Fluids at Brown and Fluids and
Thermal Sciences Joint Seminar Series
Tuesday, February 25, 2020
Barus & Holley, Room 190
Stuart Thomson, MIT
Title: Collective vibrations of confined levitating droplets
Abstract: Classifying emergent properties of many-body systems, both passive and active, is a central theme of contemporary soft matter physics. In this talk, I will discuss a new type of active oscillator, whose active units are self-propelled millimetric droplets bouncing on the surface of a vertically vibrating bath of viscous fluid. For sufficiently large forcing, experiments show that this hydrodynamic lattice exhibits collective vibrations in the form of out-of-phase oscillations or solitary-like waves, depending on the proximity of neighboring droplets. Moreover, the transition to each of the aforementioned states may be characterized by the onset of a super- and sub-critical Hopf bifurcation, respectively. By modelling the lattice as a memory-endowed system with spatially-nonlocal coupling, I will rationalize the different bifurcations in the system through a set of amplitude equations, derivable from the droplets’ governing equations of motion. We will also find, through energy considerations, some configurations that are precluded by geometrical constraints of the lattice wave field.
This talk will contain elements of active matter, experimental fluid mechanics, nonlinear waves, dynamical systems, and asymptotic analysis. Our system suggests several future directions in these areas, some of which I will discuss in conclusion.