Solidification leading to Clogging in Powder Flows/Impact Strengths and Particle Mixing in Granular Shear Flows

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Prof C S Campbell Yi Zhang and Paul Cleary
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Research Area: 
Powder Flow
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United States

This proposal originally addressed the issue of why stagnant zones, such as funnel flows in hoppers, appear in particle flows. To that end, we studied computer simulations of a Couette flow with gravity acting on a system of two-dimensional discs. These were largely described in last year’s report. In those simulations, gravity acted to force a stagnant zone of material to form, so that the conditions that led to the transition from fluid-like to solid-like behavior could be observed and studied. Much to our surprise, the initial motion of the layer occurred in a quasistatic manner with the location of the interface coinciding with a constant value of the ratio of shear to normal stress. We have continued this work in three directions. (1) Extension of the model from two to three dimensions. This phase is almost complete. (2) Shear cell tests on our simulated material. As we have shown that the yielding appears to follow a Mohr-Coulomb failure criterion, similar to that used in plasticity models, why then, did plasticity models fail in predicting and describing funnel flows in hoppers? One answer is that the plasticity models depended on friction angles measured in Jenike or other, similar, shear cells and, because of the different flow conditions, the observed yielding behavior may be different. To test this hypothesis, we created a simulation of a shear tester to perform the equivalent of a shear test on our simulated material and, indeed, in preliminary results, it appears that the stress ratios measured in the shear cell are larger than those that govern the location of the yield interface in the Couctte flow with gravity simulation. (3) Inclined chute flows: Chute flows have an odd yielding behavior in which they often move largely as a solid block over a thin shearing basal layer. At first glance, this seemed to be in contradiction to the Couette flow results. However, simulations show that the two results arc indeed consistent. But at the same time, they pose other questions. In the Couette flow situation, the location of yielding could be determined more or less on the basis of a frictional criterion. In the chute flow simulation, while the stress ratio at the yield point wus numerically similar to that observed in the Couette flow simulation, one could not determine its location baaed on such a criterion. Consequently, there must be some unexplained connection between the location of the interface and the flow mechanics. As it probably has implications in other flow situations, this is a problem worthy of further study.

At the Teaneck meeting in 1989, Gordon Butters asked me on behalf of the TC, to see if my work could shed some light on the fracture problem. On further consultation with Paul Isherwood, I learned that there was a general lack of information about the forces that are exerted by the flow induced particle collisions. While the simulations have been previously made stress tensor measurements and thus determined averaged forces applied to particles, these are generally irrelevant to the fracture problem as the most damage will be caused by the maximum and not the average forces. Thus, I conducted a series of simulations to determine the maximum collisional impulses that the particles experience in a simple shear flow and their dependence on particle properties and solids concentration. The impulses are divided into their components normal and tangential to the particle surface as it was felt that the two might contribute to different attrition characteristics. The normal impulses - which might lead to large scale particle fracture - was always significantly larger than their tangential counterparts - which would tend to shear off the microroughness that lead to the interparticle surface friction. Along the way, histograms of the distribution of collision impulses as well as their geometric distribution over the surface of the particle were recorded.

Also, at the Teaneck meeting, Hans Buggish, not on behalf of anybody but himself, suggested that I might be able to contribute to his IFPRI sponsoned work on the flow induced mixing of particles in his granular shear cells. Be had observed that the mixing might be modeled as a diffusion process, similar to that of molecules in a gas or liquid. The use of a computer simulation was particularly attractive in such a study as his experimental technique was limited to measuring the diffusion of particles in only the direction parallel to the velocity gradient, while the computer simulation could measure the diffusion in all directions. The results show that the particles do mix by diffusion except at the highest concentrations when the particles become tightly packed in a crystalline microstructure and unable to move relative to their neighbors. However, the diffusion in a shear flow is not isotropic and is only appropriately modeled as a tensor of diffusion coefficients. By far, the largest mixing occurring in the direction of flow. The components of the diffusion tensor were measured both by particle tracking and by a statistical technique developed by Taylor (1922). Furthermore, it showed that the mixing in a granular flow flow was an example of Taylor diffusion by which the diffusion of particles in the direction of the velocity gradient greatly enhanced their mixing.

Finally, this report describes a preliminary attempt to model the flow through pinmills. Like the impulse strength studies mentioned above, this work done pursuant to Gordon Butters’ request that 1 attempt to apply computer simulations to fracture problems. This work was intended to study a situation of more direct interest to industry than a simple shear flow. However, the project has been abandoned due to a general lack of interest in pinmills within the industrial community.