(80b) Shear Flow Of Assemblies Of Cohesive Granular Materials

Authors: 
Aarons, L. R. - Presenter, Princeton University


It is well known that assemblies of granular materials behave differently under different flow conditions. Under rapid flow conditions, the particles interact with each other predominantly through binary collisions, while at slow shear rates the interaction is dominated by enduring contacts. Campbell [1] carried out discrete element method (DEM) simulations of sheared assemblies of cohesionless particles in periodic domains and under constant volume conditions and presented a map of the different regimes of flow. Aarons & Sundaresan [2] performed similar simulations for cohesive granular materials and showed how the stresses varied with particle volume fraction, shear rate and particle properties including the strength of the cohesive interaction. This study revealed that inter-particle attractive forces expand the range of particle volume fractions and shear rates over which the quasi-static flow regime is observed. Furthermore, this study identified how the stresses in this regime should be scaled and showed that the apparent coefficient of friction varied systematically with particle volume fraction.

In practical devices, flows of granular materials rarely occur under constant volume conditions, and compaction and dilation do occur locally in response to the stresses. This and the fact that laboratory rheological experiments are often performed under constant applied overburden levels have prompted researchers to investigate regime maps under conditions of constant applied normal stress. The discrete element method (DEM) simulations performed by Campbell [3,4] revealed that the flow regime map for assemblies of cohesionless particles sheared at constant applied normal stress differed from the flow regime map he previously constructed for such assemblies sheared at constant volume [1].

In the present study, we have analyzed shear flow of cohesive granular materials under constant applied normal stress and compared the results with those obtained under constant volume conditions.

We consider the plane shear flow of particle assemblies in periodic domains, employing Lees ? Edwards boundary conditions [5] across the faces. Simulations were performed for different strengths of cohesion, shear rates, and applied normal stresses. From each simulation, we have extracted the average volume fraction, apparent coefficient of friction, and coordination number. We have also extracted results on the statistics of the temporal fluctuations in the stresses.

Our simulations reveal that in a time-averaged sense shearing under constant applied stress turns out to be identical to shearing at constant volume. That is, the volume fraction ? shear rate ? stress relation is the same for both types of shearing. The probability distribution functions of the shear stress fluctuations under constant volume and constant applied normal stress conditions exhibit very similar behavior, becoming narrower as the strength of cohesion increases. In the inertial regime, the stress fluctuations show a relatively weak dependence on cohesion.

The apparent coefficient of friction for the cohesive assemblies varied systematically with volume fraction. Over the entire range of particle volume fractions studied, the apparent coefficient decreases with increasing volume fraction.

[1] C. S. Campbell, Granular Shear Flows at the Elastic Limit, J. Fluid Mech. 465 (2002) 261-291.

[2] L. Aarons, S. Sundaresan, Shear flow of assemblies of cohesive and non-cohesive granular materials, Powder Technol. 169 (1) (2006) 10-21.

[3] C. S. Campbell, Stress-controlled elastic granular shear flows, J. of Fluid Mech. 539 (2005) 279-297.

[4] C. S. Campbell, Granular material flows ? An overview, Powder Technol. 162 (3) (2006) 208-229.

[5] A. W. Lees, S. F. Edwards, The computer study of transport processes under extreme conditions, Physics C: Solid State Phys. 5 (1972) 1921-1929.