Daniel I. Goldman* University of California Berkeley Department of Integrative Biology

1. 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@berkeley.edu http://socrates.berkeley.edu/~digoldma/

2. 2 cm Signatures of glass formation and jamming in a fluidized bed of hard spheres Phys. Rev. Lett. 96, 145702 (2006) Question: how do grains stop moving as flow is reduced? 100x100x700 250±10 mm glass spheres 1 mm 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 • 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 v<0.3 cm/sec water Q (0-100 mL/min) Support: Welch, DOE, IC Postdoc Fellowship, Burroughs Wellcome Fund

3. 5 cm Fluidized beds: relevance to locomotion Goldman, Korff, Wehner, Berns, Full, 2006 UC Berkeley, Dept of Integrative Biology Mojave desert 5 cm Outer Banks, NC

4. Fossil fuel refinement Relevance of fluidized beds Cat cracker: $200 billion/year Laboratory fluidized bed Goldman & Swinney, UT Austin Texaco 50 m 10 cm

5. 1 permeability Physics of fluidization Kozeny-Carman

6. water (cohesionless particles) Fluidized bed basics 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

7. 100 to 1000 mm glass beads Experimental apparatus Goldman & Swinney, Phys. Rev. Lett., 2006

8. Volume fraction & pressure measurement Goldman & Swinney, submitted to Phys. Rev. Lett., 2005 Side view of bed Sensitivity:0.6 Pa Top of bed h 5 mm resolution Bottom of bed 1 cm Volume fraction

9. 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 fa≡volume fraction no longer changes with changes in Q

10. fa≈0.59 achieved after defluidization is independent of particle size, aspect ratio, cross-sectional area Ojha, Menon and Durian (2000) Gas-fluidized bed (or hydrodynamic forces) f

11. Phenomena associated with glass formation (large literature, many types of systems) Rate dependence REVIEW ARTICLE: Ediger, Angell, Nagel (1996) Dynamical Heterogeneity Growing time-scale Weeks et al (2000) Pan, Garrahan, Chandler (2004) NMR: Sillescu, 1999, Ediger, 2000 Glotzer (2000)

12. *rapid slowing of dynamics with no apparent change in static structure Glass formation* in hard spheres occurs near fg ≈ 0.58 • 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

13. 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

14. Dynamical Heterogeneity  Difference of images taken DT=0.3 sec apart Goldman & Swinney, Phys. Rev. Lett., 2006 t+DT t 3x speed Particle motion is spatially correlated for characteristic correlation time. f=0.57 Side view of bed = Moved in DT camera 60 PD Immobile 1 PD= 250 mm

15. mirror camera Heterogeneity observed at surface of bed Difference of images taken DT=0.3 sec apart f~0.56 3x speed Top view of bed Indicates that the dynamics in the interior are also heterogeneous f~0.59 1 mm

16. Time evolution of heterogeneity snapshot Goldman & Swinney, Phys. Rev. Lett., 2006 f=0.568 f=0.590 t 40 PD space Heterogeneity persists for characteristic time t

17. 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

18.  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

19. Difference of images taken DT=0.3 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

20. 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 xx=xy=x) 3. Average over independent images at fixed f DT=0.3 sec

21. 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

22. --loss of mobility on particle diameter scale occurs near fg

23. Scaling of correlation length and time Pan, Garrahan, Chandler (2004) For f<fg

24. 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?

25. Change in curvature near fg ≈ 0.58 Inflection point Goldman & Swinney, Phys. Rev. Lett., 2006 Hard sphere systems undergo glass transition at fg≈ 0.58 Ramp rate: 1.82 mL/min2 CURVATURE CHANGE Pusey 1987 van Megen 1993 Speedy 1998 Weeks 2000 “defluidization”

26. 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

27. Pressure drop vs. Q Goldman & Swinney, Phys. Rev. Lett., 2006 fluidized defluidized

28. Speedy 1998 DP can no longer remain near unity fg fa Goldman & Swinney, Phys. Rev. Lett., 2006

29. 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

30. tDWS Correlation time of multiply scattered light Goldman & Swinney, Phys. Rev. Lett., 2006 Basically ~ 1/e point

31. Divergence and arrest Goldman & Swinney, Phys. Rev. Lett., 2006 fa fg?

32. 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

33. Motion on short time and length scales Doliwa 2000 0.5 Particles move < 1/1000 of their diameter 0.58 Ballistic motion between collisions Caging Fit region Short time plateau indicates particles remain in contact

34. Loss of ballistic motion between collisions at fg Exponent of fit

35. 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 system—particle motion is arrested at fa This explains observation of Ojha et al, that all non-cohesive fluidized beds achieve same final volume fraction f≈0.59 The bed thus defluidizes and arrests ~ f≈0.59 because of glass formation ~ f≈0.58

36. 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 fg=0.585±0.005 results in arrest of particle motion at fa=0.593±0.004

37. Arrested state continues to slowly decrease as Q decreases fg fa

38. Incoherent illumination Particles visible under incoherent illumination Multiple scattered laser light imaged on CCD resolves motions of <1 nm Each pixel receives randomly scattered light that has combined from all paths through bed Laser light probes short length and timescale motion “Speckle” pattern CCD array l=532 nm R=1 cm 5 m z=50 cm Integrate over 1/30 sec 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

39. Microscopic motion persists in defluidized state Turn flow off suddenly: Free sedimentation The particles appear to arrest but the speckle does not indicating microscopic motion persists g Look at time evolution of row of pixels 250 mm Laser on Laser off

40. Slight increase in Q jams the grains Decrease Q through the glass & arrest transitions Liu, Nagel 1998 Time (sec) 300

41. Jamming creates hysteresis

42. Jammed state doesn’t respond to small changes in flow rate Q increasing Q decreasing

43. 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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