1. 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

2. Velocity q
fracture
vs plastic flow

3. 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

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

5. Momentum Conservation

6. Shear Stress

7. 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!

8. 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, (2002)
E. Longhi, N. Easwar, N. Menon

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

10.  = 2.7
 = 1.5

11. 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.

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