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≲0.1, viscosity is controlled by the characteristic cluster size deduced from the kinetic clustering model. For
Re_p∼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≳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.