Dense granular flow of mixtures of spheres and dumbbells down a rough inclined plane: Segregation and rheology

Abstract

We study the flow of equal-volume binary granular mixtures of spheres and dumbbells with different aspect ratios down a rough inclined plane, using the discrete element method. We consider two types of mixtures -- in the first type the particles of the two species have equal volume but different aspect ratios (EV) and in the second type they have variable volumes and aspect ratios (VV). We also use mixtures of spheres of two different sizes (SS) with the same volume ratios as in the mixtures of the second type, as the base case. Based on the study of Guillard, Forterre and Pouliquen [\textit{J. Fluid Mech.} \textbf{807}, R1--R11 (2016)], the inclination angle of the base for each mixture is adjusted and maintained at a high value to yield the same pressure and shear stress gradients for all mixtures and a high effective friction ($μ$) for each. This ensures that the segregation force and resulting extent of segregation depend only the size and shape of the particles. The species with larger effective size, computed in terms of the geometric mean diameter, floats up in all cases and the dynamics of the segregation process for all the mixtures are reported. The concentration profiles of the species at steady state agree well with the predictions of a continuum theory. The $μ-I$ and $ϕ-I$ scaling relations, where $I$ is the inertial number and $ϕ$ is the solid volume fraction, extended to the case of mixtures, are shown to describe the rheology for all the cases.