The Multi Intruder Brazil Nut Problem Supervisors: Heinrich M. - - PowerPoint PPT Presentation

The Multi Intruder “Brazil Nut” Problem

Supervisors: Heinrich M. Jaeger Sidney R. Nagel Matthias E. Möbius Detlef Lohse

Internship Chicago, Summer 2002 Peter Eshuis

Overview

• Intro to Granular Material (GM)
• “Brazil Nut” Problem
• Experiment
• Results

– Density dependence – Size dependence (single & multi) – Miscellaneous

• Conclusions & Discussion
• Recommendations

Intro to Granular Material (GM)

• Examples of GM: sand, salt, sugar etc…
• GM can act as solid, fluid and gas

“Fourth state of matter” Applications:

– Pharmaceutical industry – Mining – Agriculture – Food processing industry – many more!

“Brazil Nut” Problem

Larger (heavier) particles segregate to the surface of a shaken container with different granular materials

Mixed Nuts Brazil Nut

“Brazil Nut” Problem

• Percolation: smaller particles slip through holes

created by the larger ones (Hong et al, 2001)

• Reorganization: during shake neighboring smaller

particles fill up gaps left behind by the larger ones (Duran et al, 1993 & Jullien et al, 1992)

• Convection: flow going up in center capturing all

particles, going down in very thin layer near wall trapping the largest particles (Knight et al, 1993)

• Condensation (MD-Sim): binary granular system

can condense either the larger or smaller particles “Reverse Brazil Nut Problem”! (Hong et al, 2000)

“Brazil Nut” Problem

2D-Movie: Convection without intruders

(Niemuth et al, unpublished)

Experiment

Cylinder (12cm diameter) filled up to filling height ‘h’ with glass beads: d=1mm & ρm=2.4 g/ml d=0.5mm & ρm=2.5 g/ml Glass beads (d=1mm) glued to cylinder wall for stable convection & reproducibility

Experiment

Once every second a 10Hz sine wave (‘tap’) is applied to the system Acceleration parameter: (typical Γ≈2.3) Γ adjusted to remain constant during all experiments

Shaker input Accelerometer output

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3 1,4 1,5

• 2,5
• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5

Acceleration (g) Time (s)

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3

• 0,4
• 0,2

0,0 0,2 0,4

Voltage (V) Time (s)

a

g a = Γ

Experiment

Spherical intruder (diameter D & density ρ) is carefully placed at depth z0 Rise time (Trise): determined when intruder is emerging at surface Problems with surfacing

• ccurred in 1mm glass

beads

Results – Density (d=1mm)

• ‘Peak’ around ρ/ρm≈0.5 less clear at lower pressure
• Overall trend for Trise is slightly increasing

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 20 30 40 50 60 70 80

Trise (taps)

ρ / ρm

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 20 30 40 50 60 70 80

Trise (taps)

ρ / ρm

Atmospheric pressure Lower pressure: 24.0 kPa

Results – Density (d=0.5mm)

• Peak around ρ/ρm≈0.5 far more pronounced for 0.5mm

glass beads

• This peak vanishes for low pressures (Möbius et al, 2001)
• No dependence on intruder surface or restitution coefficient

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 50 100 150 200 250 300

Trise (taps)

ρ / ρm

0.5mm glass beads 1mm glass beads

Results – Density (2D vs 3D)

No peak in 2D situation (Niemuth et al, unpublished) and also a clear decrease of Trise for denser intruders instead of a slight increase as in 3D 2D in agreement with Liffman et al, 2001

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 20 40 60 80 100 120 140 160 180 200 220 240 260 280

Trise (taps)

ρ / ρm

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 20 30 40 50 60 70 80

Trise (taps)

ρ / ρm

2D 3D d=1mm

Results – Size (single)

10 20 30 40 50 60 70 80 90 20 40 60 80 100 120 140 160 180 200 220 240

Trise (taps) Relative Diameter D/d Wood (ρ/ρm = 0.25) Steel (ρ/ρm = 3.10) Nylon (ρ/ρm = 0.45)

5 10 15 20 25 30 10 20 30 40 50 60 70 80

Nylon (ρ/ρm= 0.47) Trise (taps) Relative Diameter D/d

d=1mm glass d=0.5mm glass

• Trise constant for nylon
• Trise increasing for nylon
• Trise decreasing if ρ/ρm far

enough from density peak

Results – Size (single)

2D Movie: single disk

(Niemuth, unpublished)

MRI Movie (3D cylinder): Glass intruder in poppy seeds (Möbius, unpublished)

Results – Size (multi)

Default intruder configurations

• Nylon intruder configurations (on ρ/ρm peak) were

more unstable than the steel ones, especially for 0.5mm glass beads

• Steel intruder configurations (far from ρ/ρm peak) were

always surfacing in the configuration they were put in and they are regarded to act as a ‘compound’

Results – Size (multi, d=1mm)

2 4 6 8 10 20 40 60 80 100

Trise (taps) Number of Intruders

1 2 3 4 5 6 7 8 20 40 60 80 100 120 140 160

Trise (taps) Number of Intruders

z0=7cm z0=4.5cm z0=2cm

Nylon Steel

solids: atm.pres dotted: low.pres 22.7 kPa 0.053 kPa

• Like in single size dependence graph: Trise constant for nylon
• For steel intruders Trise is decreasing if the size of the

compound is increased (atmospheric and lower pressure)

Results – Size (multi)

• In 1mm glass beads the ¾” and ½” steel intruders are

rising faster for increasing #intruders (1” intruders constant)

• For all sizes of steel intruders used in 0.5mm glass beads,

Trise is decreasing for larger sizes of the compound

1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Trise (taps) Number of Intruders

1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Trise (taps) Number of Intruders

d=1mm glass d=0.5mm glass

■ – 1” steel

• – ¾” steel

▲ – ½” steel

Results – Size (multi, d=0.5mm)

1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 55 60 65 70

8.5

Trise (taps) Number of Intruders

10 20 30 40 50 60 10 20 30 40 50 60

23.8 14.5 8.3

Trise (taps) Volume (cm

3)

■ – 1” steel

• – ¾” steel

▲ – ½” steel

Effective diameter: To obtain same Trise (rule of thumb): 1 1” intruder ~ 1.5 ¾” intruders ~ 3.1 ½” intruders

Results – Size (multi, d=0.5mm)

• Nylon configurations over 5 intruders can not be considered

as a ‘compound’ anymore; some intruders stay behind

• Trise approximately constant for nylon just as in single size

dependence graph and for 1mm glass beads Nylon Steel

1 2 3 4 5 6 7 8 9 10 50 100 150 200 250

Trise (taps) Number of Intruders

1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Trise (taps) Number of Intruders ■ – 1” intruder(s)

• – ¾” intruder(s)

▲ – ½” intruder(s)

Results - Miscellaneous

Placing three ¾” steel intruders vertical something interesting

• ccurred: the 2nd intruder

caught up with the 1st intruder! (1mm glass) This phenomenon is very sensitive to the initial offset of the 2nd intruder: its center has to be ≈½radius from the axis of the cylinder

Conclusions & Discussion (1)

• Density dependence (ρ/ρm):

– d=0.5mm glass: Trise peak around ρ/ρm≈0.5 a factor 3 higher than Tasymptote – d=1mm glass: Trise shows barely a peak around ρ/ρm≈0.5, just

• unstable. Trise is considered to be slightly increasing
• Size dependence (D/d):

– The single as well as multi intruder experiments (both glass bead sizes) show for intruders far from the density peak: a larger single intruder or a larger ‘compound’ configuration rises faster – Intruders (single & multi) near this peak rise at a constant speed if 1mm glass beads are used. In 0.5mm the single intruder rises slower if the diameter is increased, but the multi nylon experiment is highly unstable – Effective diameter: ‘rule of thumb’ relating 3 different sizes of steel intruders: 1 1” intruder ~ 1.5 ¾” intruders ~ 3.1 ½” intruders

Conclusions & Discussion (2)

• Miscellaneous:

– Depth dependence: considered to be linear slowing down a bit in the upper layer – A different filling height does not seem to affect the result, but more data is required to check this more profoundly – Using different configurations for 3 intruders did not affect Trise significantly in our experiment. This experiment needs to be performed with more than 3 intruders to be sure for all intruders – Three intruders vertical: 2nd intruder can catch up with 1st one if

• ffset is ≈½radius. This result has to be treated with great

cautiousness, because of the sensitivity of the system: various

• ther experiments are needed to investigate it thoroughly

Recommendations

• 3D-Flow visualization using MRI; try to reveal the

interactions happening inside the 3D-cylinder

• To improve the ‘rule of thumb’ considering the effective

diameter more experiments have to be performed

• In general more data is needed to get more significant

results regarding all granular material experiments

Acknowledgements

I wish to thank Heinrich, Sid and Matthias for supervising my project and Detlef for informing me about the internship available at the University of Chicago. Furthermore I’d like to thank the rest of the Jaeger/Nagel- group for the helpful reflections during the weekly group meetings and for helping me out on other moments. I want to address a special “thank you” to Brenda for conquering all my problems regarding my Social Security Number, flight tickets, payroll and many more…

Questions?