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

Dubertrand, R., Hubert, M., Schlagheck, P., Vandewalle, N., Bastin, T., & Martin, J. (2016). Scattering theory of walking droplets in the presence of obstacles. arXiv preprint arXiv:1605.02370.

We aim to describe a droplet bouncing on a vibrating bath. Due to Faraday instability a surface wave is created at each bounce and serves as a pilot wave of the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by Couder et al [Phys. Rev. Lett. 97, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. Here we present a simple and highly versatile model inspired from quantum mechanics. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to Helmholtz equation with Neumann boundary conditions on the
obstacle(s) and outgoing conditions at infinity. For a single slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It
stands for a promising.

http://arxiv.org/pdf/1605.02370.pdf

Brandenbourger, M., Vandewalle, N., & Dorbolo, S. (2016). Displacement of an Electrically Charged Drop on a Vibrating Bath. Physical review letters, 116(4), 044501.

In this work, the manipulation of an electrically charged droplet bouncing on a vertically vibrated, bath is investigated. When a horizontal, uniform and static electric eld is applied to it, a motion is induced. The droplet is accelerated when the droplet is small. On the other hand, large droplets appear to move with a constant speed that depends linearly on the applied electrical eld. In the latter regime, high speed imaging of one bounce reveals that the droplet experiences an acceleration due to the electrical force during the ight and decelerates to zero when interacting with the surface of the bath. Thus, the droplet moves with a constant average speed on a large time scale. We propose a criterion based on the force necessary to move a charged droplet at the surface of the
bath to discriminate between constant speed and accelerated droplet regimes.

http://orbi.ulg.ac.be/bitstream/2268/194253/1/PhysRevLett.116.044501.pdf

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

Richardson, C. D., Schlagheck, P., Martin, J., Vandewalle, N., & Bastin, T. (2014). On the analogy of quantum wave-particle duality with bouncing droplets.arXiv preprint arXiv:1410.1373.

We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit difraction and double-slit interference patterns that strongly resemble those reported in experiment and that re ect a striking resemblance to quantum diraction and interference on a phenomenological level. We, however, identify evident dierences from quantum mechanics which arise from the governing equations at the fundamental level.

http://arxiv.org/pdf/1410.1373.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

Terwagne, D., Ludewig, F., Vandewalle, N., & Dorbolo, S. (2013). The role of the droplet deformations in the bouncing droplet dynamics. Physics of Fluids (1994-present), 25(12), 122101.

http://www.grasp.ulg.ac.be/article/2013_terwagne_POF.pdf

ArXiv Preprint  :

Terwagne, D., Ludewig, F., Vandewalle, N., & Dorbolo, S. (2013). The role of deformations in the bouncing droplet dynamics. arXiv preprint arXiv:1301.7463.

http://arxiv.org/pdf/1301.7463v1.pdf

Editor Postprint :

http://orbi.ulg.ac.be/handle/2268/159838

Automatic droplet generator

Period doubling transition of bouncing droplet, bifurcation diagram

Simulation with mass-spring system

Terwagne, D. (2011). Bouncing droplets, the role of deformations.

http://bictel.ulg.ac.be/ETD-db/collection/available/ULgetd-09262011-010800/unrestricted/2011_Terwagne_these.pdf

APENDIX C describes a automatic droplet generator