Granular Materials: A window to studying the Transition from a non-Newtonian Granular Fluid To A "Glassy" system: aka "The fluid-glass transition for hard spheres" John Drozd and Dr. Colin Denniston

Velocity Savage and Jeffrey J. Fluid Mech. 130, 187, 1983. q Collision rules for dry granular media as modelled by inelastic hard spheres As collisions become weaker (relative velocity vn small), they become more elastic. C. Bizon et. al., PRL 80, 57, 1997.

 polydisperse monodisperse vy dvy/dt P y Polydispersity means 300 (free fall region) Donev et al PRL96 "Do Binary Hard Disks Exhibit an Ideal Glass Transition?"  polydisperse monodisperse 250 (fluid region) vy 200 (glass region) dvy/dt 150 P y Polydispersity means Normal distribution of particle radii x z y Donev et al PRE 71

The density in the glassy region is a constant. In the interface between the fluid and the glass does the density approach the glass density exponentially? 0 = 0.9 0 = 0.95 0 = 0.99 Interface width seems to increase as 0  1  vy y How does  depend on (1  0) ?

Density vs Height in Fluid-Glass Transition

Length Scale in Transition "interface width diverges" Slope = 0.428  0.007

Y Velocity Distribution Mono-disperse (crystallized) y only z x 300 (free fall region) Poiseuille flow 250 (fluid region) Plug flow snapshot 200 (glass region) Mono-disperse (crystallized) only Mono kink fracture 150 y x z

Granular Temperature y x z 300 (free fall region) fluid 250 (fluid region) 235 (At Equilibrium Temperature) 200 (glass region) equilibrium 150 y glass x z

Fluctuating and Flow Velocity Experiment by N. Menon and D. J. Durian, Science, 275, 1997. 16 x 16 32 x 32 v Simulation results In Glassy Region ! J.J. Drozd and C. Denniston vf Europhysics Letters, 76 (3), 360, 2006 "questionable" averaging over nonuniform regions gives 2/3

  1 in fluid glass transition For 0 = 0.9,0.95,0.96,0.97,0.98,0.99 Subtracting of Tg and vc and not averaging over regions of different vx2 Down centre Slope  = 0.9-1.0

"Particle Dynamics in Sheared Granular Matter" Physical Review Letters 85, Number 7, p. 1428 (2000) Experiment: (W. Losert, L. Bocquet, T.C. Lubensky and J.P. Gollub)

Velocity Fluctuations vs. Shear Rate Slope = 0.406  0.018 Experiment Slope = 0.4 From simulation Must Subtract Tg ! Physical Review Letters 85, Number 7, (2000)

Conclusions A gravity-driven hard sphere simulation was used to study the glass transition from a granular hard sphere fluid to a jammed glass. We get the same 2/3 power law for velocity fluctuations vs. flow velocity as found in experiment, when each data point is averaged over a nonuniform region. When we look at data points averaged from a uniform region we find a power law of 1 as expected. We found a diverging length scale at this jamming (glass) to unjamming (granular fluid) transition. Silbert, Liu and Nagel (PRL 95, 098301 (2005)) also found diverging length scales near the unjamming transition for vibrations with jammed packings. Finally, we compared our simulation to experiment on the connection between local velocity fluctuations and shear rate and found quantitative agreement.