Sphere-Sphere and Sphere-Surface Interactions in Viscoelastic Fluids

0851552R。与涉及牛顿流体的类似问题相比，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仍然是相对未被研究的。聚合物溶液和熔体中的颗粒之间的这些相互作用可能导致聚集、链接以及朝向或远离流动边界的壁面移动。即使是这样看似简单的问题，比如沿其中心线沉积的两个球体是会一起运动形成一个二重体，还是会分开运动，仍然没有答案。同样，有限发表的关于垂直于平面(即朝向或远离平面)的球体下落速度的实验数据与理论预测定性地不一致。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，在复合材料加工、支撑剂颗粒在石油开采中的使用以及微电子器件的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结构使它们既可以进行实验测量，也可以进行数值计算。在拟议的研究中，将使用粒子图像测速仪(PIV)测量两个沉降球和垂直于界面运动的球体周围平面区域的速度场。粒子速度也将通过使用电荷耦合器件(CCD)相机直接测量。实验将在具有可忽略剪切变稀的弹性的聚合物溶液中进行(即，Boger流体)，具有强烈剪切变稀但表现出非常弱弹性的溶液，以及同时具有强弹性和剪切变稀的溶液。球形粒子的大小和密度将使Deborah数具有数量级单位，但雷诺数和斯托克斯数将很小，从而隔离了相对于惯性的非牛顿流变学的影响。对球形颗粒粘弹性流动的数值计算将采用一种考虑本构方程的双曲性和动量守恒方程的椭圆性的方法。所提出的方法能够解决在有限Deborah数的颗粒周围的粘弹性流动中存在的应力边界层和严重聚合物拉伸区域。初步计算表明，在具有强烈弹性和剪切变稀的流动中，形成了负尾迹，即流体沿与沉降球相反的方向运动的区域。负尾迹的形成与PIV进行的两个球体沉积的实验测量在质量上是一致的。智慧价值拟议的工作包括在最简单的几何形状中精心选择的实验，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分布的定量测量，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个研究领域建立密切联系的重要性。它在广泛的领域中都有应用，包括开发新的复合材料和纳米复合材料，提高石油采收率，以及设计新的“芯片实验室”微器件。本科生将从代表性不足的群体中招募，以帮助研究和制作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