EXPANDED VERSION OF TALK GIVEN AT SOUTHERN WORKSHOP ON GRANULAR MATERIALS, VINA DEL MAR, CHILE 2006

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EXPANDED VERSION OF TALK GIVEN AT SOUTHERN
WORKSHOP ON GRANULAR MATERIALS, VINA DEL MAR,
CHILE 2006
Daniel I. Goldman University of California
Berkeley Department of Integrative
Biology Poly-PEDAL Lab starting Assistant
Professor at Georgia Tech, January 2007 CONTACT
digoldma_at_berkeley.edu http//socrates.berkeley.edu
/digoldma/
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Signatures of glass formation and jamming in a
fluidized bed of hard spheres
2 cm
Phys. Rev. Lett. 96, 145702 (2006)
Question how do grains stop moving as flow is
reduced?
100x100x700 25010 mm glass spheres

• Daniel I. Goldman
• University of California Berkeley
• Department of Integrative Biology
• Poly-PEDAL Lab
• starting Assistant Professor at Georgia Tech,
  January 2007
• Harry L. Swinney
• University of Texas at Austin
• Physics Department
• Center for Nonlinear Dynamics

1 mm

• Fluidized bed allows
• Uniform bulk excitation
• 2. Fine control of system parameters (like solid
  volume fraction f) by control of flow rate Q

Thanks to Mark Shattuck, Matthias Schröter, David
Chandler, Albert Pan, Juan Garrahan, and Eric
Weeks
vlt0.3 cm/sec
water
Q (0-100 mL/min)
Support Welch, DOE, IC Postdoc Fellowship,
Burroughs Wellcome Fund
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Fluidized beds relevance to locomotion
5 cm
Goldman, Korff, Wehner, Berns, Full, 2006
UC Berkeley, Dept of Integrative Biology
Mojave desert
5 cm
Outer Banks, NC
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Relevance of fluidized beds
Fossil fuel refinement
Cat cracker 200 billion/year
Laboratory fluidized bed
Goldman Swinney, UT Austin
Texaco
50 m
10 cm
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Physics of fluidization
Kozeny-Carman
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Fluidized bed basics
(cohesionless particles)
Increasing flow leads to fluidization at Qf
Height

• Final state is independent of particle size,
  aspect ratio, container shape,
• 0.59

Decreasing flow leads to defluidization f
independent of Q
100x100x700 250 mm glass spheres
height
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Experimental apparatus
100 to 1000 mm glass beads
Goldman Swinney, Phys. Rev. Lett., 2006
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Volume fraction pressure measurement
Goldman Swinney, submitted to Phys. Rev. Lett.,
2005
Side view of bed
Sensitivity0.6 Pa
Top of bed
h
5 mm resolution
Bottom of bed
1 cm
Volume fraction
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Fluidized bed basics
Bed height
fluidization
--Goldman, Shattuck Swinney, 2002 --Schröter,
Goldman Swinney 2005
fa
defluidization
flow pulses
In slow fluidization cycle, initial state is not
unique, final state is.
Pressure drop
favolume fraction no longer changes with changes
in Q
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fa0.59 achieved after defluidization is
independent of particle size, aspect ratio,
cross-sectional area
(or hydrodynamic forces)
f
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Rate dependence
Phenomena associated with glass formation (large
literature, many types of systems)
REVIEW ARTICLE Ediger, Angell, Nagel (1996)
Growing time-scale
Dynamical Heterogeneity
Weeks et al (2000)
Pan, Garrahan, Chandler (2004)
NMR Sillescu, 1999, Ediger, 2000
Glotzer (2000)
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Glass formation in hard spheres occurs near fg
0.58
rapid slowing of dynamics with no apparent
change in static structure

• Colloids Pusey 1987, van Megen 1993, Weeks 2000
• Simulation Speedy 1998, Heuer 2000

Deviation from ideal gas PV/NkT
Speedy 1998
Pusey 1987 van Megen 1993 Speedy 1998 Weeks 2000
f
Dynamical heterogeneity observed in hard disks
Beyond fg spheres can no longer move greater than
a particle diameter
Heuer 2000
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fa depends on rate of decrease of Q
?
Goldman Swinney, Phys. Rev. Lett., 2006
Ramp rate, dQ/dt
mL/min2
Water-fluidized bed
defluidization no visible particle motion
fa
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Dynamical Heterogeneity
Difference of images taken DT0.3 sec apart
?
Goldman Swinney, Phys. Rev. Lett., 2006
tDT
t
Particle motion is spatially correlated for
characteristic correlation time.
3x speed
f0.57
Side view of bed

Moved in DT
camera
60 PD
Immobile
1 PD 250 mm
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Heterogeneity observed at surface of bed
Difference of images taken DT0.3 sec apart
f0.56
3x speed
Top view of bed
Indicates that the dynamics in the interior are
also heterogeneous
f0.59
1 mm
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Time evolution of heterogeneity
snapshot
Goldman Swinney, Phys. Rev. Lett., 2006
f0.568
f0.590
t
40 PD
space
Heterogeneity persists for characteristic time t
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Measure correlation time, t
I(x,y,t)
Particle motion causes pixel intensity
fluctuations

t
Side view
1. For each pixel, perform autocorrelation of
I(t) 2. measure 1/e point for each correlation
curve t
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Increasing average correlation time
?
Goldman Swinney, Phys. Rev. Lett., 2006
Distribution of correlation times increases as
well
eg. lattice model of Pan et al 2004
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Difference of images taken DT0.3 sec apart
Length-scale of heterogeneity, x increases with
increasing f
Side view of bed
40 PD
x
x
Goldman Swinney, Phys. Rev. Lett., 2006
250 mm glass spheres
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Determine correlation length
1. Perform 2D spatial autocorrelation on single
difference image, for fixed DT 2. Measure length
x at which correlation function has decayed by
1/e (We find xxxyx) 3. Average over independent
images at fixed f
DT0.3 sec
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Increasing dynamic correlation length
COLLOIDS
FLUIDIZED BED
fg
Weeks et al, Science 2000.
Goldman Swinney, PRL, 2006
Loss of mobility on particle diameter scale
occurs near fg
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--loss of mobility on particle diameter scale
occurs near fg
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Scaling of correlation length and time
Pan, Garrahan, Chandler (2004)
For fltfg
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Hard sphere glass physics

• In the fluidized bed, we observe
• Rate dependence
• Increasing time-scale
• Dynamical heterogeneity
• Does this relate to hard sphere glass formation?

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Inflection point
Change in curvature near fg 0.58
Goldman Swinney, Phys. Rev. Lett., 2006
Ramp rate 1.82 mL/min2
Hard sphere systems undergo glass transition at
fg 0.58
CURVATURE CHANGE
Pusey 1987 van Megen 1993 Speedy 1998 Weeks 2000
defluidization
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Inflection point near fg
fg
fa
Goldman Swinney, Phys. Rev. Lett., 2006
As fg is approached, system can no longer pack
sufficiently in response to changes in Q
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Pressure drop vs. Q
Goldman Swinney, Phys. Rev. Lett., 2006
fluidized
defluidized
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DP can no longer remain near unity
fg
fa
Goldman Swinney, Phys. Rev. Lett., 2006
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Diffusing Wave Spectroscopy (DWS) to probe the
interior at short length and timescales
Pine, Weitz, Chaikin, Herbolzheimer PRL 1988
2.5 cm
I(t) intensity of interfering light at point
Laser light
Use DWS theory, from g(t) obtain
Resolution estimate 532 nm/100 particles across
5 nm particle displacements, microsecond
timescales
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Correlation time of multiply scattered light
Goldman Swinney, Phys. Rev. Lett., 2006
Basically
1/e point
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Divergence and arrest
Goldman Swinney, Phys. Rev. Lett., 2006
fa
fg?
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Decoupling macro and microscopic motions
fg
fa
Goldman Swinney, Phys. Rev. Lett., 2006
tDWS
Same functional forms below fg
SOLID LINE t measured by camera imaging scaled
by 3x105
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Motion on short time and length scales
Doliwa 2000
0.5
Particles move lt 1/1000 of their diameter
0.58
Ballistic motion between collisions
Caging
Fit region
Short time plateau indicates particles remain in
contact
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Loss of ballistic motion between collisions at fg
Exponent of fit
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Our picture

• We propose that at fg, the bed undergoes a glass
  transition
• Many spheres must now move cooperatively for any
  sphere to move so the system begins to undergo a
  structural arrest
• f can no longer change adequately with changes
  in Q so DP can no longer be maintained close to
  1.
• DP drops rapidly effectively freezing the
  systemparticle motion is arrested at fa

This explains observation of Ojha et al, that all
non-cohesive fluidized beds achieve same final
volume fraction f0.59
The bed thus defluidizes and arrests f0.59
because of glass formation f0.58
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Conclusions on defluidization
Goldman Swinney, Phys. Rev. Lett., 2006

• Dynamics of fluidized bed similar to supercooled
  liquids becoming glasses
• Glass formation explains fa independent of
  particle size, etc.
• Nonequilibrium steady state suspension shows
  similar features of glass transition as seen in
  equilibrium hard spheres

Multiple lines of evidence indicate a transition
at fg0.5850.005 results in arrest of particle
motion at fa0.5930.004
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Arrested state continues to slowly decrease as Q
decreases
fg
fa
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Multiple scattered laser light imaged on CCD
resolves motions of lt1 nm

• Laser light probes short length and timescale
  motion

Particles visible under incoherent illumination
Each pixel receives randomly scattered light that
has combined from all paths through bed
Speckle pattern
CCD array
l532 nm
R1 cm
5 m
z50 cm
Integrate over 1/30 sec
Crude estimate light to darkchange in path
length of 532 nm, 100 particles across, if each
moves 532/1005 nm per particle, 256
grayscales5/2550.02 nm motions
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Microscopic motion persists in defluidized state
The particles appear to arrest but the speckle
does not indicating microscopic motion persists
Turn flow off suddenly Free sedimentation
g
Look at time evolution of row of pixels
250 mm
Laser on
Laser off
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Slight increase in Q jams the grains
Decrease Q through the glass arrest transitions
Liu, Nagel 1998
300
Time (sec)
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Jamming creates hysteresis
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Jammed state doesnt respond to small changes in
flow rate
Q increasing
Q decreasing
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Summary

• Decreasing flow to fluidized bed displays
  features of a supercooled liquid of hard spheres
  becoming a glass
• Hard sphere glass formation governs transition to
  defluidized bed
• In arrested state, microscopic motion persists
  until state is jammed

USE WELL CONTROLED FB TO STUDY HARD SPHERE
GLASSES GLASSES CAN INFORM FB

• Fluidized bed allows
• Uniform bulk excitation
• 2. Fine control of system parameters (like solid
  volume fraction f) by control of flow rate Q

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END