Hydrodynamic analog of particle trapping with the Talbot effect

Abstract

We present the results of an experimental study of the standing waves produced on the surface of a vertically shaken fluid bath just above the Faraday threshold, when a row of equally spaced pillars protrudes from the surface. When the pillar spacing is twice the Faraday wavelength, the resulting wave field is marked by images of the pillars projected at integer multiples of a fixed distance from the row. This projection effect is shown to be analogous to the well-known Talbot or self-imaging effect in optics, and a Faraday-Talbot length is defined that rationalizes the location of the images. A simple model of point sources emitting circular waves captures the observed patterns. We demonstrate that the images may serve as traps for bouncing and walking droplets.

Swimming of a ludion in a stratified sea

“…This is the case for instance in the experiments presented in figure 13(a) where after the introduction of three divers in the stratified layer, they were all of them attracted to three places that, as can be observed in figure 13(b), seem to correspond to trapped locations in an underlying eigenmode that possesses an eigenfrequency very close to the forcing frequency. This particle trapping is similar to what happens in the walker system where the bouncing drops are attracted and pinned in a periodic wave pattern (Sungar et al 2017). Note that an important constraint in respect for this pinning is the identical phase difference between each ludion and the mode itself as the three divers are locked at the same phase difference to the forced pressure oscillations.…”

Walking droplets in a circular corral: Quantisation and chaos

“…In addition, the erratic trajectories do not typically execute loops, but instead, move along straight lines. We note the preponderance of trapped states at L z = 0 and R = 0.7, denoted by blue circles, indicating the walker's propensity to be trapped 38 at the radius of the unstable large orbit [Fig. 2(c)].…”

Bouncing droplet dynamics above the Faraday threshold

“…First, Sampara and Gilet explored the dynamics of bouncing droplets on a bath forced by two frequencies. 25 Second, Sungar et al 26 introduced an array of pillars to the bath and observed that, for γ /γ F 1.02, the form of the Faraday waves in the vicinity of the pillars is analogous to that arising in the optical Talbot effect. 27 The resulting Faraday-Talbot wave pattern was capable of trapping both walking and bouncing droplets in its troughs, a hydrodynamic analog of particle trapping with the Talbot effect.…”