Eileen graduated from the University of Limerick with a BSc in Mathematics and Physics in 2018. Her final year project involved applying asymptotic techniques to non-linear ordinary differential equations in order to model a fluid dynamics problem. Eileen enjoys mathematical modelling and applied mathematics. During her degree, she completed a placement with Philips Healthcare in the Netherlands. Following her Bachelor’s degree, she completed a research internship at the University of Limerick, which involved Markov Chains. Outside of Maths, Eileen enjoys playing camogie and Gaelic football.

Research project title:
Faraday wave-droplet dynamics: Stochastic analysis of the droplet trajectory

Supervisor(s):
Paul Milewski, Tim Rogers

Project description:
For a suitably vibrating bath of fluid, a small droplet of the same fluid will “walk” across the surface due to the propulsive interactions with the waves generated by the previous droplet-bath impacts. As the bath vertically vibrates at a sufficiently large (yet sub-critical) amplitude, the droplet will bounce periodically. The bouncing droplet does not make contact with the bath, it is instead propelled back into the air due to the cushioning effect of the lubrication layer of air trapped between the bath and droplet visible only on a microscopic scale. As the amplitude increases, the droplet will destabilise and receive a “kick” in the horizontal direction resulting in the drop walking along the surface. Increasing the forcing vibration will increase the Faraday wave’s decay time yielding a longer path “memory” from previous drop impacts. In an infinite domain, the walking droplet will continue in a straight line at a constant speed. If we confine the droplet to a coral, a wavelike statistical pattern emerges from the complex trajectory. Eileen will derive and analyse this pattern using a combination of fluid mechanics and stochastics.