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

屈服应力流体的建模和数值模拟，以及两种不混溶流体流动中的粘弹性和约束研究

基本信息

批准号：
1311707
负责人：
Yuriko Renardy
金额：
$ 19.28万
依托单位：
Virginia Polytechnic Institute and State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2013
资助国家：
美国
起止时间：
2013-08-15 至 2017-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311707&HistoricalAwards=false
关键词：
Modeling numerical simulation yield stress

项目摘要

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.

该项目致力于屈服应力流体的建模和数值模拟，以及两种不相容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)最近的发展使对一类被称为触变屈服应力流体的悬浮液的性质进行了详细的测量。一个例子是在外加压力下番茄酱的流动。以前的理论模型需要输入测量的量，如屈服应力，或者为微部件的结构提出唯象方程。相反，该项目探索了一种新的数学观点，即屈服是在大松弛时间限制下系统推导的粘弹性本构模型的输出。直接的数值模拟与基于慢和快时间尺度的多尺度摄动技术相结合，将能够预测几个实验观察到的现象，例如外加应力的上下倾斜的滞后环。(Ii)向更小规模发展的技术驱动，为小到液滴本身的设备中的液滴演变带来了新的建模和模拟挑战。约束可以提高液滴延伸率，导致液滴破碎的新模式，并在本构关系和界面跟踪方面引入数值困难。毛细管聚焦是最近发展起来的一种用于生产单分散亚微米级液滴的技术，目前还不完全了解。这个项目通过对Hele-Shaw几何模型的建模和直接的数值模拟，阐明了工作中的物理机制。(3)将两种不同液体的预期性质结合起来生产一种新的混合混合物的优点是众所周知的。共混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化过程，并预测各组分的流变性对液滴的影响具有重要的现实意义。本项目将开发和实现一种新的粘弹性高度函数算法，并针对可能存在高应力梯度的液滴破碎模拟进行优化。该项目有助于理解控制实际应用的物理机制，如回收塑料以实现环境可持续性，预测用于生物医学药物输送的受限流动中的液滴和颗粒的动态，以及了解为制药行业改进纳米流体技术的基本过程。XSEDE等计算基础设施的使用将使直接数值模拟能够与实验数据进行比较。从这项研究中获得的知识将在有关数学、物理和工程的会议上以及通过期刊出版物向更广泛的科学受众传播。其成果包括对研究生的培训，与当地K-12受众的接触，以及跨学科伙伴关系。