NSF Award
2321357
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.<br/> <br/>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.<br/><br/>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.
