The Effect of Particle-polymer Interactions on the Rheology and Structure of Dilute Particle-filled Polymeric Liquids

聚合物分子和悬浮固体颗粒的溶液用于从油漆和涂料到医疗保健和食品的一系列产品。聚合物分子和悬浮颗粒协同作用，产生一系列复杂的流体行为，影响它们的加工。虽然人们对颗粒和聚合物如何独立作用来改变流体反应了解甚多，但对它们的耦合效应知之甚少。该项目将发展理论来预测1)由颗粒引起的流动干扰引起的聚合物分子的拉伸和排列，2)在聚合物存在下拉长的固体颗粒或纤维如何排列，以及3)颗粒和聚合物混合物的流动响应。流速，流动历史和流动几何对聚合物-颗粒混合物行为的影响将被检查。作为这项研究的一部分，一名研究生和几名本科生将接受流体动力学、理论和数值方法方面的培训。首席研究员和研究生都将参与指导一名来自STEM领域代表性不足群体的本科生。粒子和聚合物应力的相互作用将在稳定剪切、振荡剪切和聚合物溶液中球和纤维悬浮液的拉伸流变学中进行探讨。颗粒的水动力扰动会显著改变周围流体中的聚合物构象，而聚合物应力会导致颗粒应力的意外变化。纤维悬浮液的流变性受到纤维取向的强烈影响。虽然先前的理论研究表明，聚合物应力诱导纤维沿稳定的简单剪切流的涡度轴排列，但实验表明，即使在低颗粒浓度下，取向的多样性也更大。本文将探讨纤维在简单剪切流中的稳定固定取向，以及取向与流体流变特性的关系。稀颗粒填充聚合物液体的流变性将用系综平均方程方法来确定。为了方便准解析结果，将进行基于小聚合物浓度的微扰分析。与先前考虑二阶流体的研究相比，这种方法可以在考虑弱聚合物应力的情况下探索流变学的应变速率（或Deborah数）依赖性。在拟体坐标系中采用有限体积法进行完全非线性计算，将对简单剪切流中纤维取向的理论研究起到补充作用。包括和排除剪切变薄和有限可扩展性在内的各种流变模型将用于理解不同聚合物流变特性对颗粒-聚合物相互作用的影响。为了扩大该领域未来研究生的多样性，项目负责人和研究生将为来自另一所大学的潜在女性或URM学生的整个本科生涯提供持续的指导，并提供复杂流体的本科研究项目。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Solutions of polymer molecules and suspended solid particles are used in a range of products from paints and coatings to health care and foods. The polymer molecules and the suspended particles act cooperatively to create a range of complex fluid behaviors that impact their processing. While much is known about how particles and polymers act independently to alter fluid responses, little is known about their coupled effects. This project will develop theories to predict 1) the stretching and alignment of polymer molecules by the disturbance to the flow caused by the particles, 2) how elongated solid particles or fibers align in the presence of polymers, and 3) the flow response of mixtures of particles and polymers. The influence of flow rate, flow history, and flow geometry on the behavior of polymer-particle mixtures will be examined. As part of this research, a graduate student and several undergraduates will receive training in fluid dynamics and theoretical and numerical methods. Both the principal investigator and the graduate student will participate in mentoring an undergraduate student from a group that is underrepresented in STEM fields.The interplay of particle and polymer stresses will be explored in steady shear, oscillatory shear, and extensional rheology of suspensions of spheres and fibers in polymer solutions. The hydrodynamic disturbance of the particles can dramatically alter the polymer conformation in the surrounding fluid while the polymer stress can lead to unexpected changes in the particle stresslet. The rheology of fiber suspensions is strongly influenced by the orientations of the fibers. While previous theoretical studies have suggested that polymer stresses induce fiber alignment with the vorticity axis of a steady simple shear flow, experiments reveal a greater diversity of orientations even at low particle concentrations. A search will be made for stable fixed orientations of fibers in simple shear flow and the dependence of the orientations on the rheological properties of the fluid. The rheology of dilute particle-filled polymeric liquids will be determined using an ensemble averaged equation approach. To facilitate quasi-analytic results, perturbation analyses based on small polymer concentration will be performed. In contrast to previous studies that considered second-order fluids, this approach allows an exploration of the strain rate (or Deborah number) dependence of the rheology even while considering weak polymeric stresses. Fully nonlinear computations using a finite volume method in a body-fitted coordinate system will complement the theoretical studies of fiber orientation in simple shear flow. A variety of rheological models that include and exclude shear thinning and finite extensibility will be used to understand the effect that different polymer rheological properties have on particle-polymer interactions. To broaden the diversity of future graduate students in the field, the PI and graduate student on the project will provide on-going mentorship throughout the undergraduate career of a prospective female or URM student from another university as well as offering undergraduate research projects on complex fluids.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.