Evolution of Sheared Dense Granular Flow Jerry Gollub. Haverford College & Univ. of Pennsylvania J.-C. Tsai G.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 Grains W U driving x z

Experimental Setup -- cross-sectional view --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 ~30d, ( Circumference ~ 800d ) Normal load W >> beads’ total weight & fluid’s viscous drag

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

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

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

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

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

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

II) Non-unique final states Grains W W U driving First Using a bumpy bottom: § Shearing with an oscillatory pre-treatment: then drive back and forth by a few cycles; (10 2 d each way) continuously shear at a fixed velocity.

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

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: x i (t) & y i (t) time x i (t) y i (t) 1d

III ) Quasi-static internal dynamics -- y i (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(*) (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*) Both boundary condition and preparation history have profound effects on crystallization transition. the reversal of crystallization never occurs. /Gollub/internal_imaging Ref: PRL 91, (2003) & subsequent papersPRL 91, (2003)

.. More info

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

III ) O scillatory shear – basic phenomena (2) Instantaneous mean velocity V x (t), measured at the same height: Disordered state Ordered state (dt ~ 0.05T d ) (sudden drop  h ~ d/5.) x z

3D structure of the velocity field

3D structure of the disordered final state (partially ordered at sidewalls) After 2 weeks of steady shearing at a driving speed 12d/s: Multiple vertical slices ( y = W 0 /3  W 0 /6 ) Multiple horizontal slices ( z = -H 0 /2  -1d )

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

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