Transcript The Dynamics of Active Matter Particles on Disordered Landscapes: Jamming, Clogging, and Avalanches (Harvard, 2015)

The Dynamics of Active Matter
Particles on Disordered
Landscapes: Jamming, Clogging,
and Avalanches
Charles Reichhardt
Cynthia Reichhardt
Zohar Nussinov
Theoretical Division
Los Alamos National Laboratory
Dipanjan Ray
Department of Physics
Notre Dame
Jamming: particles impede each other's motion
Industrial applications
Granular matter
Traffic flow
Liquid-solid transition
Reichhardt et al, Science 2009
Is jamming different from clogging when obstacles are
present?
Exponents measured through scaling:
Density axis, O’Hern et al: 0.71
PRE 68, 011306 (2003)
Load axis, Olsson and Teitel: 0.6 + 0.1
PRL 99, 178001 (2007)
Exponent measured directly:
Drocco et al: 0.6 to 0.7
PRL 95, 088001 (2005)
Suggests: Jamming is second order phase transition
with a diverging length scale as jamming is
approached
Is clogging the same as the jamming transition?
Well below jamming: Single driven particle with no quenched
disorder
Brown disks:
stationary
Red disks: in
force contact
with driven
disk
Blue disk:
driven
=0.67
Close to jamming
Brown disks:
stationary
Red disks: in
force contact
with driven
disk
Blue disk:
driven
=0.801
At jamming
Brown disks:
stationary
Red disks: in
force contact
with driven
disk
Blue disk:
driven
=0.839
Bidisperse grains flowing through fixed obstacles
Jamming density: 0.843
Uniform drive applied
to all grains
Red dots:
Immobile disks
Black lines:
Disk trajectories
Will the system
organize into a
jammed or clogged
state over time?
At jamming
density, a single
obstacle will pin
entire system
At what density of immobile disks does all motion stop?
Simulation
Jamming as a function of increasing quenched disorder
density
200
150
100
50
10
Fd=0.5
Without quenched
disorder, jamming
density is 0.8433
Phase diagram: obstacle density vs jamming density
Obstacle
density
(Unpinned)
(Pinned)
Disk
density
What do the jammed states look like at 0.838 and 0.678?
Density 0.838: Jamming occurs instantaneously
Jammed
states appear
homogeneous
Total density 0.838
Almost no plastic
rearrangements
at finite drive
Away from point J Jamming does not occur instantly, but
takes time to organize to a clogged state
r=0.675
Clogged state organizes over time via coarsening of an
anisotropic void
Density
0.675
Density becomes heterogenous with local high density
regions at point
Later time
Early time
Clogged state is jammed in only one direction
Driving previously clogged system at 90 degrees:
Heterogeneity introduced by previous driving is
preserved
With no previous driving, system clogs
Drive in x-again system also clogs in x
Clogged state is not unique – has memory of previous drive
Jamming near point J; clogging at lower density
Small disorder:
Jamming
behavior
dominates
Larger
disorder:
behavior more
consistent with
clogging
Schematic of pinned, clogged, and
jammed states
Jamming Vs Clogging
Near Point J for small amounts of disorder, jamming is homogeneous and
appears to be dominated by the physics of Point J (growing correlation
length, etc)
•Jammed systems are jammed in all directions
•
For lower densities away from Point J, the jamming transition is replaced
by a clogging transition, characterized by long transient motion during
which anisotropic voids organize until the flow is cut off, density becomes
heterogeneous.
•
Clogged systems are only clogged for the original driving direction, and
may be unclogged for different driving directions
•
•
Clogging and jamming are distinct transitions.
Clogging in Active Matter in systems?
Nonequilibrium particle-based systems
with internal, not external, propulsion.
Possible collective behaviors
Active matter: Bacteria
Run-and-tumble dynamics
During the run, detailed balance is broken
Possible to extract useful work from system
Artificial active matter
Swimmers
(Pine/Chaikin group, NYU)
Light-activated Janus particles
(Bechinger group, Stuttgart)
Phase diagram of onset of
clustering or phase segregation
G.S. Redner, M.F. Hagan, and A. Baskaran, PRL 108, 235702 (2012)
Living Crystals of Light-Activated
Colloidal Surfers
J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013)
Clustering due to steric active
particle collisions
I. Buttinoni et al, PRL 110, 238301 (2013)
Motility
Run-and-tumble dynamics
Ballistic motion during a time
interval corresponding to a
distance lb
Tumbling times are asynchronous
Comparison: Nonswimming bacteria
For instance, dead, or genetically engineered to have no flagella
Brownian motion: detailed
balance is preserved
Simulation Model
 Swimmers
 Massless (overdamped), Spherical, Rigid
 Equations of motion:
 Compute forces between all pairs of particles

Fij = k( rij - reff )
F
å
Calculate particle displacements:
Fi =
ij
j in contact
r = r + Fi × Dt
i
t+1
i
t
F
 Temperature free
reff
r
Simulation Model
 Swimmers
 Massless (overdamped), Spherical, Rigid
 Equations of motion:
 Compute forces between all pairs of particles
å
Fi =
Fij = k( rij - reff )
Fij
j in contact
 Calculate particle displacements:
r = r + Fi × Dt
i
t+1
 Temperature free
i
t
F
reff
r
Active matter patterns
Phase separation (clustering) of swimming particles
“Self-trapping” of run-and-tumble particles into patterns in a
one-dimensional sample - J. Tailleur, M.E. Cates, Phys.
Rev. Lett. 100, 218163 (2008)
Phase separation of active Brownian particles into amorphous
clusters - Y. Fily, M.C. Marchetti, Phys. Rev. Lett. 108,
235702 (2012)
Clustering should occur whenever particle velocity becomes
density dependent - M.E. Cates, J. Tailleur, EPL 101,
20010 (2013)
Experimental observation of “living crystals” - J. Palacci, S.
Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science
339, 6119 (2013)
Cluster formation with increasing
density
Density 0.16
Density 0.53
Density 0.3927
Density 0.825
Cluster formation with increasing
run length at density 0.667
Rl=.05
Rl=20
Rl=4
Rl=100
Onset of clustering as a function of
run length
L = 100,
Depinning geometry
Open circles:
Active particles
Filled circles:
Stationary particles
Dashed lines:
Trajectories
Arrow:
Drift force direction
Increasing thermal fluctuations increases
mobility for a particle on a random substrate
Single active particles driven
through obstacle arrays
G. Volpe et al, Soft Matter 7, 8810 (2011)
Mobility decreases with increasing
run length
Density 0.667
Optimal mobility at specific run
lengths
Connecting the clogging at zero
activity to the clogging at large
activity
Run length: Infinitesimal
Local jamming
Larger run length
System behaves like a liquid
Long run length:
Active jamming occurs
Formation of clusters leads to
reduction in mobility
CL: fraction of particles in largest cluster
<Vx>: net velocity in drift direction
Gas phase particles can avoid obstacles
Clusters of particles can be trapped by obstacles
Clogging at low activity and
Clogging and high activity
Infinite run length:
Defects nucleate crystals
Active
Active
Dynamically frozen
Dynamically frozen
Nucleation into a crystal
Increasing disorder reduced the
next flux of active particles through
the system
At disorder = 0.15 the active particle
motion occurs in avalanches
Mobility of a single pushed probe
particle through an active matter
bath
Velocity fluctuations in the active
dense regime have avalanche
characteristics
Active matter with obstacles
Rl = 20
Measuring forces exerted by active
matter: Casimir geometry
Plate length: l
Plate spacing: d
Compute net force on
each plate to
determine if attractive
or repulsive
Visitation density depletion between
walls
What is going on (2)
Force as function of wall separation
Large and small run lengths
Density depletion reduced when
steric interactions cause clustering
Summary
•Passive particles moving through obstacles can exhibit jamming
behavior at high particle densities, distinguished by a growing
correlation length and a homogeneous density.
•Clogging occurs at lower densities and forms a fragile state with
heterogeneous density.
•For active particles, increasing the activity can cause transport
through obstacle arrays to increase. At low activity the particles
exhibit passive clogging behavior, while for large activity the
particles undergo a novel active clogging transition.