I ) Crystallization transition -- rheological change -- role of B.C.

z Udriving W x Grains Evolution of Sheared Dense Granular FlowJerry Gollub . Haverford College & Univ. of PennsylvaniaJ.-C. TsaiG.Voth I ) Crystallization transition -- rheological change -- role of B.C. -- ‘quantization’ effects II ) Non-unique final states -- ‘stochastic’ selection -- stabilization of disordered state III ) Quasi-static internal dynamics: crystallized vs. disordered states

~30d, ( Circumference ~ 800d ) Experimental Setup --cross-sectional view Normal load W >> beads’ total weight & fluid’s viscous drag --Glass beads: d = 0.6mm immersed in fluid --Driving: constant speed, fixed normal load --Fluid: index-matched fluorescent dye + laser sheet * Volume measurement (height of upper surface) ** Shear force measurement

Movie : the initial state (with driving speed = 8 d/s)

z Udriving W x Grains Vertical slice (XZ plane): Horizontal slice (XY plane): x I) Crystallization transition -- internal slices

z Udriving W x Grains I) Crystallization transition -- movies XZ slice: XY slice (before trans.) XY slice (after trans.) (9hrs total @ ~900X)

I) Crystallization transition-- time-resolved measurements The ordering transition results in step changes of granular volume (), shear force (), and particle speed (stronger decay downwards). ( -3 %) ( -15 %)

I ) -- Role of boundary condition Final states (after a long steady shearing from above) with flat bottom or mono-layer bottom | bumpy bottom

* Final volume: ** Degree of final ordering: (case of thin layers) Final states vs. Total mass (movies) 14 13 layers incomplete ordering 12 incomplete ordering I )-- “Quantization effects” (Volume quantization is found to exist for flows as thick as 23~24 layers!)

I) Crystallization transition -- timescales & behavior of dry particles (Driven at the same speed:) (ii) Dry particles:  Ordering transition occurs, but takesmuch longer! {Fig.5, PRL 91,064301} (i) Dependence on layer thickness:

Udriving W W Grains Grains II) Non-uniquefinal states Using a bumpy bottom: § Shearing with an oscillatory pre-treatment: First then drive back and forth by a few cycles; (102 d each way) continuously shear at a fixed velocity.

II) --stochastic selection of final states (MOVIEs) 1 0 0 2 --- partial ordering

II) --stochastic evolution (movies) 1 2

II) -- stabilization of disordered state “Effectiveness” of partial ordering by oscillatory shear before the | after the long unidirectional shearing long unidirectional shearing

II ) Non-unique final states Facts: * Both states can be stablized. * Transition is possible ONLY when uncompacted; preparation history matters. * Reversal of crystallization transition NEVER occurs. * Crystallized state: less shear force, stronger velocity decay, less dissipative.  “preferred state”  How is history ‘recorded’ in granular packing?  “Attractors ? ”

III ) Quasi-static internal dynamics-- comparing velocity profiles

III ) Quasi-static internal dynamics-- particle trajectories: xi(t) & yi(t) xi(t) 1d time yi(t)

III ) Quasi-static internal dynamics-- yi(t): ordered vs. disordered states

* ) Additional information Steady shearing of binary mixture (The r.m.s. size dispersion in the previous experiments is about 4%.) Binary mixture: (d=1.0 mm vs. 0.6 mm), (25% vs. 75%) by weight, with some of the 1.0 mm grains painted black as tracers. (~3000X Real time)

Summary & Theoretical challenges(*) http://www.haverford.edu/physics-astro /Gollub/internal_imaging (1*) Shear flows can have non-unique final states. (2) For a nearly mono-disperse packing, rheology of cyrstallized state and disordered state are compared. (3*) Bothboundary condition and preparation history have profound effects on crystallization transition. the reversal of crystallization never occurs. Ref: PRL 91, 064301 (2003) & subsequent papers

.. More info

Temporary volume decrease induced by oscillatory shearing (of sufficiently compacted packing): Oscillatory driving –basic phenomena (1)

z x III ) Oscillatory shear –basic phenomena (2) Instantaneous mean velocity Vx(t), measured at the same height: Disordered state Ordered state (dt ~ 0.05Td) (sudden drop Dh ~ d/5.)

3D structure of the velocity field

After 2 weeks of steady shearing at a driving speed 12d/s: 3D structure of the disordered final state (partially ordered at sidewalls) Multiple horizontal slices (z = -H0/2  -1d ) Multiple vertical slices (y = W0/3 W0/6)

III ) Quasi-static internal dynamics-- comparing velocity profiles (24 layers) (22 layers)

z x (2) velocity profile & displacement timescales Time-averaged grain velocity of the ordered state (@~30X)

I ) Crystallization transition -- rheological change -- role of B.C.