Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T21:09:45.389Z Has data issue: false hasContentIssue false
  • English
  • Français

The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation

Published online by Cambridge University Press:  20 April 2006

John F. Brady  and
Georges Bossis
John F. Brady
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Georges Bossis
Affiliation:
Laboratoire de Physique de la Matière Condensée, Université de Nice, Parc Valrose, 06034 Nice Cedex
Get access Rights & Permissions [Opens in a new window]

Abstract

The newly developed simulation method known as Stokesian dynamics is used to investigate the rheological behaviour of concentrated suspensions. Both the detailed microstructure (e.g. pair-distribution function) and the macroscopic properties are determined for a suspension of identical rigid spherical particles in a simple shear flow. The suspended particles interact through both hydrodynamic and non-hydrodynamic forces. For suspensions with purely hydrodynamic forces, the increase in the suspension viscosity with volume fraction ϕ is shown to be caused by particle clustering. The cluster formation results from the lubrication forces, and the simulations of a monolayer of spheres show a scaling law for the cluster size: lc ∼ [1 − (ϕ/ϕm)½]−1, where ϕm is the maximum volume fraction that can shear homogeneously. The simulation results suggest that the suspension viscosity becomes infinite at the percolation-like threshold ϕm owing to the formation of an infinite cluster. The predicted simulation viscosities are in very good agreement with experiment. A suspension with short-range repulsive interparticle forces is also studied, and is seen to have a non-Newtonian rheology. Normal-stress differences arise owing to the anisotropic local structure created by the interparticle forces. The repulsive forces also reduce particle clustering, and as a result the suspension is shear-thickening.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 105 - 129
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adler, P. M., Zuzovsky, M. & Brenner, H. 1985 Intl J. Multiphase Flow (to appear).
Arp, P. A. & Mason, S. G. 1977 J. Coll. Interface Sci. 61, 21.
Bagnold, R. A. 1954 Proc. R. Soc. Lond. A 225, 49.
Batchelor, G. K. 1970 J. Fluid Mech. 41, 545.
Batchelor, G. K. 1974 Ann. Rev. Fluid Mech. 6, 227.
Batchelor, G. K. 1977 J. Fluid Mech. 83, 97.
Batchelor, G. K. & Green, J. T. 1972a J. Fluid Mech. 56, 375.
Batchelor, G. K. & Green, J. T. 1972b J. Fluid Mech. 56, 401.
Beenakker, C. W. J. 1984 Physica A 128, 44.
Beenakker, C. W. J. & Mazur, P. 1983 Physica A 120, 338.
Belzons, M., Blanc, R., Bouillot, J. L. & Camoin, C. 1981 C. R. Acad. Sci. Paris 292, 939.
Bossis, G. & Brady, J. F. 1984 J. Chem Phys. 80, 5141.
Bouillot, J. L., Camoin, C., Belzons, M., Blanc, R. & Guyon, E. 1982 Adv. Coll. Interface Sci. 17, 299.
Brenner, H. 1974 Intl J. Multiphase Flow 1, 195.
Einstein, A. 1906 Annalen Phys. 19, 298 (and 34, 591).
Evans, D. J. 1979 Mol. Phys. 37, 1745.
Frankel, N. A. & Acrivos, A. 1967 Chem. Engng Sci. 22, 847.
Gadala-Maria, F. A. 1979 Ph.D. Thesis, Stanford University.
Gadala-Maria, F. A. & Acrivos, A. 1980 J. Rheol. 24, 799.
Hoffman, R. L. 1972 Trans. Soc. Rheol. 16, 155.
Husband, D. M. & Gadala-Maria, F. A. 1984 Proc. 9th Intl Congr. Rheology, Acapulco, Mexico.
Jeffrey, D. J. & Acrivos, A. 1976 AIChE J. 22, 417.
Jeffrey, D. J. & Onishi, Y. 1984 J. Fluid Mech. 139, 261.
Kim, S. & Mifflin, R. T. 1985, Phys. Fluids (to appear).
Krieger, I. M. 1972 Adv. Coll. Interface Sci. 3, 111.
Mazur, P. & van Saarloos, W. 1982 Physica A 115, 21.
Nunan, K. C. & Keller, J. B. 1984 J. Fluid Mech. 142, 269.
O'Brien, R. W. 1979 J. Fluid Mech. 19, 17.
Pätzold, R. 1980 Rheol. Acta 19, 322.
Peterson, J. M. & Fixman, M. 1963 J. Chem. Phys. 39, 2516.
Russel, W. H. 1978 J. Fluid Mech. 85, 673.
Russel, W. B. 1980 J. Rheol. 24, 287.
Vervey, E. G. & Overbeek, J. T. G. 1948 Theory of the Stability of Lyophobic Colloids. Elsevier.