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: [email protected]http://socrates.berkeley.edu/~digoldma/
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Daniel I. Goldman* University of California Berkeley Department of Integrative Biology
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 - PowerPoint PPT Presentation
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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 BiologyPoly-PEDAL Lab
*starting Assistant Professor at Georgia Tech, January 2007
Increasing average correlation time Goldman & Swinney, Phys. Rev. Lett., 2006
eg. lattice model of Pan et al 2004
Distribution of correlation times increases as well
Length-scale of heterogeneity, increases with increasing
250 m glass spheresGoldman & Swinney, Phys. Rev. Lett., 2006
40 PD
Difference of images taken T=0.3 sec apart
Side view of bed
Determine correlation length1. Perform 2D spatial autocorrelation on single difference image, for fixed T2. Measure length at which correlation function has decayed by 1/e (We find xy=3. Average over independent images at fixed
T=0.3 sec
Increasing dynamic correlation length
Loss of mobility on particle diameter scale occurs near g
Weeks et al, Science 2000.Goldman & Swinney, PRL, 2006
g
COLLOIDSFLUIDIZED BED
--loss of mobility on particle diameter scale occurs near g
Scaling of correlation length and time
Pan, Garrahan, Chandler (2004)
2/3~ 4/1max ~
For <g
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?
Change in curvature near g ≈ 0.58
Inflection point
Goldman & Swinney, Phys. Rev. Lett., 2006
Ramp rate:1.82 mL/min2
CURVATURE CHANGE
Pusey 1987van Megen 1993 Speedy 1998Weeks 2000
g a
Inflection point near g
Goldman & Swinney, Phys. Rev. Lett., 2006
As g is approached, system can no longer pack sufficiently in response to changes in Q
Pressure drop vs. Q
Goldman & Swinney, Phys. Rev. Lett., 2006
fluidized
defluidized
P can no longer remain near unityg a
Speedy 1998
Goldman & Swinney, Phys. Rev. Lett., 2006
Diffusing Wave Spectroscopy (DWS) to probe the interior at short length and timescales
SOLID LINE: measured by camera imaging scaled by 3x105
Same functional forms below g
DWS
g aGoldman & Swinney, Phys. Rev. Lett., 2006
Fit region
Ballistic motion between collisionsCaging
Short time plateau indicates particles remain in contact
Motion on short time and length scales Particles move < 1/1000 of
their diameter
Doliwa 2000
0.58
0.5
Loss of ballistic motion between collisions at g
Exponent of fit
~)(r 2
Our picture
• We propose that at g, 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
• can no longer change adequately with changes in Q so P can no longer be maintained close to 1.
• P drops rapidly effectively freezing the system—particle motion is arrested at a
The bed thus defluidizes and arrests ~ ≈0.59 because of glass formation ~ ≈0.58
Conclusions on defluidization
• Dynamics of fluidized bed similar to supercooled liquids becoming glasses
• Glass formation explains a 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 g=0.585±0.005 results in arrest of particle motion at a=0.593±0.004
Goldman & Swinney, Phys. Rev. Lett., 2006
Arrested state continues to slowly decrease as Q decreases
a
g
Multiple scattered laser light imaged on CCD resolves
motions of <1 nm
5
“Speckle” pattern
Each pixel receives randomly scattered light that has combined
from all paths through bed
Integrate over 1/30 sec
Laser light probes short length and timescale motion
Crude estimate: light to dark=change in path length of 532 nm, 100 particles across, if each moves 532/100=5 nm per particle, 256 grayscales=5/255=0.02 nm motions
=532 nm R=1 cm
z=50 cm
CCD arrayIncoherent illumination
Particles visible under incoherent illumination
Microscopic motion persists in defluidized state
g
Laser off Laser on
The particles appear to arrest but the speckle does not indicating microscopic motion persists
Look at time evolution of row of pixels
Turn flow off suddenly: Free sedimentation
250 m
Decrease Q through the glass & arrest transitions
Slight increase in Q jams the grains
300Time (sec)
Jamming creates hysteresis
Jammed state doesn’t respond to small changes in flow rate
Q increasing Q decreasing
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 by control of flow rate Q