Fluid dynamics of interacting particles: bouncing droplets and colloid-polymer mixtures

Interacting particles are a common theme across various physical systems, particularly on the atomic and sub-atomic scales. While these particles cannot be seen with the human eye, insight into such systems can be gained by observing macroscopic systems whose physical behavior is similar. This dissertation consists of three different chapters, each presenting a different problem related to interacting particles, as follows: Chapter 1 explores chaotic trajectories of a droplet bouncing on the surface of a vertically vibrating fluid bath, with a simple harmonic force acting on the droplet. The bouncing droplet system has attracted recent interest because it exhibits behaviors similar to those previously observed only in the microscopic quantum realm. In this investigation, an approximation is presented for an existing model that describes a walking droplet's trajectories in the xy-plane. Simulations of the approximate model show that it captures behaviors of the full model, but is less computationally expensive to simulate. Chapter 2 presents the results of a theoretical investigation of one-dimensional chains of bouncing droplets, with particular attention to the case in which the drop at one end of the chain is oscillated periodically. Numerical simulation results are also presented, and are found to compare favorably with predictions based on linear theory. Both demonstrate the existence of resonant forcing frequencies, as well as the presence of an oscillatory instability in the chain as the forcing acceleration is increased. For sufficiently high forcing frequencies, dynamic stabilization of the chain into a new bouncing state is observed. The results of this investigation highlight the role of temporally nonlocal interactions in the dynamics of this unique system, and have been published in the journal Comptes Rendus Mecanique. Chapter 3 investigates the phase behavior of colloid-polymer suspensions in a microgravity environment. Phase transitions in such suspensions give valuable insight into atomic-scale ...