1. Introduction

Fundamental understanding of the flow behavior of bulk solids is essential for granular material handling and the design of relevant industrial processes and equipment, such as hoppers, silos and blenders. The Schulze Ring Shear Tester (SRST) is one of the most popular testers of bulk solids flow properties and it can measure the shear stresses under various normal stresses. Therefore, the internal friction angle, wall friction angle, unconfined yield strength, bulk density and flow function of the tested granular material can also be provided1,2. In addition, numerical approaches such as Discrete Element Method (DEM) are also increasingly applied to investigate the flow behavior of granular materials. Detailed information at the individual particle level, such as the particle position, particle velocity and forces exerted on the particle, can be obtained from DEM simulations, which is helpful for exploring the mechanisms of particle behavior3,4.
Both previous experimental and numerical research has shown that the flow behavior of bulk solids could be influenced by many factors. The effect of particle shape was investigated by Baran et al.5 and results shown that the shear stress for spherical particles was considerably lower than that of aspherical particles. Shear stress for aspherical particles were found larger than that for spherical ones, for both monodisperse6 and binary mixtures7. The internal friction angle was increased by preventing particle rotation8. The shear stress was also found to increase with increasing coefficient of friction between particles2,5,9. On the other hand, the shear cell size, shear rate, particle shear modulus, particle Poisson’s ratio, the coefficient of restitution and particle-particle cohesion were argued to have insignificant influence on the shear stress2,5,9.
Among the factors affecting the flow properties of bulk solids, particle size polydispersity is known to have an important effect on particle flow behavior7,10–12. Rule of Mixture (ROM) approaches are often employed in predicting the flow behavior of binary or higher-order powder systems. In ROM frameworks, the predicted properties are calculated using the properties of constitutive components, which are weighted by their composition of the final blend using various averaging techniques. For example, the flow function coefficient for binary mixtures of acetaminophen and starch were found to decrease with increasing mass fraction of acetominophen, which exhibits poorer flow behavior than starch as a pure material13. For binary systems, any property predicted using ROM will always fall between those of the raw components. However, this approach ignores many complex interactions inherent to mixtures of particles, and even seemingly simple systems deviate from trends predicted by ROM approaches.
Analogs to the systems evaluated here have previously been shown to exhibit behavior that cannot be explained by simple ROM approaches. Vallejo12 conducted laboratory tests on mixtures of large (5000 µm) and small (400 µm) glass beads to evaluate the shear strength of the resultant blends, and reported a strong dependence on the relative concentration of the mass fraction of large and small particles. In the range of 40-70% mass fraction of large particles, shear strength decreased with decreasing fraction of large particles. However, shear strength was controlled by the frictional resistance of the large particles if the mass fraction of large particles exceeded 70%, whereas the effect of small particles dominated when below 40%. Vallejo argued that these limits resulted from changes in mixture porosity and particle configuration.
In order to evaluate the effect of particle size polydispersity on the flow behavior, experiments are set up to obtain shear stress data in a simple flow configuration (SRST) using a model system of well-characterized, binary mixtures of spherical glass beads. By varying the ratio of small to large particles in the system, this approach facilitates a detailed study of the effect of polydispersity on the flow behavior of particle mixtures. Furthermore, in order to investigate the fundamental underpinnings associated with the flow behavior (i.e. shear stress trend), DEM is applied to model the shear flows of such mixtures in the ring shear cell. First, the experimental data are used to validate the model predictions. Then, via DEM, the effects of particle rotation, particle contact type, particle contact number and force network are investigated. By analyzing these effects, potential underlying mechanisms giving rise to the variation in mixture flowability are proposed and explored.