Microstructure and stress differences in shearing flows

Steady shearing flows of highly inelastic particles are simulated using rigid and slightly deformable sphere models. Large first normal stress differences in small systems are observed, which are consistent with the recent kinetic theory of Richman and Chou [1989] at low solids fractions and restitution coefficients. However, as the number of particles in the system increases, the stress difference deviates (with significantly larger values) from the theoretical predictions in a small range of solids fractions near 0.1. Long-time fluctuations of the total kinetic energy in the calculational cell coupled with visualizations of the particle positions in this solids fraction range clearly indicate the existence of a granular mocrostructure, characterized by the formation and break-up of particle clusters in the flow. A different type of microstructure is exhibited in the dense solids fraction region in which particle contacts occur at approximately 45° in the shearing plane.