Walking droplets & galloping bubbles
University of North Carolina
Abstract
Blending experiments, simulations and theory, we will discuss two different problems that are motivated by fundamental questions in physics and engineering.
In the first part, we present a classical wave-particle analog of Anderson localization using walking droplets, or “walkers,” which self-propel across a vibrating fluid bath via a resonant interaction with their guiding wave field. These droplets push the boundaries of classical mechanics by exhibiting behaviors previously thought to be exclusive to the quantum realm. Investigating the erratic motion of walkers over submerged random topographies, we demonstrate the emergence of localized statistics analogous to those of quantum particles. Analysis of walker trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography, driven by a wave-mediated resonant coupling that generates an attractive wave potential. This hydrodynamic quantum analog illustrates how a classical particle may localize like a wave.
The second part introduces a new symmetry-breaking mechanism that enables bubbles to “gallop” along horizontal surfaces in a vertically vibrated fluid chamber, propelled by coupling between shape oscillation modes. These active bubbles exhibit diverse trajectory regimes – rectilinear, orbital, and run-and-tumble – tunable by external forcing. By leveraging periodic body deformations and inertial forces, galloping bubbles achieve self-propulsion without external forcing in their direction of motion. Proof-of-concept demonstrations illustrate the potential of galloping locomotion for bubble manipulation, transport and sorting, navigation through complex fluid networks, and surface cleaning.
About the speaker
Dr. Pedro Sáenz is an Assistant Professor and the director of the Physical Mathematics Laboratory in the Department of Mathematics at UNC. From 2015 to 2019, he was an Instructor in Applied Mathematics at MIT. Pedro received his Ph.D. from the University of Edinburgh in 2015 and held a postdoctoral research position at Imperial College London the same year. He was awarded an Alfred P. Sloan Research Fellowship in 2023 and an NSF CAREER award in 2021. Pedro was also the recipient of a Caja Madrid Fellowship, presented in person by King Felipe VI and Queen Letizia of Spain, among several other grants and academic accolades. Pedro has earned multiple scientific visualization awards, including the American Physical Society Gallery of Fluid Motion award on three occasions, including the most recent edition. Pedro’s research combines theory, numerical simulations, and experiments to address fundamental problems that find motivation in physics and engineering.
