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.