Granular shear flows of flat disks and elongated rods without and with friction

Abstract

Granular shear flows of flat disks and elongated rods are simulated using the Discrete Element Method. The effects of particle shape, interparticle friction, coefficient of restitution, and Young's modulus on the flow behavior and solid phase stresses have been investigated. Without friction, the stresses decrease as the particles become flatter or more elongated due to the effect of particle shape on the motion and interaction of particles. In dense flows, the particles tend to have their largest dimension aligned in the flow direction and their smallest dimension aligned in the velocity gradient direction, such that the contacts between the particles are reduced. The particle alignment is more significant for flatter disks and more elongated rods. The interparticle friction has a crucial impact on the flow pattern, particle alignment, and stress. Unlike in the smooth layer flows with frictionless particles, frictional particles are entangled into large masses which rotate like solid bodies under shear. In dense flows with friction, a sharp stress increase is observed with a small increase in the solid volume fraction, and a space-spanning network of force chains is rapidly formed with the increase in stress. The stress surge can occur at a lower solid volume fraction for the flatter and more elongated particles. The particle Young's modulus has a negligible effect on dilute and moderately dense flows. However, in dense flows where the space-spanning network of force chains is formed, the stress depends strongly on the particle Young's modulus. In shear flows of non-spherical particles, the stress tensor is found to be symmetric, but anisotropic with the normal component in the flow direction greater than the other two normal components. The granular temperature for the non-spherical particle systems consists of translational and rotational temperatures. The translational temperature is not equally partitioned in the three directions with the component in the flow direction greater than the other two. The rotational temperature is less than the translational temperature at low solid volume fractions, but may become greater than the translational temperature at high solid volume fractions.

Stresses and orientational order in shearing flows of granular liquid crystals

“…The results of our simulations are in agreement with physical experiments on flows of glass cylinders and wooden pegs, characterized by L/d in the range 3.3-5, in a split bottom shear cell [3]. As already shown [17], flat cylinders (L/d equal to or less than 0.5) align again in the plane of shear [ Fig. 2(a)], but the alignment angle is always larger than 45…”

“…Intermediate values indicate that we are in the presence of granular liquid crystals. Figure 2(b) shows that the order parameter usually increases with the solid volume fraction and the maximum between L/d and d/L, as previously noticed [3,17]. Cylinders with aspect ratios equal to 0.8 and 1 are in the granular gas state for the entire range of solid volume fraction [ Fig.…”

“…Figure 4(a) shows the dimensionless viscosity as a function of the solid volume fraction obtained from our numerical simulations. As previously noticed [3,16,17], the particle alignment in the plane of shear causes the viscosity to be greatly reduced with respect to the isotropic case, L/d = 1. Unlike the pressure, the shear stress is sensitive to the flow anisotropy, so that the numerical data do not collapse onto a single curve and Eq.…”

“…1(b)]. This is due to the fact that the particle projected area on the plane perpendicular to the flow is essentially independent of the particle alignment, so that there is no preferential orientation of the particles to minimize the particle contacts [17]. For the other aspect ratios, the flow is in the granular liquid crystal state.…”

“…Hence, ad hoc, but physically sound, modifications of classic kinetic theory have been proposed to take into account velocity correlation among the particles at large solid volume fractions [6][7][8][9][10][11][12], particle surface friction [13,14], and finite stiffness [15]. Recently [16,17], discrete element simulations on simple shear flows of cylinders at different solid volume fractions have been performed to study the influence of length-to-diameter (aspect) ratio, coefficient of collisional restitution, surface friction, and stiffness on the stresses, highlighting differences and similarities with the predictions of the kinetic theory for spheres.…”