Computational study of drop deformation in systems with two immiscible liquids

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该项目致力于开发和实施新的算法，用于分离两种不混溶液体的界面的变形和破裂的建模和计算研究。大部分的努力是集中在以下四个主题：（一）微分本构模型粘弹性液体，如Giesekus模型将被用来研究液滴悬浮在基质液体和变形的简单剪切，停止剪切，和大应变跳。(ii)微尺度装置的最新发展已经为与液滴本身一样小的物理装置中的液滴演变产生了新的建模和模拟挑战。该项目将研究壁关闭对粘弹性系统的影响，实验发现了新的破碎场景。(iii)将研究液-液-固系统中接触线的运动。相场公式和流体体积高度函数方法的组合将被追求。前者更适合于解决接触线的物理问题，但对于整个流场的使用来说，资源过于密集。接触线问题的一个挑战是如何获得网格独立的结果。最近的工作表明存在一个“主曲线”，它可以用来确定一个网格依赖的“强加”的接触角作为所需的“宏观”接触角的函数。一个具体的计算应用是电润湿，这可能是用于液滴致动的最广泛使用的技术，因为较低的功耗，并且因为施加的电压移动液滴而不需要泵和阀。在这方面，将研究流体动力学和麦克斯韦方程耦合系统的移动接触线。(iv)磁性药物靶向涉及使用铁磁流体液滴作为药物载体，其被引导通过生物组织到达特定位置。可行性的一个重要量是渡越时间。 对非均匀磁场下磁性流体液滴在粘性介质中的运动进行了直接数值模拟。该项目包括指导一名博士后研究助理和培训研究生。研究结果将在有关数学、物理和工程的国家和国际会议上以及通过期刊出版物传播。跨学科和国际合作伙伴关系将与获得实验数据的科学家进行比较，并与数值结果进行比较。将两种不同液体的所需特性相结合以产生新的混合物的优势是众所周知的。共混物的质量在很大程度上取决于其微观结构，例如分散液滴的大小及其在最终产品中的分布。因此，了解液滴如何在周围液体中演变并预测这如何受到每种组成流体的流变特性的影响具有实际重要性。这将通过使用内部最先进的并行化算法进行直接数值模拟来实现，这些算法针对可扩展性和计算成本进行了优化。该项目的主题有助于理解在回收塑料，环境可持续性，生物医学药物输送和微流体设备中的液滴操作中出现的复杂多尺度系统。密集使用计算基础设施，如TeraGrid，将允许数学模型与原始实验数据进行定量比较。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The project is devoted to development and implementation of new algorithms for the modeling and computational investigation of deformation and breakup of interfaces that separate two immiscible liquids. The majority of the effort is focused on the following four themes: (i) Differential constitutive models for viscoelastic liquids such as the Giesekus model will be used to study drops suspended in a matrix liquid and deformed by simple shear, cessation of shear, and large strain jumps. (ii) The recent development of microscale apparatuses has spawned new modeling and simulation challenges for droplet evolution in physical devices that are as small as the droplet itself. The project will investigate the effect of walls closing in on viscoelastic systems, for which novel breakup scenarios have been discovered experimentally. (iii) The motion of contact lines in liquid-liquid-solid systems will be investigated. A combination of the phase-field formulation and the volume-of-fluid height function method will be pursued. The former is more suited for resolving the physics of the contact line, but too resource intensive for use in the entire flow field. A challenge in contact line problems is how to obtain mesh independent results. Recent work has suggested the existence of a 'master curve' which can be used to determine a mesh dependent 'imposed' contact angle as a function of the desired 'macroscopic' contact angle. A specific computational application is electrowetting, which is perhaps the most widely used technique for drop actuation because of lower power consumption and because an applied voltage moves the drop without the need for pumps and valves. In this context, moving contact lines for the coupled system of hydrodynamic and Maxwell equations will be studied. (iv) Magnetic drug targeting involves using a ferrofluid drop as a drug carrier, which is guided through biological tissue to a specific location. An important quantity for feasibility is the transit time. Direct numerical simulations will be carried out for the motion of ferrofluid drops in viscous media under non-uniform magnetic fields. This project involves the mentoring of a postdoctoral research associate and the training of graduate students. Results will be disseminated at national and international conferences on mathematics, physics and engineering, and through journal publications. Cross-disciplinary and international partnerships will take place with scientists who obtain experimental data for comparison with numerical results.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 its microstructure, such as the size of the dispersed droplets and their distribution in the final product. Therefore, it is of practical importance to understand how a droplet evolves in the surrounding liquid and to predict how this is influenced by the rheological properties of each constituent fluid. This will be accomplished by performing direct numerical simulations with in-house state-of-the-art parallelized algorithms that are optimized for scalability and computational cost. The topics in this project contribute to the understanding of complex multi-scale systems that arise in recycling plastics, environmental sustainability, biomedical drug delivery, and droplet manipulation in microfluidic devices. Intensive use of computational infrastructures such as the TeraGrid will allow for quantitative comparison of mathematical models with raw experimental data.