Clustering and viscosity in a shear flow of a particulate suspension

A shear flow of particulate suspension is analyzed for the qualitative effect of particle clustering on viscosity using a simple kinetic clustering model and direct numerical simulations. The clusters formed in a Couette flow can be divided into rotating chainlike clusters and layers of particles at the channel walls. The size distribution of the rotating clusters is scale invariant in the small-cluster regime and decreases rapidly above a characteristic length scale that diverges at a jamming transition. The behavior of the suspension can qualitatively be divided into three regimes. For particle Reynolds number Re(p) less than or approximately equal 0.1, viscosity is controlled by the characteristic cluster size deduced from the kinetic clustering model. For Re(p) approximately 1, clustering is maximal, but the simple kinetic model becomes inapplicable presumably due to onset of instabilities. In this transition regime viscosity begins to increase. For Re(p) greater than or approximately equal 10, inertial effects become important, clusters begin to breakup, and suspension displays shear thickening. This phenomenon may be attributed to enhanced contribution of solid phase in the total shear stress.