1. Modeling of Cohesionless Granular Flows
By Liz Uribe
Research Mentor Eduardo Sáez
Department of Chemical and Environmental Engineering University of Arizona
NASA Space Grant Symposium
April 19, 2008

2. Rheology of Granular Materials
Made up of discrete solid particles (> 1μm) that are large enough that thermal agitation (Brownian motion) is negligible.
The interstitial space between particles is usually filled with air, in most cases this has little to no effect on the mechanics of the material.
Examples of applications:
Motion of solids in silos
Transport of solids
Avalanches
Geophysical motion
Milling
Types :
Cohesive (electrostatics), characteristic of fine, dry particles
Cohesionless

3. Granular Flow
No single constitutive relation has been able to describe granular behavior over varying degrees of fluidization and shear rates.
This work uses a new constitutive equation to describe the flow of a granular material over an inclined plane in one dimension.

4. Constitutive Equations
Newtonian Fluid
t: shear stress
m: viscosity
: deformation rate
Proposed Constitutive Equation

5. Flow Down an Inclined Plane
Friction Law:
Inertial Number:
Yield stress

6. Flow Down an Inclined Plane
Model:
Conservation of mass and momentum
Solids fraction:
constant
(linear υ)
(Jop’s υ )

7. Flow Down and Inclined Plane
Fig. 1: Experimental set up of granular flows on a pile between rough sidewalls (Jop et. al. 2006).

8. Volumetric Flow Rate Jop’s υ

9. Volumetric Flow Rate Linear υ

10. Conclusions
Experimental data on granular flows over inclined surfaces can be modeled with the constitutive equations presented here.
We have also shown that a non-linear solids fraction does not significantly improve the model.