Multidimensional Problems in Granular Plasticity
E. Bruce Pitman Principal Investigator
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DMS-9802520 Pitman This interdisciplinary proposal addresses scientific issues regarding the dynamics of granular materials coupled with interstitial fluid. The investigation is composed of three parts: modeling, analysis, and numerical computation. Models of particle-fluid motion must determine which physical mechanisms are dominant and which may be neglected without detrimental effect. In particular, traditional models of these flows treat the particle phase as a fluid-like material with a viscosity that depends on the particle volume fraction. A significant component of this research program is to study the effects of modeling the particle phase as a frictional material. Analysis will be primarily directed toward a study of the stability of distinguished solutions to the model equations. Numerical simulations will provide an understanding of nonlinearity in the equations, especially the effect of the particle phase model. These complementary methods of investigation will be guided by recent experiments that highlight the need for a new approach to the question of particle-fluid interaction. The combined flow of particles and fluid has many industrial applications, such as particle coating and drying, particle flow in pressurized vessels and cat-crackers, transport by lubrication, and heat transfer. New xerographic and metallurgic technology necessitate very fine powders. In these latter applications, however, as particle size decreases, transport and handling become more difficult, and the effects of interstitial gas become more important. Without better characterization of particle-fluid flows, products that exploit new technologies may not come on-line as quickly, nor with sufficient reliability. In this regard, it is useful to note a study by the Rand Corporation showing that, because of an inability to accurately predict powder behavior, solids-producing manufacturing plants performed on average at 63% of design capacity, compared to 84% for liquids-producing plants . This project will study new mathematical models for the behavior of very fine powders. The results of this project will be compared with concurrent experimental work by industrial researchers.