Antonin Eddi

Path-memory induced quantization of classical orbits

A droplet bouncing on a liquid bath can self-propel due to its interaction with the waves it generates. The resulting “walker” is a dynamical association where, at a macroscopic scale, a particle (the droplet) is driven by a pilot-wave field. A specificity of this system is that the wave field itself results from the superposition of the waves generated at the points of space recently visited by the particle. It thus contains a memory of the past trajectory of the particle. Here, we investigate the response of this object to forces orthogonal to its motion. We find that the resulting closed orbits present a spontaneous quantization. This is observed only when the memory of the system is long enough for the particle to interact with the wave sources distributed along the whole orbit. An additional force then limits the possible orbits to a discrete set. The wave-sustained path memory is thus demonstrated to generate a quantization of angular momentum. Because a quantum-like uncertainty was also observed recently in these systems, the nonlocality generated by path memory opens new perspectives.

Initial spreading of low-viscosity drops on partially wetting surfaces

Liquid drops start spreading directly after coming into contact with a partially wetting substrate. Although this phenomenon involves a three-phase contact line, the spreading motion is very fast. We study the initial spreading dynamics of low-viscosity drops using two complementary methods: molecular dynamics simulations and high-speed imaging. We access previously unexplored length and time scales and provide a detailed picture on how the initial contact between the liquid drop and the solid is established. Both methods unambiguously point toward a spreading regime that is independent of wettability, with the contact radius growing as the square root of time.

Information stored in Faraday waves: the origin of a path memory

On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely.When approaching the Faraday instability onset, the droplet couples to the wave itgenerates and starts propagatinghorizontally.Theresultingwave–particleassociation,called a walker, was shown previously to have remarkable dynamical properties,reminiscent of quantum behaviours. In the present article, the nature of a walker’swave field is investigated experimentally, numerically and theoretically. It is shownto result from the superposition of waves emitted by the droplet collisions with theinterface.Asingleimpactisstudiedexperimentallyandinafluidmechanicstheoreticalapproach. It is shown that each shock emits a radial travelling wave, leaving behinda localized mode of slowly decaying Faraday standing waves. As it moves, the walkerkeeps generating waves and the global structure of the wave field results from thelinear superposition of the waves generated along the recent trajectory. For rectilineartrajectories, this results in a Fresnel interference pattern of the global wave field. Sincethe droplet moves due to its interaction with the distorted interface, this means that itis guided by a pilot wave that contains a path memory. Through this wave-mediatedmemory, the past as well as the environment determines the walker’s present motion.Key words: drops, Faraday waves, pattern formation

Wave propelled ratchets and drifting rafts

Several droplets, bouncing on a vertically vibrated liquid bath, can form various types of bound states, their interaction being due to the waves emitted by their bouncing. Though they associate droplets which are individually motionless, we show that these bound states are self-propelled when the droplets are of uneven size. The driving force is linked to the assymetry of the emitted surface waves. The direction of this ratchet-like displacement can be reversed, by varying the amplitude of forcing. This direction reversal occurs when the bouncing of one of the drops becomes sub-harmonic. As a generalization, a larger number of bouncing droplets form crystalline rafts which are also shown to drift or rotate when assymetrical.

Archimedean lattices in the bound states of wave interacting particles

The possible periodic arrangements of droplets bouncing on the surface of a vibrated liquid are investigated. Because of the nature of the interaction through waves, the possible distance of binding of nearest neighbors is multi-valued. For large amplitude of the forcing, the bouncing becomes sub-harmonic and the droplets can have two different phases. This effect increases the possible distances of binding and the formation of various polygonal clusters is observed. From these elements it is possible to assemble crystalline structures related to the Archimedean tilings of the plane, the periodic tesselations which tile uniformly the 2D plane with convex polygons. Eight of the eleven possible configurations are observed. They are stabilized by the coupling of two sub-lattices of droplets of different phase, both contributing to sustain a common wave field.

Time reversal and holography with spacetime transformations

Using a water bath subject to a sudden vertical jolt — representing a change in the effective gravity — researchers demonstrate the concept of a ‘time mirror’, where time-reversed waves return to their point source following a downward jolt.

Marangoni spreading due to a localized alcohol supply on a thin water film

Bringing two miscible fluids into contact naturally generates strong gradients in surface tension. Here, we investigate such a Marangoni-driven flow by continuously supplying isopropyl alcohol (IPA) on a film of water, using micron-sized droplets of IPA-water mixtures. These droplets create a localized depression in surface tension that leads to the opening of a circular, thin region in the water film. At the edge of the thin region, there is a growing rim that collects the water of the film, reminiscent of Marangoni spreading due to locally deposited surfactants. In contrast to the surfactant case, the driving by IPA-water drops gives rise to a dynamics of the thin zone that is independent of the initial layer thickness. The radius grows as r ∼ t 1/2, which can be explained from a balance between Marangoni and viscous stresses. We derive a scaling law that accurately predicts the influence of the IPA flux as well as the thickness of the thin film at the interior of the spreading front.

Oscillating instability in bouncing droplet crystals

Bouncing droplets on a vibrated liquid bath can interact via the surface waves they emit and form various types of stable crystalline clusters. When increasing the forcing acceleration over an onset value, the aggregates present a global and spontaneous vibration mode. Here, we investigated experimentally these vibrations in hexagonal and square lattice clusters and show that there is a long-range selection amongst the modes. We propose a physical interpretation of the instability based on the intrinsic delay due to wave propagation and a simple model that explains the observed features of the vibrations.

Faraday wave lattice as an elastic metamaterial.

Metamaterials enable the emergence of novel physical properties due to the existence of an underlying subwavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern undergoes an oscillating secondary instability and exhibits spontaneous vibrations that are analogous to transverse elastic waves. By locally forcing these waves, we fully characterize their dispersion relation and show that a Faraday pattern presents an effective shear elasticity. We propose a physical mechanism combining surface tension with the Faraday structured interface that quantitatively predicts the elastic wave phase speed, revealing that the liquid interface behaves as an elastic metamaterial.