PhD Thesis : “In this work, we focus on a droplet, that can bounce on a liquid surface. More surprisingly this droplet can even move along a liquid surface. It is propelled by its own waves, generated at each bounce, and evolves at a well defined speed. This curious macroscopic object is called a « walker ». Moreover, it seems to present various analogies with the world of quantum mechanics and it has fascinated the scientists since its discovery in 2005 [34]. Indeed, the droplet is associated with its own waves, such that the droplet behaviour is intimately linked to the waves, which is a striking curiosity. In this thesis, we investigate further this subject of a droplet between wave-particle physics and fluid mechanics. Various experiments have been performed for a better understanding of walkers. They cover a wide range of 2d systems [35]. Some experiments develop methods to confine or trap droplets, upon using 2d harmonic potential (…)
However, there are only a few studies reported on a 1d system droplet. We wonder then, how to confine a droplet in 1d. Can we find a method to constrain its trajectory along a 1d path? Can experiments of walkers in 1d open new doors through other curiosities related to quantum mechanics? If not, how close to the wave-particle physics can we go? Is the walker entity a real analog to the quantum world, or just a curiosity ? As a starting point, we study the influence of the liquid height on the droplet behaviour. We wonder then how a linear cavity can trap a drop, and how the width of this cavity influences the confinement of a drop. How does droplet confinement affect the interactions between walkers? In this manuscript, we give answers to those different questions, and shed light on other curiosities.”

Proposition of an interferometer for walkers !

Filoux, B (2017), Walking droplet above cavities, Thèse, GRASP, Univ. Liège

orbi.ulg.be/bitstream/2268/214607/1/Thesis_BFiloux_WDAC.pdf

ABSTRACT : “When a droplet is placed onto a vertically vibrated bath, it can bouncewithout coalescing. Upon an increase of the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well-defined speed.We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that one-dimensional confinement is optimal for narrow channels of width of D  1.5λF . Thereby, the walker follows a quasilinear path.We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.”

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2017). Walking droplets in linear channels. Physical Review Fluids, 2(1), 013601.

https://www.researchgate.net/publication/312353846_Walking_droplets_in_linear_channels

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2015). Waveguides for walking droplets. arXiv preprint arXiv:1507.08228.

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce permanently. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well dened speed. We investigate the connement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d connement is optimal for narrow channels. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.

http://arxiv.org/pdf/1507.08228.pdf

Filoux, B., Hubert, M., & Vandewalle, N. (2015). Strings of droplets propelled by coherent waves. arXiv preprint arXiv:1504.00484.

Bouncing walking droplets possess fascinating properties due to their peculiar wave/particle interaction. In order to study such walkers in a 1d system, we considered the case of a few droplets in an annular cavity. We show that, in this geometry, they spontaneously form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster
than single walkers. The formation of this coherent wave and the collective droplet behaviors are captured by a model, which sheds a new light on droplet/wave interactions.

http://arxiv.org/pdf/1504.00484.pdf