John Drozd Colin Denniston

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Presentation transcript:

John Drozd Colin Denniston Simulations of Collision Times and Stress In Gravity Driven Granular Flow John Drozd Colin Denniston • bottom sieve • particles at bottom go to top • reflecting left and right walls • periodic or reflecting front and back walls 3d simulation  Snapshot of 2d simulation from paper: “Dynamics and stress in gravity-driven granular flow” Phys. Rev. E. Vol. 59, No. 3, March 1999 Colin Denniston and Hao Li

Velocity q fracture vs plastic flow

Fluctuating and Flow Velocity Experiment by N. Menon and D. J. Durian, Science, 275, 1997. v2 Simulation results by summer student Nehal Al Tarhuni vf

Normal Stresses Along Height Momentum Conservation kik+gi = 0 Normal Stresses Along Height Weight not supported by a pressure gradient.

Momentum Conservation

Shear Stress

Power Laws for Collision Times = time between collisions Collision Time: time between collisions spheres in 2d 3d spheres 2d disks Similar power laws for 2d and 3d simulations!

Comparison With Experiment : experiment 1.5 vs. simulation 2.7 Discrepancy as a result of experimental response time and sensitivity of detector.  Experiment Pressure Transducer “Spheres in 2d”: 3d Simulation with front and back reflecting walls separated one diameter apart   Figure from experimental paper: “Large Force Fluctuations in a Flowing Granular Medium” Phys. Rev. Lett. 89, 045501 (2002) E. Longhi, N. Easwar, N. Menon

Simulation  Experiment  (Longhi, Easwar) Quasi-1d Theory  Most frequent collisions contributing to smallest impulses Simulation  Experiment  (Longhi, Easwar) Quasi-1d Theory  (Coppersmith, et al)

 = 2.7  = 1.5

Conclusions Same power laws for 2d disks and spheres in 2d for collision times. Similar power law for 3d simulations for collision times. Compared with experiment. Dynamics (collision directions) lead to static stresses.

Experimental data from the book: “Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials” By Jacques Duran.