Multidimensional Problems in Granular Plasticity
E. Bruce Pitman Principal Investigator
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This award supports a unified research program of modeling, analysis<br/>and computation to better characterize and understand granular flows,<br/>in particular, granular flows in the presence of interstitial fluid.<br/>Dry granular materials may be characterized as a fourth state of matter.<br/>Granular media can support stresses like a solid, but also<br/>can flow like a liquid, or, under some conditions, like a gas.<br/>While deforming, a granular sample may dilate or consolidate,<br/>depending on packing conditions. These features lead to a dynamics <br/>of granular materials whose richness and scope rivals that of fluid dynamics.<br/>At the same time, particle materials used in technological applications are<br/>becoming smaller, and, consequently, the presence of interstitial fluid is<br/>becoming increasingly important. This is particularly true<br/>in the use of toner powders in xerography, where the small size<br/>of the power particles means higher quality copies. As they move, these <br/>small light particles (about 10 micron diameter) are strongly influenced <br/>by the surrounding gas, and particle motion is intimately coupled to fluid motion.<br/>Furthermore, owing to van der Waals attraction, these toner powders<br/>are cohesive, often tending to clump. The introduction of controlled <br/>fluid flow, through fluidization and vibration, is a common mechanism<br/>for breaking the cohesive attractions and controlling particle motion.<br/>In a very different application, new ideas for drying and coating<br/>larger particles (about 500 micron diameter) use rapid vertical vibration <br/>of a flat plate to accelerate a granular mass. Because of the large <br/>acceleration, interstitial fluid again plays an important role in the <br/>motion of particles. Theoretical and numerical techniques will be used to<br/>characterize state diagrams, study the stability of layers of fluidized powder<br/>under tilting, and study the onset of bubbling and clumping.<br/><br/>The combined flow of particles and fluid has many other industrial<br/>applications, such as particle flow in pressurized vessels, cat-cracking,<br/>transport by lubrication, and heat transfer. In these applications, <br/>transport and handling of powders presents a significant difficulty.<br/>Without a better understanding of particle-fluid flows, products that<br/>exploit new particle technologies may not come on-line as quickly, nor with<br/>sufficient reliability. In this regard, it is useful to<br/>note a study by the Rand Corporation showing that, because of an<br/>inability to accurately predict powder behavior, solids-producing<br/>manufacturing plants performed on average at 63% of design capacity,<br/>compared to 84% for liquids-producing plants.<br/>The analysis and computations performed during this project, together with<br/>experiments by other academic and industrial researchers,<br/>will help to provide the needed characterization of these flows.