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Clogging in bottlenecks: from inert particles to active matter

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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)

Iker Zuriguel [email protected]

Dpto. Física y Mat. Aplicada

Universidad de Navarra

31080 Pamplona, Spain.

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging in bottlenecks

Traffic

Grains (Picture from K. To, PRL 2001)

Traffic

Panic flow

Embolization with microparticles

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging in silos

R

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)

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Mean avalanche size

Flow rate

Divergence or not? Critical R?

Modified Beverloo expression

A. Janda et al. EPL 2008

A. Janda et al. PRL 2012

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging in silos in the presence of an obstacle

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging in silos in the presence of an obstacle

I. Zuriguel et al. PRL 2011

<s> may increase more than 100 times.

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

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

Mean avalanche size

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

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.

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging with sheep: Cubel (Zaragoza)

Video-surveillance system

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

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).

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

time

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

time

Clog

“Burst”

(burst size s = 17)

tCi

tCi+1

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging and unclogging of sheep

Clogging time: power-law tail

withoutobstacle

with obstacle

A. Clauset, C. R. Shalizi and M. E. J. Newman,

“Power-Law Distributions in Empirical Data”

SIAM Review 51, 661-703 (2009)

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

Clogging and unclogging of sheep

Clogging time: power-law tail

Histogram of burst sizes s/<s>:

an exponential

withoutobstacle

with obstacle

with 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)

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

But the dynamics in silos are completely different…

…once the system is clogged, the flow is not resumed by itself.

Vibrated silo.

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

- 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

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

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

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

G= 0.10

- 0.15
- 0.20
- 0.26

a=

1.6

1.9

2.0

2.2

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

G= 0.10

- 0.15
- 0.20
- 0.26

a ≥ 2 The mean of the distribution converges.

a< 2 The mean of the distribution does not converge.

a=

1.6

1.9

2.0

2.2

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

G= 0.10

- 0.15
- 0.20
- 0.26

a ≥ 2 The mean of the distribution converges.

a< 2 The mean of the distribution does not converge.

a=

1.6

1.9

2.0

2.2

- R = 4.00
- 4.50
- 4.65
- 4.76
- 4.84

a=

1.7

1.9

2.0

2.2

2.3

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

G= 0.10

- 0.15
- 0.20
- 0.26

a ≥ 2 The mean of the distribution converges.

a< 2 The mean of the distribution does not converge.

a=

1.6

1.9

2.0

2.2

- R = 4.00
- 4.50
- 4.65
- 4.76
- 4.84

a=1.9

High layer of grains

a=

1.7

1.9

2.0

2.2

2.3

P

a=4.7

Low layer of grains

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

- Avalanche and burst size distributions exponential decay.
- Clogging time distributions power-law decays with exponent (a).
- a< 2 mean clogging time diverges, average flow rate cannot be defined.
- Going from a≥ 2 to a< 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 a) 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.

- Avalanche and burst size distributions exponential decay.
- Clogging time distributions power-law decays with exponent (a).
- a< 2 mean clogging time diverges, average flow rate cannot be defined.
- Going from a≥ 2 to a< 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 a) 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)

Department of Physics and Applied Mathematics

Nonlinear transport, dynamics and fluctuations in condensed matter physics.

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)

Iker Zuriguel [email protected]

Dpto. Física y Mat. Aplicada

Universidad de Navarra

31080 Pamplona, Spain.

http://www.unav.es/centro/gralunarlab

2nd IMA Conference on Dense Granular Flows

Cambridge, 1-4 July, 2013.

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