Sphere-Sphere and Sphere-Surface Interactions in Viscoelastic Fluids

0851552 r。悬浮在非牛顿流体中的粒子如何相互作用以及如何与附近的表面相互作用，这一重要问题与涉及牛顿流体的类似问题相比，仍然相对未被研究。聚合物溶液和熔体中的微粒之间的这些相互作用会导致聚集、链化和向流动壁移动或远离流动壁。即使是这样一些看似简单的问题，比如沿着中心线沉积的两个球体是会一起移动形成双线，还是会分开，也没有答案。同样，关于垂直于（即朝向或远离）平面的球体的下落率的有限的已发表的实验数据与理论预测在质量上不一致。这两个问题，即两个球体的轴对称沉降和一个球体垂直于平面的运动，在复合材料的加工、支撑剂颗粒在采油中的使用以及“片上实验室”微电子器件的应用等应用中具有重要的实际意义。它们也是基础研究的理想候选者，因为它们的轴对称几何形状使它们既可以进行实验测量，也可以进行数值计算。在本研究中，粒子图像测速（PIV）将用于测量两个沉积球周围平面区域的速度场，以及向界面法向运动的球。粒子速度也将通过电荷耦合器件（CCD）相机直接测量。实验将在具有可忽略剪切稀化的弹性聚合物溶液（即Boger流体）、具有强剪切稀化但具有非常弱弹性的溶液以及同时具有强弹性和剪切稀化的溶液中进行。球形粒子的大小和密度将使德博拉数是有序的，但雷诺兹和斯托克斯数将是小的，隔离非牛顿流变相对于惯性的影响。围绕球形颗粒的粘弹性流动的数值计算将通过一种方法来执行，该方法考虑了本构方程的双曲性质和动量守恒方程的椭圆性质。所提出的方法能够解决应力边界层和严重的聚合物拉伸区域，存在于粘弹性流动的颗粒在有限的黛博拉数。初步计算表明，在具有强弹性和剪切变薄的流动中，会形成负尾迹，或流体向与沉积球相反方向运动的区域。负尾流的形成与PIV对两球沉降的实验测量结果在定性上是一致的。智力上的优点：提议的工作包括在最简单的几何中精心挑选的实验，这些实验仍然与几乎所有非牛顿悬浮液的流动有关。这些实验将涉及速度剖面的定量测量，可以与我们小组和其他人所做的计算进行定量比较。参与的学生将获得对实验和计算工作的欣赏，以及在处理复杂材料时在这两种研究途径之间建立密切联系的重要性。更广泛的影响这项研究将为研究生和本科生提供一个极好的教育机会。它在许多领域都有广泛的应用，包括开发新的复合材料和纳米复合材料，提高石油采收率，设计新的“芯片实验室”微设备。本科学生将从代表性不足的群体中招募，以帮助进行研究并创建用于课堂教学的教学材料

0851552R. PhillipsThe important problem of how particles suspended in non-Newtonian fluids interact with each other and with nearby surfaces remains relatively unstudied in comparison with similar problems involving Newtonian fluids. These interactions between particulates in polymer solutions and melts can result in aggregation, chaining, and movement toward or away from the walls bounding a flow. Even such seemingly simple questions such as whether two spheres sedimenting along their line-of-centers will move together to form a doublet, or move apart, remain unanswered. Similarly, the limited published experimental data on the rate of fall of a sphere perpendicular to (i.e., toward or away from) a flat surface disagrees qualitatively with theoretical predictions. These two problems, the axisymmetric sedimentation of two spheres and the movement of a sphere normal to a planar surface, are of practical importance in applications such as the processing of composite materials, the use of proppant particles in oil recovery, and the application of "lab-on-a-chip" microelectronic devices. They are also ideal candidates for fundamental research, because their axisymmetric geometry makes them accessible to both experimental measurement and numerical calculations. In the proposed research, particle image velocimetry (PIV) will be used to measure velocity fields in planar regions around two sedimenting spheres and spheres moving normal to interfaces. Particle velocities will also be measured directly, by using charge couple device (CCD) cameras. Experiments will be performed in polymer solutions that exhibit elasticity with negligible shear thinning (i.e., Boger fluids), solutions that are strongly shear thinning but exhibit very weak elasticity, and solutions that are both strongly elastic and shear thinning. The sizes and densities of the spherical particles will be such that the Deborah numbers are of order unity, but the Reynolds and Stokes numbers will be small, isolating the effects of the non-Newtonian rheology relative to inertia. Numerical calculations of viscoelastic flow around spherical particles will be performed by an approach that accounts for the hyperbolic nature of the constitutive equations and the elliptic nature of the momentum conservation equations. The proposed methods are capable of resolving the stress boundary layers and regions of severe polymer stretching that are present in viscoelastic flow around particles at finite Deborah numbers. Preliminary calculations show the formation of a negative wake, or region where the fluid moves in the direction opposite to that a sedimenting sphere, in flows with strong elasticity as well as shear thinning. The formation of a negative wake is qualitative agreement with experimental measurements of two-sphere sedimentation performed by PIV.Intellectual MeritThe proposed work consists of carefully chosen experiments in the simplest possible geometries that are still relevant to nearly all flows of non-Newtonian suspensions. These experiments will involve quantitative measurements of velocity profiles that can be compared quantitatively to calculations done by our group and by others. The students involved will gain an appreciation for both experimental and computational work, as well as the importance of establishing a close connection between these two avenues of research when dealing with complicated materials.Broader ImpactThis research will provide an excellent educational opportunity for graduate and undergraduate students. It has applications in a wide range of areas, including developing new composite and nanocomposite materials, improving oil recovery, and designing new "lab-on-a-chip" microdevices. Undergraduate students will be recruited from underrepresented groups, both to help with the research and to create instructional materials to be used in classroom teaching