A study of the rheology of planar granular flow of dumbbells using discrete element method simulations

Abstract

Granular materials handled in industries are typically non-spherical in shape and understanding the flow of such materials is important. The steady flow of mono-disperse, frictional, inelastic dumbbells in two-dimensions is studied by soft sphere, discrete element method simulations for chute flow and shear cell flow. The chute flow data are in the dense flow regime, while the shear cell data span a wide range of solid fractions. Results of a detailed parametric study for both systems are presented. In chute flow, increase in the aspect ratio of the dumbbells results in significant slowing of the flow at a fixed inclination and in the shear cell it results in increase in the shear stress and pressure for a fixed shear rate. The flow is well-described by the μ-I scaling for inertial numbers as high as I = 1, corresponding to solid fractions as low as ϕ = 0.3, where μ is the effective friction (the ratio of shear stress to pressure) and I is the inertial number (a dimensionless shear rate scaled with the time scale obtained from the local pressure). For a fixed inertial number, the effective friction increases by 60%-70% when aspect ratio is increased from 1.0 (sphere) to 1.9. At low values of the inertial number, there is little change in the solid fraction with aspect ratio of the dumbbells, whereas at high values of the inertial number, there is a significant increase in solid fraction with increase in aspect ratio. The dense flow data are well-described by the Jop-Forterre-Pouliquen model [P. Jop et al., Nature 441, 727–730 (2006)] with the model parameters dependent on the dumbbell aspect ratio. The variation of μ with I over the extended range shows a maximum in the range I ∈ (0.4, 0.5), while the solid fraction shows a faster than linear decrease with inertial number. A modified version of the JFP model for μ(I) and a power law model for ϕ(I) is shown to describe the combined data over the extended range of I.