CAREER: An integrated study of wave-particle interaction on liquid interfaces

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This CAREER project will investigate how millimeter-size particles move and interact on the surface of a vibrating fluid. Understanding the interplay between small particles and liquid surfaces is a broad area of research with many applications, including the transport and removal of floating litter and aerosol generation from rain drops merging with the sea surface. Most of the studies available in the literature focus on situations involving either a single particle impacting on a liquid surface or multiple floating particles. However, an interesting regime, which has received much less attention, emerges when the underlying liquid bath is vibrated vertically. In this case, small droplets may bounce and even “walk” along the liquid interface as they interact with surface waves caused by rebounds. The goal of this project is to demonstrate new dynamics that characterize this intermediate regime. The investigators will combine experiments and theory to study new bouncing and walking modes, behaviors of groups of interacting particles, and new transport effects emerging from the interaction between bouncing particles and submerged features. This project will provide new multidisciplinary research experiences and educational modules for high school, undergraduate, and graduate students. The investigators will develop a new course that interweaves rigorous mathematical training with direct exposure to realistic research settings. This project will also develop specific initiatives to instill strong communication skills in the trainees, including a dedicated bootcamp for students to develop expertise 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.This project will develop new experimental techniques and mathematical models to generate a fundamental understanding of the interaction between capillary-size particles and a vibrating liquid interface. In 2005, Yves Courder and co-workers discovered that a millimetric liquid drop can spontaneously walk along the surface of a vibrating fluid bath, self-propelled through a resonant interaction with the waves created when it strikes the fluid surface. By virtue of the coupling with their wave fields, these walking droplets, or “walkers”, exhibit surprisingly rich dynamics, including complex bouncing modes, bound states, and dual wave-particle behaviors. This project will extend and exploit the remarkable walker dynamics for fundamental research relevant to practical settings involving granular materials on liquid interfaces. The investigator will first focus on broadening the current parameter regime of bouncing and walking dynamics to include new combinations of fluids and solid particles of different shapes. The second aim will be to investigate new self-assembly and collective dynamics with large ensembles of walkers coupled by wave-mediated forces. The final aim will be to examine the interaction between walking droplets and submerged features at the bottom of the liquid bath, including periodic and disordered bottom topographies. This class of problems will lead to a better understanding of the interplay between particles and liquid interfaces, and offer design principles for the development of new methods of self-assembly, particle sorting, and transport of granular materials on liquid interfaces.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.