4.4 Summary
231
scale structure change of forces usually happens suddenly and intermittently. The
mechanisms can be summarized as follows:
When the particles are being removed at the bottom, the structure of local forces
may change slightly and depart from the local force equilibrium. Still, its influence
is restricted within a local region. A large-scale structure of force or particle distributions is maintained, though its strength may be gradually attenuated. The forthcoming
change of the large-scale structure is delayed, but the degree of large-scale instability
is increasing;
As time progresses, particles are removed continuously. The force structures and
the base at the bottom for supporting the upside particles become weaker. At some
time, the sudden change of large-scale structure takes place, which behaves like an
internal “quake” of the particle assembly. This sudden change is always accompanied
by the internal bulk motion of falling, during which the overall magnitude of the mean
velocity of particles must increase. The autocorrelation functions and its Fourier
spectrum are utilized to show the differences in the mechanisms of the slow and the
fast particle flows. Based on the observations and performed analyses, the gravitydriven particle flows can be divided into two regimes:
• Kinetics-characterized regime Termed as slow particle flows, it is characterized
mainly by the existence of an evident characteristic period or fundamental frequency of time variation of the mean contact force. As the contact force is viewed
as a dynamic variable, this type of particle flow is known as a kinetics-dominated
or kinetics-characterized flow. The intermittency characteristics are mainly related
to the dynamic variables.
• Kinematic regime Considered as kinematic flow, it is related to fluid-like flow
behavior and termed as a fast dense flow regime, featured mainly by kinematic
variables, such as velocity. The kinematic variables rapidly vary so that they exhibit
a continuous spectrum and the distribution of particles and force structures could
always be in an unsteady state. 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.
The underlying complex mechanisms of slow particle flows, as well as some
important issues on flow regime characterization, via exploring the intermittency
characteristics of a slow particle flow comparing to a fast dense flow are provided.
The kinetic energy of the granular system and the phenomena of pebble avalanche and
flow intermittence are illustrated in detail. As a quantitative method, the “single-peak”
distribution rule is introduced to characterize the time-energy distribution feature of
gravity-driven dense particle flows. A new general statistical criterion is proposed
to subdivide the elastic–quasi-static regime, which may help to characterize dense
particle flows under gravity. According to the span of energy magnitude (E span ) and
the standard deviation σ , the specific subdivision criteria for subdividing the flow
regime of gravity-driven dense particle flow are as follows:
• σ b <0.1,E span >1: Extremely slow flow;
• σ b >0.1: Intermittent flow;
• σ b <0.1,E span <1: Consistent flow.
231
scale structure change of forces usually happens suddenly and intermittently. The
mechanisms can be summarized as follows:
When the particles are being removed at the bottom, the structure of local forces
may change slightly and depart from the local force equilibrium. Still, its influence
is restricted within a local region. A large-scale structure of force or particle distributions is maintained, though its strength may be gradually attenuated. The forthcoming
change of the large-scale structure is delayed, but the degree of large-scale instability
is increasing;
As time progresses, particles are removed continuously. The force structures and
the base at the bottom for supporting the upside particles become weaker. At some
time, the sudden change of large-scale structure takes place, which behaves like an
internal “quake” of the particle assembly. This sudden change is always accompanied
by the internal bulk motion of falling, during which the overall magnitude of the mean
velocity of particles must increase. The autocorrelation functions and its Fourier
spectrum are utilized to show the differences in the mechanisms of the slow and the
fast particle flows. Based on the observations and performed analyses, the gravitydriven particle flows can be divided into two regimes:
• Kinetics-characterized regime Termed as slow particle flows, it is characterized
mainly by the existence of an evident characteristic period or fundamental frequency of time variation of the mean contact force. As the contact force is viewed
as a dynamic variable, this type of particle flow is known as a kinetics-dominated
or kinetics-characterized flow. The intermittency characteristics are mainly related
to the dynamic variables.
• Kinematic regime Considered as kinematic flow, it is related to fluid-like flow
behavior and termed as a fast dense flow regime, featured mainly by kinematic
variables, such as velocity. The kinematic variables rapidly vary so that they exhibit
a continuous spectrum and the distribution of particles and force structures could
always be in an unsteady state. 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.
The underlying complex mechanisms of slow particle flows, as well as some
important issues on flow regime characterization, via exploring the intermittency
characteristics of a slow particle flow comparing to a fast dense flow are provided.
The kinetic energy of the granular system and the phenomena of pebble avalanche and
flow intermittence are illustrated in detail. As a quantitative method, the “single-peak”
distribution rule is introduced to characterize the time-energy distribution feature of
gravity-driven dense particle flows. A new general statistical criterion is proposed
to subdivide the elastic–quasi-static regime, which may help to characterize dense
particle flows under gravity. According to the span of energy magnitude (E span ) and
the standard deviation σ , the specific subdivision criteria for subdividing the flow
regime of gravity-driven dense particle flow are as follows:
• σ b <0.1,E span >1: Extremely slow flow;
• σ b >0.1: Intermittent flow;
• σ b <0.1,E span <1: Consistent flow.