Model reduction for bouncing drops

Type : Semester project

Figure: Adapted from [1]. a) Scheme of a drop bouncing on a solid substrate which oscillates vertically. b) Spatio-temporal dynamics of rebounds showing a drop oscillating in phase, with the same frequency as the substrate (orange line).

Drops bouncing on a vibrating substrate exhibit rich and sometimes chaotic dynamics [1]. Similar to bouncing balls, they can undergo period-doubling bifurcations and transition to chaos. In this project, we will investigate whether the dynamics of bouncing drops can be described by a reduced model inspired by existing models for bouncing balls.

The project will combine numerical experiments and data-driven model reduction. Using Basilisk [2], a Navier-Stokes solver, we will simulate drops bouncing on a vibrating substrate and analyze their dynamics over a range of forcing conditions. The resulting data will then be used with tools such as PySINDy [3] to identify a simplified dynamical model. In particular, we will investigate how concepts such as restitution coefficients, commonly used for bouncing balls, can be defined and measured for liquid drops.

The project is primarily computational and requires an interest in coding, numerical simulations, and data analysis. Previous experience with Python is a plus, but no prior knowledge of Basilisk, PySINDy, or the physics of bouncing drops is required.

[1] Molefe, Lebo, et al. “Drops Can Perpetually Bounce over a Vibrating Wettable Solid.” Physical Review Letters 135.14 (2025): 144001.
[2] https://basilisk.fr
[3] https://pysindy.readthedocs.io/

Supervisors: Aliénor Rivière & Grégoire Le Lay