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)



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]


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



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




I. Zuriguel et al. PRL 2011

<s> may increase more than 100 times.




I. Zuriguel et al. PRL 2011

<s> may increase more than 100 times.The flow rate is not affected.



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



Clogging with sheep: Cubel (Zaragoza)



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).



Experiment without obstacleExperiment without obstacle



Clogging times, burst size…Clogging times, burst size…



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)



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)



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)



with obstacle



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

Vibrated silo.

But the dynamics in silos are completely different…

Vibrated silo



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.



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



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

=




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.




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

=

=



converge.

R =




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

=



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



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. AplicadaUniversidad de Navarra31080 Pamplona, Spain.

Thank you!Thank you!

Clogging in bottlenecks: from inert particles to active matter

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