluids. Oxford University Press.Google Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.CrossRefGoogle Scholar
Lenoble, M., Sabre, P. & Pouligny, B. 2005 The flow of a very concentrated slurry in a parallel-plate device: Influence of gravity. Phys. Fluids 17, 073303.CrossRefGoogle Scholar
Mueth, D. M., Debregeas, G. F., Karczmar, G. S., Eng, P. J., Nagel, S.R. & Jaeger, H. M. 2000 Signatures of granular microstructure in dense shear flows. Nature 406, 385–389.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A. L. & Abbott, J. R. 1992 A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A 4, 30–40.CrossRefGoogle Scholar
Raynaud, J. S., Moucheront, P., Baudez, J. C., Bertrand, F., Guilbaud, J. P. & Coussot, P. 2002 Direct determination by nuclear magnetic resonance of the thixotropic and yielding behavior of suspensions. J. Rheol. 46, 709–732.CrossRefGoogle Scholar
Rodts, S., Bertrand, F., Jarny, S., Poullain, P. & Moucheront, P. 2004 Développements récents dans l'application de l'IRM á la rhéologie et á la mécanique des fluides. C. R. Chimie 7, 275–282.Google Scholar
Wolthers, W., van den Ende, D., Duits, M. H. G. & Mellema, J. 1996 The viscosity and sedimentation of aggregating colloidal dispersions in a Couette flow. J. Rheol. 40, 55–67.CrossRefGoogle Scholar