the rigidwalls made of 80 (20×4) particles each. The radius of thewall
particles is 50 μm (slightly larger than the free-flowing particles), and
the top wall is sheared at a constant rate of 0.1 m/s. Periodic boundary
conditions are applied at the open faces of the shear cell. The physical
properties of the particles are shown in Table 1. These values were
chosen to simulate silica—a material commonly used to make
nanoparticles.
In the results that follow, the shear stress that the top wall
experiences is calculated at each time-step and averaged over a length
of time after it has stabilized (once there is no long-time trend either
up or down in the shear stress). The shear stress is related to the
amount of energy dissipated by the flowing particles. Particles with
higher dissipation require a higher shear force to keep the top wall
moving at a constant velocity.
As seen in Fig. 3 the packing density (reported here as the fraction
solids) has a large effect on the shear stress. Higher solid fractions
produce higher shear stresses. This is a logical relationship resulting
from the greater number of particle contacts being formed and broken
in the denser configurations. As more particle contacts are created and
broken, the total energy dissipated increases, causing a higher shear
stress. Fig. 3 shows that the increase in the shear stress can be several
orders of magnitude.
In our contact force model with adhesion hysteresis, the energy
release rates of loading and unloading can be changed independently.
Both the loading and unloading energy release rates have a large effect
on the resulting shear stress. The shear stresses reported in Fig. 4 were
calculated by changing the energy release rate during unloading (Γr)
while holding the energy release rate during loading constant (Γa).
Increasing Γr in this manner increases the force required to break
particle contacts and increases the energy dissipated for each broken
contact. This increased dissipation again causes a corresponding
increase in the shear stress.