Report

Evolution of Sheared Dense Granular Flow z Udriving W x Jerry Gollub . Haverford College & Univ. of Pennsylvania Grains J.-C. Tsai I ) Crystallization transition G.Voth -- 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 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 ~30d, ( Circumference ~ 800d ) Movie : the initial state (with driving speed = 8 d/s) I) Crystallization transition -- internal slices z Udriving W x Grains Vertical slice (XZ plane): a t = 0s t=10000s t=20000s t=30000s t=10000s t = 0s (t)-h(0)) / H0 b Horizontal slice (XY plane): 0.00 0 x -0.01 -150 -0.02 -300 h(t)-h(0) (mm) L I) Crystallization transition -- movies z W x Grains XZ slice: XY slice (before trans.) XY slice (after trans.) (9hrs total @ ~900X) Udriving I) Crystallization transition a t=0 t=60000s Spatial Ordering 0.004 -- time-resolved measurements 0.002 G0 I The ordering transition 0.001 f(kx) results in step changes of 0.000 0.0 0 b 10 20 30 0.00 Volume Change -0.03 ( -3 %) (h(t)-h(0)) / H0 granular volume (), Instantenous FFT Spectrum ( t = 60000s ) 0.1 L 40 kx / (2p/L) 0 -450 -900 -0.06 cc0.24 Shear Force 0.21 (a.u.) t(t) shear force (), 0.18 ( -15 %) 0.03 0.00 dc < Vx >G0 / Udriving and particle speed (stronger decay downwards). h(t)-h(0) (mm) (1) 0.003 Particle Speed (averaged over region G0) -4 1.0 x 10 0.0 0 20000 40000 Time: t (s) 60000 80000 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” ** Degree of final ordering: * Final volume: < h >final- h100g (mm) (case of thin layers) 1200 14 1000 800 13 layers Final states vs. Total mass (movies) 600 400 200 0 incomplete ordering 12 incomplete ordering 96 100 104 108 112 116 120 Mass (gram) (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:) (i) Dependence on layer thickness: (mm) c {Fig.5, PRL 91,064301} a Fluid-immersed particles 200g (24 layers) 0 168g (20 layers) 136g (16 layers) 120g (14 layers) 116g (14 layers) 111g (13 layers) 108g (13 layers) -600 h(t) - hi -1200 -1800 (ii) Dry particles: 0 b Dry particles 200g (24 layers) -600 100 1000 10000 100000 Time (s) Ordering transition occurs, but takes much longer! II) Non-unique final states Using a bumpy bottom: § Shearing with an oscillatory pre-treatment: First then W W Grains Grains drive back and forth by a few cycles; (102 d each way) Udriving continuously shear at a fixed velocity. II) --stochastic selection of final states Number of oscillatory cycles applied prior to one-way shearing: 0 7 1 7 2 -300 (MOVIEs) 0 h(t) (mm) -400 1 -500 -600 0 3 4 5 6 2 8 9 10 -700 -800 100 1000 Time (s) --- partial ordering 10000 100000 II) --stochastic evolution (movies) 2 1 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*) Both boundary 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 Oscillatory driving –basic phenomena (1) Temporary volume decrease induced by oscillatory shearing U0(t) (d/s) (of sufficiently compacted packing): 12 0 -12 h(t) (mm) -300 -400 30 cycles 10 cycles a b Disordered Ordered -500 -600 -700 -800 -900 14200 14400 14600 14800 Time (s) 15000 0 3000 6000 t - t (s) 9000 III ) Oscillatory shear –basic phenomena (2) Instantaneous mean velocity Vx(t), measured at the same height: Vx (t) x Disordered state Udriving( t ) / 10 0 200 400 600 Time step (dt = 0.2s) 800 1000 400 600 Time step (dt = 0.2s) 800 1000 Udriving( t ) / 10 Ordered state Vx (t) z 0 200 (dt ~ 0.05Td) (sudden drop Dh ~ d/5.) 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 = W0/3 W0/6) Multiple horizontal slices (z = -H0/2 -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 < Vx > / Udriving 10 z 0 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 x Other driving speeds z/5d ae 0.12 d/s : Driving speed 12 d/s sampling rates : 0.06 fps 0.6 fps 1.2 fps 2.4 fps 4.8 fps 12 fps 60 fps 0.02 fps 0.00667 fps 0 -5 -10 1.2 d/s : z/d be -15 z/d -20 -25 (@~30X)