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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，以及两种不混溶流体流动中的粘弹性和约束研究。大部分的努力集中在以下三个主题：（i）最近的发展已经能够详细测量一类悬浮液的特性，称为触变屈服应力流体。一个例子是番茄酱在施加应力下的流动。先前的理论模型需要输入测量的量，如屈服应力，或对微元件的结构提出一个唯象方程。与此相反，一个新的数学视角，探索在这个项目中，屈服是一个系统推导的粘弹性本构模型在大松弛时间的限制输出。直接数值模拟，结合多尺度扰动技术的基础上慢和快的时间尺度，将能够预测几个实验观察到的现象，如滞后环的上下斜坡施加的应力。(ii)朝向更小尺度的技术驱动已经为与液滴本身一样小的设备中的液滴演变产生了新的建模和模拟挑战。限制可以提高液滴的伸长率，导致新的模式的液滴破碎，并介绍了数值计算的困难方面的本构关系和界面跟踪。毛细管聚焦是最近发展起来的用于生产单分散亚微米尺寸液滴的技术，其尚未完全理解。该项目揭示了工作中的物理机制，通过建模的Hele-Shaw几何和直接数值模拟。(iii)将两种不同液体的所需性质组合以产生新的共混混合物的优点是众所周知的。共混物的质量在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，预测各组分流变特性对液滴流变特性的影响，具有重要的实际意义。一种新的粘弹性高度函数算法将在本项目中开发和实现，并优化可能具有高应力梯度的液滴破碎模拟。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发展，预测生物医学药物输送的受限流中液滴和颗粒的动态，以及了解改善制药行业纳米流体技术的基本过程。使用计算基础设施，如XSEDE将使直接数值模拟与实验数据进行比较。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，推广到当地的K-12观众，和跨学科的伙伴关系。