Journal of Fluid Mechanics

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

John F.  Brady a1 and Georges  Bossis a2
a1 Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
a2 Laboratoire de Physique de la Matière Condensée, Université de Nice, Parc Valrose, 06034 Nice Cedex

Article author query
brady jf   [Google Scholar] 
bossis g   [Google Scholar] 


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 [similar] [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.

(Published Online April 20 2006)
(Received October 3 1984)