Multidimensional Problems in Granular Plasticity

这个跨学科的提案解决了关于颗粒材料与间隙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。粒子流体运动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不利影响。特别是，这些流动的传统模型将颗粒相视为具有粘度取决于颗粒体积分数的流体状物质。本研究计划的一个重要组成部分是研究作为摩擦材料的颗粒相建模的影响。分析将主要针对模型方程微分解的稳定性研究。数值模拟将提供对非线性方程的理解，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，这些实验强调需要一种新的方法来解决粒子-流体相互作用的问题。颗粒和流体的组合流动有许多工业应用，如颗粒涂层和干燥，压力容器和裂解器中的颗粒流动，润滑输送和传热。新的静电照相和冶金技术需要非常精细的粉末。然而，在后一种应用中，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很快上线，也不会有足够的可靠性。在这方面，值得注意的是，兰德公司（Rand Corporation）的一项研究表明，由于无法准确预测粉末的行为，生产固体的制造工厂的平均产能利用率为63%，而生产液体的工厂的平均产能利用率为84%。该项目将研究非常细粉末行为的新数学模型。这个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.