The Effects of Fluid-Particle and Particle-Particle Interactions on the Structure and Flow Properties of Suspensions of Fibers and Disks

摘要CTS-0332902D。科赫，康奈尔大学智力优势：对结构材料和复杂流体的科学理解和工程设计的一个主要挑战是确定流体流动对非球形颗粒悬浮液结构和性能的影响。本课题将采用理论分析、计算机模拟和实验相结合的方法来研究两个问题：(A)高雷诺数层流和湍流中细长纤维的取向问题；(B)流体中颗粒-颗粒相互作用对圆盘悬浮液结构和流变性的影响。虽然对于粘性流体中纤维悬浮液中的流动诱导结构已有详细的理论模型和仔细的实验测量，但当流体惯性在纤维长度尺度上起重要作用时，对纤维的旋转知之甚少。更广泛地说，对于其尺寸相当于或大于湍流最小旋涡尺寸的颗粒-流体相互作用的正确描述构成了描述含颗粒的湍流流动的最重要的当前挑战。在所提出的项目中，将开发一种新的模拟方法，该方法将细长体描述沿纤维的力分布与Navier-Stokes方程的谱解相结合来描述湍流中的颗粒-流体相互作用，当纤维的长度与湍流中的涡旋的大小相当并且惯性影响由纤维产生的流体速度扰动时。该模型将用于预测湍流引起的纤维位置和取向的弥散以及纤维在湍流中的沉积速率。关于有限雷诺数下纤维运动的最基本问题是，纤维在中等雷诺数的简单剪切流中如何旋转。在PIS目前由NSF赞助的研究中，已经得到了分析预测，表明惯性效应导致纤维取向向简单剪切流的涡量轴漂移。这项研究包括对单根纤维在Couette池中运动的实验研究，以验证对纤维取向迁移方向和速率的预测。拟议的项目还将扩展用于研究流体介导的纤维-纤维相互作用的实验和分析方法，以了解填充有圆盘状颗粒的材料中这种相互作用的性质。微型光刻技术将被用来制作刚性圆盘的模型系统，适用于研究在一定颗粒浓度范围内牛顿流体中圆盘的流变性和流动诱导取向。这项实验研究将通过对圆盘-圆盘相互作用的理论分析来预测流体动力相互作用对圆盘悬浮液的取向、分布和流变性的影响。更广泛的影响：高纵横比纤维和圆盘通常用于增强聚合物材料的机械、热和电性能。当材料在熔融状态下加工时，这些性能对流体流动引起的结构高度敏感。目前，基于低雷诺数牛顿流体中纤维旋转和旋转扩散来描述纤维与纤维相互作用的商业软件被广泛用于预测纤维复合材料的结构。圆盘-圆盘相互作用对圆盘取向影响的实验和理论研究将为开发云母片和硅粘土颗粒等片状颗粒填充的聚合物材料中流动诱导结构的工程模型提供第一步。在造纸过程中，悬浮在水中的纸浆纤维流到多孔传送带上，形成纤维网络。人们希望使用湍流将纤维均匀分散在各向同性取向的空间中。在这些流动中，基于纤维长度的雷诺数为O(10)。该项目开发的模拟方法将首次对纤维在这些条件下的运动进行严格描述。该项目将培训一名博士生和本科生研究人员，使他们能够将分析方法与计算机模拟相结合，并通过实验验证他们的模型。

AbstractCTS-0332902D. Koch, Cornell UniversityIntellectual Merit: A major challenge for the scientific understanding and engineering design of structured materials and complex fluids is to determine the effects of fluid flow on the structure and properties of non-spherical-particle suspensions. A balanced approach of analytical theory, computer simulation and experiment will be applied to two problems on the forefront of this topic: (a) The orientation of slender fibers in high Reynolds number laminar and turbulent flows; and (b) The effects of fluid-mediated particle-particle interactions on the structure and rheology of suspensions of disks. While detailed theoretical models and careful experimental measurements are available for the flow-induced structure in fiber suspensions in viscous fluids, relatively little is known about the rotation of fibers when fluid inertia is important on the fibers length scale. More generally, the proper description of particle-fluid interactions for particles whose size is comparable to or larger than the size of the smallest eddies of a turbulent flow constitutes the most important current challenge in the description of particle-laden turbulent flows. In the proposed project, a novel simulation method will be developed that couples a slender-body description of the force distribution along a fiber with a spectral solution of the Navier-Stokes equations to describe particle-fluid interactions in a turbulent flow when the fiber length is comparable with the size of the eddies of the turbulent flow and inertia influences the fluid velocity disturbances produced by the fiber. This model will be applied to predict the turbulence-induced dispersion of fiber positions and orientations and the rate of sedimentation of fibers in turbulent flows. The most basic question concerning the motion of fibers at finite Reynolds number is how a fiber will rotate in a moderate Reynolds number simple shear flow. In the PIs current NSF sponsored research, analytical predictions have been obtained indicating that inertial effects cause a fibers orientation to drift toward the vorticity axis of a simple shear flow. The proposed study includes an experimental investigation of the motion of single fibers in a Couette cell to validate the predictions for the direction and rate of migration of fiber orientation. The proposed project will also extend the experimental and analytical approaches used to study fluid-mediated fiber-fiber interactions to understand the nature of such interactions in materials filled with disk-shaped particles. Microlithography methods will be used to produce model systems of rigid disks suitable for studies of the rheology and flow-induced orientation of disks in Newtonian fluids over a range of particle concentrations. This experimental study will be complemented by a theoretical analysis of disk-disk interactions to predict the effects of hydrodynamic interactions on the orientation distribution and rheology of the disk suspensions. Broader Impacts: High-aspect ratio fibers and disks are commonly used to enhance the mechanical, thermal and electrical properties of polymeric materials. These properties are highly sensitive to the structure induced by fluid flow when the materials are processed in the molten state. At the present time, commercial software based on the rotation of fibers in a low Reynolds number Newtonian fluid with a rotary diffusion to describe fiber-fiber interactions is widely used to predict structure in fiber composites. The experimental and theoretical studies of the effects of disk-disk interactions on disk orientation will provide the first step toward developing engineering models for the flow-induced structure in polymeric materials filled with platelet shaped particles such as mica flakes and silica clay particles. During the production of paper, pulp fibers suspended in water flow onto a porous conveyer belt to form a fiber network. It is desirable to use a turbulent fluid flow to disperse the fibers uniformly in space with isotropic orientations. In these flows, the Reynolds number based on the fiber length is O (10). The simulation method developed in this project will provide the first rigorous description of fiber motion under these conditions. The project will train a doctoral student and undergraduate researchers with the ability to interface analytical approaches with computer simulation and validate their models experimentally.