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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。大部分工作集中在以下三个主题：（i）最近的发展已经能够对称为触变屈服应力流体的一类悬浮液的特性进行详细测量。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（例如屈服应力），或者提出微元件结构的唯象方程。相比之下，该项目探索了一种新的数学视角，其中屈服是在大松弛时间限制下系统导出的粘弹性本构模型的输出。直接数值模拟与基于慢速和快速时间尺度的多尺度扰动技术相结合，将能够预测几种实验观察到的现象，例如施加应力上下斜坡的磁滞回线。 (ii) 向更小尺度发展的技术驱动力为与液滴本身一样小的设备中的液滴演化带来了新的建模和模拟挑战。限制可以增强液滴伸长，导致液滴破裂的新模式，并引入本构定律和界面跟踪方面的数值困难。毛细管聚焦是一项最近开发的用于生产单分散亚微米级液滴的技术，但目前尚未完全了解。该项目通过 Hele-Shaw 几何模型建模和直接数值模拟，揭示了工作中的物理机制。 (iii) 结合两种不同液体的所需特性以产生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尺寸及其分布。因此，了解液滴在基质流体中如何演化并预测每种成分的流变特性的影响具有实际意义。该项目将开发和实施一种新颖的粘弹性高度函数算法，并针对可能具有高应力梯度的液滴破裂模拟进行优化。该项目有助于理解控制实际应用的物理机制，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的受限流中液滴和颗粒的动态，以及了解改进制药行业纳米流体技术的基本过程。使用 XSEDE 等计算基础设施将能够直接进行数值模拟，以便与实验数据进行比较。从这项研究中获得的知识将通过数学、物理和工程会议以及期刊出版物传播给更广泛的科学受众。成果包括研究生培训、当地 K-12 受众的推广以及跨学科合作。