Flow-Induced Alignment of Dispersed Particles: Closure Model for Particle-Fluid Interactions

摘要本项目的目标是开发流体中颗粒取向的闭合模型。对悬浮液微观结构特征的低阶统计性质的模型预测，通常基于粒子取向并矢矩(二阶矩)的矩方程。这个方程的解需要一个与颗粒/流体相互作用有关的颗粒取向四边形(四阶矩)的封闭模型。这项理论工作将提出一种新的取向四边形的闭合理论，它保留了精确取向四边形的六重对称性和六重投影性质。这项基础性研究将集中于寻找高阶张量的闭包近似和低阶张量。对于一类简单的流动(剪切和拉伸)，颗粒/流体相互作用的新表示将通过比较二阶矩的预测和由对流-扩散型方程控制的颗粒取向分布函数得到的二阶矩的精确行为来验证。对于表现出微结构的材料的性能测定，该领域重新引起了人们的兴趣。标准的工业流动模拟器现在结合了颗粒取向的张量描述，这项研究可能有助于使这些模拟更准确和高效。

AbstractThe objective of this project is to develop a closure model for the orientation of particles in a fluid. Model predictions of low-order statistical properties, characteristic of the microstructure of suspensions, are often based on a moment equation for the particle orientation dyadic (second-order moment). The solution to this equation requires a closure model for the particle orientation tetradic (fourth-order moment) associated with particle/fluid interactions. This theoretical work will address a new closure theory for the orientation tetradic that retains the six-fold symmetry and the six-fold projection properties of the exact orientation tetradic. This fundamental research will focus on finding closure approximations of higher order tensors in terms of lower order tensors. The new representation for particle/fluid interactions will be validated for a class of simple flows (shear and extensional) by comparing second-order moment predictions with the exact behavior of the second-order moment derived from the particle orientation distribution function governed by a convective-diffusive type equation. There has been renewed interest in this field for property determination of materials that exhibit a microstructure. Standard industrial flow simulators now incorporate tensor descriptions of particle orientations, and this research may be useful in making those simulations more accurate and efficient.