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. 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. This work has been performed for both two-dimensional simulations of disc flows and three dimensional simulations of spheres. Large portions of this project involved the development of soft particle simulation models that can be applied to this, as well as other, studies.
The results indicate that this is a problem that runs the gamut of granular flow regimes, from the molecular like, rapid flow regime, to the slow quasistatic regime. As such, it covers the transition between the two limiting states, an area that hss not been tackled theoretically. It was observed that, while a region demonstrating molecular-like behavior may exist, the transition to solid behavior is not, as was originally hoped, an analog to a phase change in real molecular systems. Instead, the first movement of the material occurs as a quasistatic yielding. The results are beginning to shed some light on the transition process. The main difference between macroscopic particles and molecules is that particles can sustain long duration contact with their neighbors (this is what makes quasistatic behavior possible) and this permits the material to push-through the phase change.
The scope of this project has been extended beyond its original proposal to include more general problems of the computer simulation of powder flows. 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 used to make 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 force. 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 aponaored work on the flow induced mixing of particle in his granular shear cells. He had observed that the mixing might be modeled as a diffusion process, similar to that of molecule 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 micrmtructure 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 tear 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 was an example of Taylor diffusion by which the diffusion of particles in the direction of the velocity gradient greatly enhanced their mixing.