Nonlinear Droplet Electrohydrodynamics in Stokes Flow Regime

1132614 Vlahovska电场提供了一种控制小规模流体和粒子运动的通用方法。PI小组最近的实验发现了不寻常的液滴行为，如翻滚，振荡和混沌动力学响应均匀直流电场。提出的研究的动机是（1）蠕动流动条件下发生的这些新的非线性现象的科学阴谋和（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。这个建议的目的是揭示机制，界面变形和充电引起的非线性液滴电流体动力学。为此，PI将整合（1）动力系统理论，以分析小变形状态下的液滴行为和向混沌的过渡;（2）基于边界积分方法的数值模拟，以探索大液滴变形和液滴的集体动力学;（3）实验，以指导和测试理论分析和计算。理论，计算和实验的结合将提供一个全面的理解液滴电变形和电流变性的乳液。这些都是在流体力学，动力系统和软凝聚态的交叉点具有挑战性和未探索的问题。该提案的潜在变革性质在于确定尚未解释的物理学，这些物理学可能产生与微尺度流动和复杂流体相关的新应用。更广泛的影响：这项建议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，包括雷暴中雨滴的破碎、喷墨打印、电流体动力雾化和石油精炼过程中乳化水与油的分离。更具体地说，这项研究将有助于推进微流体等工程应用，其中混沌粒子动力学可用于原位微混合。 该项目融合了物理学，应用数学和工程方法，从而为博士生和本科生提供了良好的培训基础。通过理论和实验之间的协同作用，该项目将激发更多的实验倾向的学生对理论的兴趣，反过来，激发好奇心的学生谁是更专注于理论的实验，激发数学模型。PI将利用布朗大学成熟和成功的外展计划，吸引科学和工程领域代表性不足的少数民族。将通过在会议、讲习班和暑期班上的介绍，广泛传播科学和技术方面的研究和有关进展。液滴振荡、翻滚和破碎是视觉上吸引人的效果，自然会让普通公众和科学与工程观众兴奋不已。

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.