Nonlinear Droplet Electrohydrodynamics in Stokes Flow Regime

1132614 vlahovska电场提供了一种控制小尺度流体和粒子运动的通用手段。PI小组最近的实验发现了不寻常的液滴行为，如翻滚、振荡和混沌动力学，以响应均匀的直流电场。提出的研究的动机是：(1)在蠕动流动条件下发生的这些新的非线性现象的科学兴趣；(2)在微流体和电流变材料相关技术中利用它们的应用兴趣。本文的目的是揭示界面变形和电荷引起非线性液滴电流体动力学的机制。为此，PI将整合(1)动力系统理论来分析小变形状态下的液滴行为和向混沌的过渡；(2)基于边界积分法的数值模拟，探索大液滴变形和液滴集体动力学；(3)实验对理论分析和计算进行指导和检验。智力优势：理论、计算和实验的结合将提供对乳剂液滴电变形和电流流变学的全面理解。这些都是流体力学、动力系统和软凝聚态物质交叉的具有挑战性和未探索的问题。该提议的潜在变革性质在于确定了尚未解释的物理现象，这些物理现象可能产生与微尺度流动和复杂流体相关的新应用。这项工作可以成为混沌非线性动力学的一个典型的物理例子。更广泛的影响：本提案的研究成果与许多涉及电场中分散两相系统的自然和工业过程有关，包括雷雨中雨滴的破裂，喷墨印刷，电流体动力雾化，以及石油炼制过程中乳化水与石油的分离。更具体地说，这项研究将有助于推进微流体等工程应用，在微流体中，混沌粒子动力学可以用于原位微混合。该项目融合了物理、应用数学和工程方法，因此为博士生和本科生提供了良好的训练基地。通过理论与实验的协同作用，该项目将激发更倾向于实验的学生对理论的兴趣，反过来，激发更专注于理论的学生对激发数学模型的实验的好奇心。该项目将利用布朗大学成熟且成功的外展项目，吸引在科学和工程领域未被充分代表的少数族裔。科学和技术方面的研究和有关进展将通过在会议、讲习班和暑期学校的发言广泛传播。液滴振荡、翻滚和破裂是视觉上吸引人的效果，自然会激发普通公众和科学和工程观众的兴趣。

1132614VlahovskaElectric fields provide a versatile means to control small-scale fluid and particle motion. Recent experiments in the PI's group have discovered unusual droplet behavior such as tumbling, oscillations and chaotic dynamics in response to uniform DC electric fields. The proposed research is motivated by (1) the scientific intrigue of these new nonlinear phenomena occurring under creeping flow conditions and (2) applied interest to exploit them in technologies related to microfluidics and electrorheological materials. The objective of this proposal is to uncover the mechanisms by which interface deformation and charging give rise to nonlinear droplet electrohydrodynamics. To this end, the PI will integrate (1) dynamical systems theory to analyze drop behavior in the small-deformation regime and the transition to chaos; (2) numerical simulations based on the Boundary Integral Method to explore large drop deformations and the collective dynamics of drops; and (3) experiments to guide and test the theoretical analyses and computations.Intellectual merit: The proposed combination of theory, computation and experiment will provide a comprehensive understanding of droplet electrodeformation and electrorheology of emulsions. These are challenging and unexplored problems at the intersection of fluid mechanics, dynamical systems, and soft condensed matter. The potentially transformative nature of the proposal lies in identifying yet unexplained physics that could yield new applications related to microscale flows and complex fluids. The work could become a prototypical physical example of chaotic nonlinear dynamics.Broader impacts: The research outcomes of this proposal are relevant to many natural and industrial processes involving disperse two-phase systems in electric fields, including the break-up of rain droplets in thunderstorms, ink-jet printing, electrohydrodynamic atomization, and separation of emulsified water from oil in the petroleum refining process. More specifically, the research will help advance engineering applications such as microfluidics, where the chaotic particle dynamics can be utilized for in-situ micro-mixing. The project blends physics, applied math, and engineering approaches and thus provides excellent training ground for doctoral and undergraduate students. By means of the synergy between theory and experiment, the project will excite the more experimentally inclined students about theory, and conversely, inspire curiosity in the students who are more focused on theory about the experiments that motivate the mathematical models. The PI will leverage well-established and successful outreach programs at Brown University to attract underrepresented minorities in science and engineering. The research and related advances in science and technology will be broadly disseminated by presentations at meetings, workshops and summer schools. Droplets oscillations, tumbling, and break up are visually appealing effects that naturally excite both general public and science and engineering audiences.