Clogging in bottlenecks: from inert particles to active matter
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Transcript of Clogging in bottlenecks: from inert particles to active matter
Clogging in bottlenecks: from Clogging in bottlenecks: from inert particles to active matterinert particles to active matter
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
People involved:
• Luis Miguel Ferrer (Veterinary Faculty, Zaragoza)• Alvaro Janda (Engineering School, Edinburgh)• Geoffroy Lumay (GRASP, Liège)• Celia Lozano (University of Navarra)• Diego Maza (University of Navarra)• Angel Garcimartín (University of Navarra)
http://www.unav.es/centro/gralunarlab
Iker Zuriguel [email protected]
Dpto. Física y Mat. AplicadaUniversidad de Navarra31080 Pamplona, Spain.
Clogging in bottlenecks
Panic flow
Traffic
Grains (Picture from K. To, PRL 2001)
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Traffic
Embolization with microparticles
Clogging in silos
0 2000 4000 6000
10-5
10-4
10-3
R=3,55
s
n R(s
)2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, [email protected]
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Avalanche size s: number of fallen grains
Particle passing probability: p
Avalanche size: n(s) = ps · (1-p)
Exponential distributions: characteristic size and time, well defined averages.
Mean avalanche: <s> = p
(1-p)
R
Clogging in silos
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
1 2 3 4 5 6100
101
102
103
104
105
s
R0 5 10 15 20 25
0
10000
20000
30000
Q (
s-1)
R
Mean avalanche size Flow rate
A. Janda et al. PRL 2012A. Janda et al. EPL 2008
Modified Beverloo expressionDivergence or not? Critical R?
Clogging in silos in the presence of an obstacle
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Clogging in silos in the presence of an obstacle
I. Zuriguel et al. PRL 2011
<s> may increase more than 100 times.
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Clogging in silos in the presence of an obstacle
I. Zuriguel et al. PRL 2011
<s> may increase more than 100 times.The flow rate is not affected.
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Mean avalanche size Flow rate
Clogging in crowd dynamics…
Helbing et al. Nature, 2000.
Transportation Science, 2005.
Clogs do not arrest the flow completely. The burst sizes can be measured
(in number of people)
An obstacle properly placed in front of the exit leads to an improvement of the evacuation. Clogs and the evacuation time are reduced.
6 tests without obstacle. 4 tests with obstacle.
Obstacle effect
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Clogging with sheep: Cubel (Zaragoza)
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Video-surveillance system
Experimental procedure Experimental procedure
Daily, sheep are taken out of the yard.The yard is cleaned and food is placed inside it.When the yard is opened again, all the sheep crowd together in front of the door.
Door width = 77 cmSheep width ~ 35 cm (Soft) Around 100 sheep
The experiment consists on:20 tests without obstacle20 tests with an obstacle of 117 cm diameter placed 80 cm behind the door(with the same sheep).
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Experiment without obstacleExperiment without obstacle
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Clogging times, burst size…Clogging times, burst size…
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
0 10 20 30 400
10
20
30
40
50
60
t (s)
# (
sh
eep
nu
mb
er)
without obstaclewith obstacle
time
Clogging times, burst size…Clogging times, burst size…
tCi
Clog
“Burst” (burst size s =
17)
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
0 10 20 30 400
10
20
30
40
50
60
t (s)
# (
sh
eep
nu
mb
er)
without obstaclewith obstacle
time
tCi+1
Clogging and unclogging of sheep
Clogging time: power-law tail
10-2
10-1
100
101
10-4
10-3
10-2
10-1
100
P(T
t
c)
tc (s)
= 4.2
= 3.1with
obstacle
without obstacle
A. Clauset, C. R. Shalizi and M. E. J. Newman,“Power-Law Distributions in Empirical Data”SIAM Review 51, 661-703 (2009)
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Clogging and unclogging of sheep
Clogging time: power-law tail
Histogram of burst sizes s/<s>:an exponential
0 2 4 6 8
10-2
10-1
100
s / s n
(s /
s
)
with obstacle
without obstacle10
-210
-110
010
110
-4
10-3
10-2
10-1
100
P(T
t
c)
tc (s)
= 4.2
= 3.1
without obstacle
A. Clauset, C. R. Shalizi and M. E. J. Newman,“Power-Law Distributions in Empirical Data”SIAM Review 51, 661-703 (2009)
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
with obstacle
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
…once the system is clogged, the flow is not resumed by itself.
Vibrated silo.
But the dynamics in silos are completely different…
Vibrated silo
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
vibrating plate
- Let the grains flow until an arch forms and stops the outpouring.
-Apply a vibration (constant amplitude , constant frequency).
- Detect the arch breaking and measure the time it has taken.
- Empty the silo and repeat the experience.
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Vibrated silo: avalanche size
A. Janda, D. Maza, A. Garcimartín, E. Kolb, J. Lanuza and E. Clément.
EPL 87 (2009), 24002.
C. Mankoc, A. Garcimartín, I. Zuriguel, D. Maza and L. A. Pugnaloni.
PRE 80 (2009), 011309.
Exponential distributions
The time that it takes the system to clog is well defined
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Vibrated silo: clogging time
10-3
10-2
10-1
100
101
102
10-3
10-2
10-1
100
P(T
t)
t (s)
R = 4.76
=
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Vibrated silo: clogging time
10-3
10-2
10-1
100
101
102
10-3
10-2
10-1
100
P(T
t)
t (s)
R = 4.76
=
≥ The mean of the distribution converges.
< 2 The mean of the distribution does not
converge.
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Vibrated silo: clogging time
10-2
100
102
0.001
0.01
0,1
1
t
Pr(
T
t)
= 0.26
10-3
10-2
10-1
100
101
102
10-3
10-2
10-1
100
P(T
t)
t (s)
R = 4.76
=
=
≥ The mean of the distribution converges.
< 2 The mean of the distribution does not
converge.
R =
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
Vibrated silo: clogging time
10-2
100
102
0.001
0.01
0,1
1
t
Pr(
T
t)
= 0.26
10-3
10-2
10-1
100
101
102
10-3
10-2
10-1
100
P(T
t)
t (s)
R = 4.76
10-2
10-1
100
101
102
103
10-3
10-2
10-1
100
t (s)
P(T
t)
R4.50mm 0.26
High layer 1.91Low layer 4.70
=
=High layer of grains
= Low layer of grains
=
≥ The mean of the distribution converges.
< 2 The mean of the distribution does not
converge.
R =
P
Department of Physics and Applied Mathematics
Nonlinear transport, dynamics and fluctuations in condensed matter physics.
Summary.Summary.
- Avalanche and burst size distributions exponential decay.
- Clogging time distributions power-law decays with exponent ().
< 2 mean clogging time diverges, average flow rate cannot be defined.
- Going from ≥ 2 to < 2 can be viewed as a clogging transition.
- In a vibrated silo, the system can be unclogged increasing or R.
- Placing the obstacle in the sheep case has a similar effect (decreasing ) than reducing the layer of grains in a vibrated silo (pressure?).
Department of Physics and Applied Mathematics
Nonlinear transport, dynamics and fluctuations in condensed matter physics.
Work in progress.Work in progress.
• Do people behave like sheep? (D. Parisi, UBA)
• Can this be generalized to colloids? (R. Cruz-Hidalgo & I. Pagonabarraga)
Summary.Summary.
- Avalanche and burst size distributions exponential decay.
- Clogging time distributions power-law decays with exponent ().
< 2 mean clogging time diverges, average flow rate cannot be defined.
- Going from ≥ 2 to < 2 can be viewed as a clogging transition.
- In a vibrated silo, the system can be unclogged increasing or R.
- Placing the obstacle in the sheep case has a similar effect (decreasing ) than reducing the layer of grains in a vibrated silo (pressure?).
Clogging in bottlenecks: from Clogging in bottlenecks: from inert particles to active matterinert particles to active matter
2nd IMA Conference on Dense Granular FlowsCambridge, 1-4 July, 2013.
[email protected]://www.unav.es/centro/gralunarlab
People involved:
• Luis Miguel Ferrer (Veterinary Faculty, Zaragoza)• Alvaro Janda (Engineering School, Edinburgh)• Geoffroy Lumay (GRASP, Liège)• Celia Lozano (University of Navarra)• Angel Garcimartín (University of Navarra)• Diego Maza (University of Navarra)
http://www.unav.es/centro/gralunarlab
Iker Zuriguel [email protected]
Dpto. Física y Mat. AplicadaUniversidad de Navarra31080 Pamplona, Spain.
Thank you!Thank you!