Effects of Long and Short Relaxation Times of Particle Interactions in Dense and Slow Granular Flows

Abstract

The rheological properties and the duration of particle interactions in a dense granular media are closely related to the formation of particle interaction networks. The behavior of particle interaction networks depends not only on the particle volume fractions but also on friction between particles. For examples, for frictionless particles, a particle interaction network may not form at particle volume fraction greater than 0.62, the random dense packing volume fraction for monodisperse spheres. Without network formation, particle interactions are short in time and mostly binary. Under this condition, the granular medium can be modeled as a viscous fluid with variable viscosity as in kinetic theory. Formation of particle interaction networks dramatically increases particle interaction time and results in a phase transition in the constitutive relations of the granular medium. Then, the stress relaxation time is inversely proportional to the macroscopic shear rate in simple shear flows, and the granular medium can be modeled as a viscoelastic material with a stress relaxation time depending on the macroscopic shear rate. For small shear rates, the stresses in the granular medium are independent of macroscopic shear rates in simple shear flows. Thus, as the shear rate approaches zero, the relaxation time approaches infinity, and the shear stress approaches a finite value, the yield stress, instead of zero. We also studied the relaxation behavior of the stress tensor under time-dependent shear rates. The dynamics of the particle interaction network leads to a nonlinear behavior of stress relaxation not exhibited by ordinary viscoelastic materials, such as polymeric fluids.