Self-Propulsion by Capillary-Dominated Faraday Instabilities

了解由分离液体和气体的界面表面的振荡产生的不稳定流动是一个广泛的研究领域，具有许多实际应用，从颗粒的传输到化学品的混合。该研究项目旨在开发一个数学框架，用于理解、预测和利用由周期性界面波产生的流体流动和自发运动，特别强调在几何受限的液体-空气系统中出现的新效应，这些系统被驱动成小振幅的垂直振荡，小于几毫米。例如，研究工作将旨在解释为什么在宽通道中振荡的波在通道狭窄时开始自发转换，以及如何利用这一现象来实现新型流体泵。教育工作的目标是培养学生在现代多学科工作和研究环境中取得成功，通过指导他们掌握各种科学和软技能，重点是强大的沟通技巧和对科学可视化艺术的熟练掌握。沟通和可视化工作将通过一系列外展活动来促进STEM的多样性。当液体层遭受周期性垂直振荡时，法拉第波就会出现，最初形成一个固定的模式，随着强迫幅度的增加，开始表现出不稳定的运动。一个相对未被探索的问题是，法拉第波的混沌动力学能否被用来产生相干运动。以前试图通过空间限制来证明这种可能性的尝试很少，而且主要集中在重力主导的大型法拉第波上。在这个研究项目中，初步的实验证明了在狭窄的环形通道中，由毛细血管主导的小法拉第波存在自发的对称性破坏，导致由于半月板和接触线动力学导致的持续波动。通过理论、模拟和实验相结合，本项目的主要目标是理解和合理化这种不稳定性，并探索类似现象如何导致限制波、段塞和气泡的新的自推进动力学。该项目将研究润湿性和接触线动力学、两层结构的影响，并探索涉及复杂流动网络和流体泵的各种混合和输送应用。将特别注意阐明流的作用。将建立一个基于Floquet理论的统一理论框架来分析观测到的法拉第不稳定性。理论进展将通过内部实验和直接数值模拟进行通知和验证。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding the unsteady flows generated by the oscillations of an interfacial surface that separates a liquid from a gas is a broad research area with numerous practical applications, from the transport of particles to the mixing of chemicals. This research project aims to develop a mathematical framework for understanding, predicting, and harnessing the fluid flows and spontaneous movements produced by periodic interfacial waves, with particular emphasis on new effects that emerge in geometrically confined liquid-air systems driven into vertical oscillations at small amplitude, less than a few millimeters. For example, research efforts will aim to explain why waves that oscillate in place in a wide channel, start to translate spontaneously when the channel is narrow, and how this phenomenon can be exploited to realize a new type of fluid pump. Educational efforts will aim to train students to succeed in modern multi-disciplinary work and research environments, by coaching them in diverse scientific and soft skills, with emphasis on strong communication skills and proficiency in the art of scientific visualization. The communication and visualization efforts will be leveraged to promote diversity in STEM through a range of outreach events. Faraday waves emerge when a liquid layer is subjected to periodic vertical oscillations, initially forming a standing pattern that begins to exhibit erratic movement as the amplitude of the forcing increases. A relatively unexplored question of interest is whether the chaotic dynamics of Faraday waves can be harnessed to produce coherent motion. Previous attempts to demonstrate this possibility through spatial confinement of the waves have been scarce and primarily focused on large, gravity-dominated Faraday waves. For this research project, preliminary experiments demonstrated the existence of spontaneous symmetry-breaking in small, capillary-dominated Faraday waves confined within narrow annular channels, resulting in persistent wave motion due to meniscus and contact-line dynamics. By integrating theory, simulations, and experiments, the main objective of this project is to understand and rationalize this instability and explore how similar phenomena can lead to new self-propulsion dynamics for confined waves, slugs, and bubbles. The project will investigate the influence of wettability and contact-line dynamics, two-layer configurations, and explore a variety of mixing and transport applications involving complex flow networks and fluid pumps. Special attention will be given to elucidating the role of streaming flows. A unified theoretical framework based on Floquet theory will be developed to analyze the observed Faraday instabilities. Theoretical advancements will be informed and validated by in-house experiments and direct numerical simulations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.