Multidimensional Problems in Granular Plasticity

DMS-9802520皮特曼这项跨学科的提案解决了有关颗粒材料与间质流体耦合的动力学的科学问题。本研究由建模、分析和数值计算三部分组成。颗粒-流体运动的模型必须确定哪些物理机制占主导地位，哪些可以忽略而不会产生有害影响。特别是，这些流动的传统模型将颗粒相视为具有取决于颗粒体积分数的粘度的类流体材料。这项研究计划的一个重要组成部分是研究将颗粒相模拟为摩擦材料的效果。分析将主要针对模型方程可分辨解的稳定性的研究。数值模拟将提供对方程中的非线性的理解，特别是粒子相模型的影响。这些互补的研究方法将以最近的实验为指导，这些实验强调了需要一种新的方法来解决颗粒-流体相互作用问题。颗粒和流体的联合流动有许多工业应用，如颗粒包衣和干燥、加压容器和爆竹中的颗粒流动、润滑输送和热传递。新的静电印刷和冶金技术需要非常细的粉末。然而，在这些后一种应用中，随着颗粒尺寸的减小，运输和处理变得更加困难，间隙气体的影响变得更加重要。如果没有更好的颗粒-流体流动特性，利用新技术的产品可能不会那么快上线，也不会有足够的可靠性。在这方面，值得注意的是，兰德公司的一项研究表明，由于无法准确预测粉末行为，固体生产工厂的平均表现为设计产能的63%，相比之下，液体生产工厂的平均表现为84%。该项目将研究超细粉末行为的新数学模型。该项目的结果将与工业研究人员同时进行的实验工作进行比较。

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.