Shear Zones in Dense Gravity Driven 2D Granular Flow
Kelsey Hattam ’09, N. Easwar, Smith College
N Menon University of Massachusetts at Amherst
N.
Background:
Granular flow vs. liquid flow
Experimental setup
Goals
Previous experiments
1.8
a
Large
8
3.0
2.5
Small
-- Small ball bearings (quasi 2D):
crystalline packing near wall, not
in center.
2.0
1.5
1.0
Center
0.5
2
1.8
1.6
1.4
4
6
8
1.2
1.0
0.8
--Bidisperse size same trend as
small
small.
Center
0.4
0.2
Center
Left edge
velocty (cm/s)
2.5cm opening
1.4cm opening
6
1
2
3
distance across hopper (cm)
4
velocity (cm/s)
Scaled velocity
S
17.0
16.5
16.0
2.5cm opening
1.4cm opening
15.5
15 0
15.0
Broader
shear zone
for faster
flows
1
2
3
distance across hopper (cm/s)
Center
4
2
4
6
8
9.5
9.0
8.5
8.0
12cm
6cm
7.5
2
4
“λ”=15-18 mm (6-7 large ball diameters)
9
Velocity Profile- Bidisperse
8
7
2
4
4
6
distance across hopper (cm)
Conclusions
--Width of shear zone does not depend on hopper width
--Shear zones depend on
-packing microstructure
4.0
3.5
Profile
Temperature
8.5
3.0
8.0
flow velocity?
-flow
2
6
8
10 10
10x10
--Fluctuations set the scale for the shear zone?
On going
--Other flow rates and widths
Next
7.0
2
800fps
-3
3
8
Center
Left edge
8
4
8
6
6
Shear zones
depend
on microstructure
Distance(cm)
2
2.5
1
8
10
7.0
7.5
Temperature
Error
6
Distance (cm)
6
9.0
8
6
Time (s)
Left edge
6
Shear zones do
not depend on
hopper width
Center
9.5
10
4
7
10
Bidisperse Mixture
2
2
Velocityy Profile-Large
g Monodisperse
p
Results: Velocity fluctuations
(2000 collisions per second, Longhi 2002)
-- We report σ2 at finite times (800fps)
4
“λ”=2-3 mm (1 ball diameter)
8
12
Left edge
Velocity Fluctuations
**Our measurements reflect
the velocity fluctuations and
are as close to temperature
measurements as possible
14
9
2
17.5
8
10
Temperature (cm/s)
Velociity
14
8
6
Velocity fluctuations σ2 = <v2> - <v>2
-- σ2 = Temperature at very short times
16
10
4
Distance across hopper (cm)
Results: Shear Zones
(dependence on velocity)
12
2
Results: Shear Zones
(dependence on microstructure)
12cm
6cm
Center
8
Mix
0.6
16
velocity (cm/s)
Bidisperse (noncrystalline)
6
Scalled velocity (cm/s)
--System
gridded
into boxes
of size d/3
4
velocity (cm/s)
Monodisperse small
2
Ф (packing fractionn)
--Particle
Particle
centers
located
Velocity (cm
m/s)
--Large ball bearings: crystalline
packing through entire hopper
Center
0.4
Left edge
Results: Shear Zones
(dependence on width)
Velocity profiles (bidisperse mixture)
0.6
Camera speed: 800 f.p.s
fps
Distance
1.0
0.8
w = 6cm or 12cm
a = 2.5cm or 1.4cm
depth = 2.7mm
Profiles
1.2
Monodisperse large (crystalline)
-- d = 2.5 and 2.0mm in equal numbers
Plexiglas hopper
w
Velociity (cm/s)
1.4
Packing fraction
Hexagonal packing
Square packing
Bidisperse
Velocity(cm/s)
1.6
-- d = 2.5mm
2 5mm
-- d = 2.0mm
--Measuring spatial packing, velocity, and
velocity fluctuations.
Results: Packing
(number density)
2.0
Monodisperse
microstructure of packing, and flow
velocity
Wh t sets
What
t the
th size
i off th
the shear
h
zone?
?
Differently packed systems
Grains used: Steel ball bearings
--Understand shear zones in hopper flow
-Dependence on hopper width
width,
--Shear in Couette flow geometry (Mueth et al.
2000,, Losert 2001))
-velocity goes to zero at center of flow
--Shear zones in vertical chute with cylindrical
grains(Pouliquen and Gutfraind 1996).
-suggests velocity fluctuations control
shear zones (but fluctuations were not
measured)
4
6
distance across hopper (cm)
8
Do fluctuations dictate the width of the shear zone?
Smith
College
Physics
Department
Polymer
Poster
Symposium
--Rough boundaries