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 Brazil Nut Mixed Nuts

“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“Brazil Nut” Problem 2D-Movie: Convection without intruders (Niemuth et al, unpublished)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 & ρ m =2.4 g/ml � d=0.5mm & ρ m =2.5 g/ml Glass beads (d=1mm) glued to cylinder wall for stable convection & reproducibility

Experiment Shaker input Accelerometer output 2,5 0,4 2,0 1,5 0,2 a Acceleration (g) 1,0 Voltage (V) 0,5 0,0 0,0 -0,5 -0,2 -1,0 -1,5 -0,4 -2,0 -2,5 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 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 Time (s) Time (s) Once every second a 10Hz sine wave (‘tap’) is applied to the system a (typical Γ≈ 2.3) Γ = Acceleration parameter: g Γ adjusted to remain constant during all experiments

Experiment Spherical intruder (diameter D & density ρ ) is carefully placed at depth z 0 Rise time (T rise ): determined when intruder is emerging at surface Problems with surfacing occurred in 1mm glass beads

Results – Density (d=1mm) 80 80 70 70 60 60 50 50 T rise (taps) T rise (taps) 40 40 Atmospheric pressure Lower pressure: 24.0 kPa 30 30 20 20 10 10 0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ρ / ρ m ρ / ρ m • ‘Peak’ around ρ / ρ m ≈ 0.5 less clear at lower pressure • Overall trend for T rise is slightly increasing

Results – Density (d=0.5mm) 300 0.5mm glass beads 1mm glass beads 250 200 T rise (taps) 150 100 50 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ρ / ρ m • Peak around ρ / ρ m ≈ 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

Results – Density (2D vs 3D) 280 80 d=1mm 260 70 240 220 60 200 180 50 2D 3D T rise (taps) T rise (taps) 160 140 40 120 30 100 80 20 60 40 10 20 0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ρ / ρ m ρ / ρ m No peak in 2D situation (Niemuth et al, unpublished) and also a clear decrease of T rise for denser intruders instead of a slight increase as in 3D 2D in agreement with Liffman et al, 2001

Results – Size (single) 80 240 70 220 Nylon ( ρ/ρ m = 0.47) 200 60 180 160 50 Wood ( ρ/ρ m = 0.25) T rise (taps) 140 T rise (taps) Steel ( ρ/ρ m = 3.10) 40 120 Nylon ( ρ/ρ m = 0.45) 100 30 80 20 60 40 d=1mm glass d=0.5mm glass 10 20 0 0 0 10 20 30 40 50 60 70 80 90 0 5 10 15 20 25 30 Relative Diameter D/d Relative Diameter D/d • T rise constant for nylon • T rise increasing for nylon • T rise decreasing if ρ / ρ m far enough from density peak

Results – Size (single) 2D Movie: single disk MRI Movie (3D cylinder): (Niemuth, unpublished) Glass intruder in poppy seeds (Möbius, unpublished)

Results – Size (multi) Default intruder configurations • Nylon intruder configurations (on ρ / ρ m peak) were more unstable than the steel ones, especially for 0.5mm glass beads • Steel intruder configurations (far from ρ / ρ m 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) 160 z 0 =7cm 100 140 120 80 z 0 =4.5cm T rise (taps) 100 T rise (taps) 60 80 z 0 =2cm 60 40 40 20 Nylon Steel 20 0 0 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 Number of Intruders solids: atm.pres Number of Intruders 0.053 kPa 22.7 kPa dotted: low.pres • Like in single size dependence graph: T rise constant for nylon • For steel intruders T rise is decreasing if the size of the compound is increased (atmospheric and lower pressure)

Results – Size (multi) 70 85 80 65 75 60 70 55 65 50 60 55 45 T rise (taps) T rise (taps) 50 40 45 35 ■ – 1” steel 40 30 35 25 30 ● – ¾” steel 25 20 20 15 ▲ – ½” steel 15 d=1mm glass d=0.5mm glass 10 10 5 5 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Number of Intruders Number of Intruders • 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, T rise is decreasing for larger sizes of the compound

Results – Size (multi, d=0.5mm) 70 60 65 60 55 50 50 45 40 T rise (taps) T rise (taps) 40 35 ■ – 1” steel 30 30 25 ● – ¾” steel 20 20 15 ▲ – ½” steel 10 10 5 0 0 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10 3 ) 8.3 14.5 23.8 Number of Intruders Volume (cm 8.5 Effective diameter: To obtain same T rise (rule of thumb): 1 1” intruder ~ 1.5 ¾” intruders ~ 3.1 ½” intruders

Results – Size (multi, d=0.5mm) 70 65 250 60 55 200 50 45 T rise (taps) T rise (taps) 40 150 ■ – 1” intruder(s) 35 30 100 ● – ¾” intruder(s) 25 20 ▲ – ½” intruder(s) 50 15 Nylon 10 Steel 5 0 0 1 2 3 4 5 6 7 8 9 10 0 Number of Intruders 0 1 2 3 4 5 6 7 8 9 10 Number of Intruders • Nylon configurations over 5 intruders can not be considered as a ‘compound’ anymore; some intruders stay behind • T rise approximately constant for nylon just as in single size dependence graph and for 1mm glass beads

Results - Miscellaneous Placing three ¾” steel intruders vertical something interesting occurred: the 2 nd intruder caught up with the 1 st intruder! (1mm glass) This phenomenon is very sensitive to the initial offset of the 2 nd intruder: its center has to be ≈ ½radius from the axis of the cylinder

Conclusions & Discussion (1) • Density dependence ( ρ / ρ m ): – d=0.5mm glass: T rise peak around ρ / ρ m ≈ 0.5 a factor 3 higher than T asymptote – d=1mm glass: T rise shows barely a peak around ρ / ρ m ≈ 0.5, just unstable. T rise 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 T rise significantly in our experiment. This experiment needs to be performed with more than 3 intruders to be sure for all intruders – Three intruders vertical: 2 nd intruder can catch up with 1 st one if offset is ≈ ½radius. This result has to be treated with great cautiousness, because of the sensitivity of the system: various other 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