4.2 Gravity-Driven Flow Regime Characterization
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discharging procedure of particles dominates the variation of mean velocity. The
characteristic period for mean velocity variation is 0.3s, and the period of discharging
is 0.01 s. Thus, to remove 30 particles on average can cause a sudden change of mean
velocity, or cause an internal bulk motion of falling. But this speed of discharging
is so fast that the falling particles are discharged from the bottom immediately even
before the tightly packed state is recovered. Thus, there is no corresponding periodic
variation of mean force, and the force is found to fluctuate intensely.
4.2.2.3 Discussion of Kinetic Regime and Kinematic Flow Regimes
Based on the observations and performed analyses, the gravity-driven particle flows
can be divided into two regimes:
• The first regime can be considered as a kinetics-characterized regime, termed as
slow particle flows. This flow regime is characterized mainly by the existence of
an evident characteristic period or fundamental frequency of time variation of the
mean contact force. It is fairly intermittent. The subsequent particle to be removed
from the bed in such an extended period after the discharge allows the force
structures for responding to the change of increasing “cavity” of particle assembly
and increasing “fault” or instability of force structures. The large structure of the
force can maintain its present state until a critical point is met when the force
structure subsequently becomes weak. The sudden internal bulk motion of the
falling and sudden change of the force structure occurs. As the contact force is
viewed as a dynamic variable, this type of particle flow is known as a kineticsdominated or kinetics-characterized flow. The intermittency characteristics are
mainly related to the dynamic variables.
• The other regime, which is considered as kinematic flow, is related to fluid-like
flow behavior and termed as a fast dense flow regime here. In this type of flow,
it is characterized mainly by kinematic variables, such as velocity. The kinematic
variables rapidly vary so that they exhibit a continuous spectrum. In this particular
case, the discharging rate is so high that the force structures are unable to maintain
a steady-state or form a fully connected stationary packing state before the subsequent particle is discharged. The distribution of particles and force structures
could thus always be in an unsteady state. The variation of mean force derivative
and velocity are closely correlated. Referring to the fluid-like motion behavior, the
correlation of mean force and velocity in fast dense flow is analogous to the correlation of pressure drop (normal internal force) and velocity in fluid flow. Thus,
this velocity-dominated or kinematic-variable-characterized flow regime could be
described by continuum theories, and the large-scale internal flow intermittency
is of secondary importance compared to the slow flow.
In conclusion, the categorization of gravity-driven particle flow can be characterized by either kinematic or kinetic flow variables. The kinematic flow regime
corresponds to a fast dense flow and the kinetic flow is related to a slow particle
flow. In the kinematic flow regime, the flow is fluid-like, dynamic stationary, and the
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discharging procedure of particles dominates the variation of mean velocity. The
characteristic period for mean velocity variation is 0.3s, and the period of discharging
is 0.01 s. Thus, to remove 30 particles on average can cause a sudden change of mean
velocity, or cause an internal bulk motion of falling. But this speed of discharging
is so fast that the falling particles are discharged from the bottom immediately even
before the tightly packed state is recovered. Thus, there is no corresponding periodic
variation of mean force, and the force is found to fluctuate intensely.
4.2.2.3 Discussion of Kinetic Regime and Kinematic Flow Regimes
Based on the observations and performed analyses, the gravity-driven particle flows
can be divided into two regimes:
• The first regime can be considered as a kinetics-characterized regime, termed as
slow particle flows. This flow regime is characterized mainly by the existence of
an evident characteristic period or fundamental frequency of time variation of the
mean contact force. It is fairly intermittent. The subsequent particle to be removed
from the bed in such an extended period after the discharge allows the force
structures for responding to the change of increasing “cavity” of particle assembly
and increasing “fault” or instability of force structures. The large structure of the
force can maintain its present state until a critical point is met when the force
structure subsequently becomes weak. The sudden internal bulk motion of the
falling and sudden change of the force structure occurs. As the contact force is
viewed as a dynamic variable, this type of particle flow is known as a kineticsdominated or kinetics-characterized flow. The intermittency characteristics are
mainly related to the dynamic variables.
• The other regime, which is considered as kinematic flow, is related to fluid-like
flow behavior and termed as a fast dense flow regime here. In this type of flow,
it is characterized mainly by kinematic variables, such as velocity. The kinematic
variables rapidly vary so that they exhibit a continuous spectrum. In this particular
case, the discharging rate is so high that the force structures are unable to maintain
a steady-state or form a fully connected stationary packing state before the subsequent particle is discharged. The distribution of particles and force structures
could thus always be in an unsteady state. The variation of mean force derivative
and velocity are closely correlated. Referring to the fluid-like motion behavior, the
correlation of mean force and velocity in fast dense flow is analogous to the correlation of pressure drop (normal internal force) and velocity in fluid flow. Thus,
this velocity-dominated or kinematic-variable-characterized flow regime could be
described by continuum theories, and the large-scale internal flow intermittency
is of secondary importance compared to the slow flow.
In conclusion, the categorization of gravity-driven particle flow can be characterized by either kinematic or kinetic flow variables. The kinematic flow regime
corresponds to a fast dense flow and the kinetic flow is related to a slow particle
flow. In the kinematic flow regime, the flow is fluid-like, dynamic stationary, and the