Clogging in bottlenecks: from inert
particles to active matter
http://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)
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
Iker Zuriguel
iker@unav.es
Dpto. Física y Mat. Aplicada
Universidad de Navarra
31080 Pamplona, Spain.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging in bottlenecks
Traffic
Grains (Picture from K. To, PRL 2001)
Traffic
Embolization with microparticles
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
Panic flow
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging in silos
-3
10
R=3,55
-4
nR(s)
10
-5
10
R
0
2000
s
4000
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.
p
Mean avalanche: <s> =
(1-p)
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
6000
Clogging in silos
Mean avalanche size
Flow rate
5
10
30000
4
10
20000
Q (s )
s
3
-1
10
2
10
10000
1
10
0
0
10
1
2
3
4
5
6
0
5
10
R
15
R
20
25
Divergence or not? Critical R?
Modified Beverloo expression
A. Janda et al. EPL 2008
A. Janda et al. PRL 2012
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging in silos in the presence of an obstacle
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://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 Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://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.
Flow rate
10
5
10
3
2000
-1
Q (s )
s
Mean avalanche size
1000
10
1
0
1
2
3
R
4
5
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
6
2
4
iker@unav.es
http://www.unav.es/centro/gralunarlab
6
R
8
10
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)
Obstacle effect
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.
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging with sheep: Cubel (Zaragoza)
Video-surveillance system
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
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 cm
Sheep width ~ 35 cm (Soft)
Around 100 sheep
The experiment consists on:
20 tests without obstacle
20 tests with an obstacle of 117 cm diameter
placed 80 cm behind the door
(with the same sheep).
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Experiment without obstacle
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging times, burst size…
time
60
# (sheep number)
50
40
30
20
without obstacle
with obstacle
10
0
0
10
20
t (s)
30
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
40
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging times, burst size…
time
Clog
“Burst”
(burst size s = 17)
60
# (sheep number)
50
tCi
tCi+1
40
30
20
without obstacle
with obstacle
10
0
0
10
20
t (s)
30
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
40
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging and unclogging of sheep
Clogging time: power-law tail
0
10
without
obstacle
-1
P(T  tc)
10
-2
10
 = 3.1
with
obstacle
 = 4.2
-3
10
-4
10 -2
10
-1
10
tc (s)
0
10
1
10
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 Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Clogging and unclogging of sheep
Clogging time: power-law tail
0
Histogram of burst sizes s/<s>:
an exponential
10
without
obstacle
-1
-2
10
 = 3.1
with
obstacle
0
10
with
obstacle
 = 4.2
n(s /  s  )
P(T  tc)
10
-3
10
-2
10
-4
10 -2
10
-1
10
-1
10
tc (s)
0
10
1
10
0
without
obstacle
2
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 Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
4
6
8
s/ s
But the dynamics in silos are completely different…
…once the system is clogged, the flow is not
resumed by itself.
Vibrated silo.
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Vibrated silo
- Let the grains flow until an arch forms and
stops the outpouring.
-Apply a vibration (constant amplitude G,
constant frequency).
- Detect the arch breaking and measure the
time it has taken.
- Empty the silo and repeat the experience.
vibrating plate
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Vibrated silo: avalanche size
Exponential distributions
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.
The time that it takes the system to clog is well defined
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Vibrated silo: clogging time
R = 4.76
0
10
G= 0.10
0.15
0.20
0.26
-1
P(T  t)
10
=
1.6
1.9
2.0
2.2
-2
10
-3
10
-3
10
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
-2
10
-1
10
iker@unav.es
http://www.unav.es/centro/gralunarlab
0
10
t (s)
1
10
2
10
Vibrated silo: clogging time
R = 4.76
0
10
 < 2 The mean of the
distribution does not
converge.
=
1.6
1.9
2.0
2.2
-2
10
-3
10
-3
10
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
0.15
0.20
0.26
-1
10
P(T  t)
 ≥ 2 The mean of the
distribution converges.
G= 0.10
-2
10
-1
10
iker@unav.es
http://www.unav.es/centro/gralunarlab
0
10
t (s)
1
10
2
10
Vibrated silo: clogging time
R = 4.76
0
10
 < 2 The mean of the
distribution does not
converge.
0.15
0.20
0.26
-1
10
P(T  t)
 ≥ 2 The mean of the
distribution converges.
G= 0.10
=
1.6
1.9
2.0
2.2
-2
10
-3
10
-3
10
-2
10
-1
0
10
10
t (s)
1
10
2
10
G = 0.26
1
R = 4.00
4.50
4.65
4.76
4.84
0,1
Pr(T  t)
=
1.7
1.9
2.0
2.2
2.3
0.01
0.001
-2
10
0
2
10
10
t
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
iker@unav.es
http://www.unav.es/centro/gralunarlab
Vibrated silo: clogging time
R = 4.76
0
10
 < 2 The mean of the
distribution does not
converge.
0.15
0.20
0.26
-1
10
P(T  t)
 ≥ 2 The mean of the
distribution converges.
G= 0.10
=
1.6
1.9
2.0
2.2
-2
10
-3
10
-3
10
-2
10
-1
0
10
10
t (s)
1
10
R = 4.00
P(T  t)
10
=4.7
layer
LowHigh
layer
 1.91
Low layer
of grains
P
=
1.7
1.9
2.0
2.2
2.3
0.01
 4.70
-3
10
0.001
-2
10
-1
10
0
10
t (s)
1
10
2
10
3
10
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
4.50
4.65
4.76
4.84
0,1
Pr(T  t)
=1.9
High layer
of grains
-1
-2
2
10
G = 0.26
R4.50mm G 0.26
0
10
1
10
-2
10
0
2
10
10
t
iker@unav.es
http://www.unav.es/centro/gralunarlab
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 G 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?).
Nonlinear transport, dynamics and
fluctuations in condensed matter physics.
Department of Physics and
Applied Mathematics
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 G 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?).
Work in progress.
• Do people behave like sheep? (D. Parisi, UBA)
• Can this be generalized to colloids? (R. Cruz-Hidalgo & I. Pagonabarraga)
Nonlinear transport, dynamics and
fluctuations in condensed matter physics.
Department of Physics and
Applied Mathematics
Clogging in bottlenecks: from inert
particles to active matter
Thank you!
http://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)
2nd IMA Conference on Dense Granular Flows
Cambridge, 1-4 July, 2013.
Iker Zuriguel
iker@unav.es
Dpto. Física y Mat. Aplicada
Universidad de Navarra
31080 Pamplona, Spain.
iker@unav.es
http://www.unav.es/centro/gralunarlab