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

摘要本课题的目的是建立流体中粒子取向的闭合模型。模型预测的低阶统计性质，特征的微观结构的悬浮液，往往是基于一个矩方程的粒子取向二进（二阶矩）。该方程的解需要一个与粒子/流体相互作用相关的粒子方向四阶矩（四阶矩）的闭包模型。这项理论工作将解决一个新的闭包理论的方向四分体，保留六重对称性和六重投影性质的确切方向四分体。本基础研究将集中于寻找高阶张量在低阶张量方面的闭包近似。通过将二阶矩预测与由对流扩散型方程控制的粒子取向分布函数得到的二阶矩的精确行为进行比较，将对一类简单流动（剪切和拉伸）的粒子/流体相互作用的新表示进行验证。在这一领域，对表现出微观结构的材料的性能测定又产生了新的兴趣。标准的工业流模拟器现在包含了粒子方向的张量描述，这项研究可能有助于使这些模拟更准确和有效。

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.