Modeling and numerical simulation of yield stress fluids, and studies of viscoelasticity and confinement in the flow of two immiscible fluids

本项目致力于屈服应力流体的建模和数值模拟，以及两种非混相流体流动中的粘弹性和约束研究。大部分工作集中在以下三个主题上：(i)最近的发展已经能够详细测量一类被称为触变屈服应力流体的悬浮液的性质。一个例子是番茄酱在施加压力下的流动。先前的理论模型需要输入测量量，如屈服应力，或为微组分的结构提出一个现象学方程。相比之下，本项目探索了一种新的数学视角，其中屈服是在大松弛时间极限下系统导出的粘弹性本构模型的输出。直接数值模拟，结合基于慢速和快速时间尺度的多尺度摄动技术，将能够预测几种实验观察到的现象，例如应用应力上下倾斜的滞后回路。（ii）技术向更小尺度的发展，为液滴在与液滴本身一样小的设备中的演变带来了新的建模和仿真挑战。约束可以提高液滴延伸率，导致新的液滴破碎模式，并在本构律和界面跟踪方面引入数值困难。毛细管聚焦技术是最近发展起来的一项技术，用于生产单分散的亚微米级液滴，但尚未完全了解。该项目通过对Hele-Shaw几何模型和直接数值模拟，揭示了工作中的物理机制。（iii）将两种不同液体的所需性能结合起来生产一种新的混合液体的优点是众所周知的。混合物的质量很大程度上取决于分散液滴的大小及其分布。因此，了解液滴在基质流体中的演变过程，并预测各组分流变特性的影响，具有重要的实际意义。本项目将开发和实现一种新的粘弹性高度函数算法，并对可能具有高应力梯度的液滴破碎模拟进行优化。该项目有助于了解控制实际应用的物理机制，例如回收塑料以实现环境可持续性，预测生物医学药物输送中受限流动中的液滴和颗粒的动力学，以及了解改善制药行业纳米流体技术的基本过程。使用诸如XSEDE之类的计算基础设施将使直接数值模拟与实验数据进行比较成为可能。从这项研究中获得的知识将在数学、物理和工程会议上以及通过期刊出版物传播给更广泛的科学受众。其成果包括研究生的培训、与当地K-12学生的接触以及跨学科的合作关系。

The project is devoted to the modeling and numerical simulation of yield stress fluids, and studies of viscoelasticity and confinement in the flow of two immiscible fluids. The majority of the effort is focused on the following three themes: (i) Recent developments have enabled detailed measurements of the properties of a class of suspensions known as thixotropic yield stress fluids. An example is the flow of ketchup under applied stresses. Prior theoretical models require the input of measured quantities such as a yield stress, or to pose a phenomenological equation for the structure of the microcomponents. In contrast, a new mathematical perspective is explored in this project, in which yielding is an output of a systematically derived viscoelastic constitutive model in the limit of large relaxation time. Direct numerical simulations, in conjunction with multi-scale perturbation techniques based on slow and fast time scales, will enable the prediction of several experimentally observed phenomena, such as the hysteretic loop for up-down ramping of applied stress. (ii) The technological drive toward smaller scales has spawned new modeling and simulation challenges for droplet evolution in devices that are as small as the droplet itself. Confinement can enhance drop elongation, lead to new modes of drop breakup, and introduce numerical difficulties with respect to the constitutive laws and interface tracking. Capillary-focusing is a recently developed technology for the production of monodisperse submicron-sized droplets, which is not completely understood. This project sheds light on the physical mechanisms at work, by modeling the Hele-Shaw geometry and with direct numerical simulations. (iii) The advantages in combining the desired properties of two different liquids to produce a new blended mixture are well known. The quality of the blend is strongly dependent on the size of the dispersed droplets and their distribution. Therefore, it is of practical importance to understand how a droplet evolves in a matrix fluid, and to predict the influence of the rheological properties of each constituent. A novel viscoelastic height function algorithm will be developed and implemented in this project, and optimized for drop breakup simulations with possibly high gradients of stress. This project contributes to the understanding of physical mechanisms that control practical applications, such as recycling plastics for environmental sustainability, predicting the dynamics of droplets and particulates in confined flows for biomedical drug delivery, and understanding fundamental processes that improve nanofluidic technology for the pharmaceutical industry. The use of a computational infrastructure such as XSEDE will enable direct numerical simulations for comparison with experimental data. The knowledge gained from this research will be disseminated to a broader scientific audience at conferences on mathematics, physics and engineering, and through journal publications. The outcomes include the training of graduate students, outreach to the local K-12 audience, and cross-disciplinary partnerships.