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Exotic states of bouncing and walking droplets
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Image of FIG. 1.
FIG. 1.

Walking drop of 20 cS silicone oil of radius 0.48 mm (a) before, (b) during, and (c) after an impact with a bath of the same liquid vibrating at 70 Hz. (d) A walking drop and its associated wave field.

Image of FIG. 2.
FIG. 2.

Schematic illustration of the experimental set-up. The vibrating bath is illuminated by two LED lamps, and the drop motion recorded by two digital video cameras. The top view camera captures images at 17.5–20 frames per second, while the side view camera records at 4000 frames per second. The video processing is done on a computer.

Image of FIG. 3.
FIG. 3.

Regime diagrams indicating the dependence of the droplet behaviour on the dimensionless driving acceleration, Γ = γ/, and the vibration number, . (a) The 20 cS-80 Hz combination, for which Γ = 4.22 ± 0.05. (b) The 50 cS-50 Hz combination, for which Γ = 4.23 ± 0.05. (c) The 20 cS-70 Hz combination, for which Γ = 3.33 ± 0.05. Coloured areas correspond to theoretical predictions, the solid red line denoting the theoretically predicted walking threshold. Experimental data are presented as square or round markers, with square markers denoting stationary bouncing states, round markers walking states, and their colour indicating the associated mode.

Image of FIG. 4.
FIG. 4.

Spatiotemporal diagrams of the bouncing modes observed for the 20 cS-80 Hz combination. (a) Bouncing mode (4, 4). Γ = 2.3, Ω = 0.45. (b) Bouncing mode (4, 3). Γ = 2.7, Ω = 0.45. (c) Bouncing mode (4, 2). Γ = 3.5, Ω = 0.42.

Image of FIG. 5.
FIG. 5.

Spatiotemporal diagrams of the modes observed for the 50 cS-50 Hz combination. (a) Walking mode (2, 1). Γ = 3.7, Ω = 0.59. (b) Walking mode (2, 1). Γ = 4.0, Ω = 0.44. (c) Chaotic bouncing with no apparent periodicity. Γ = 4, Ω = 0.94.

Image of FIG. 6.
FIG. 6.

Spatiotemporal diagrams of the modes observed for the 20 cS-70 Hz combination. (a) The exotic bouncing mode (13, 10), highly complex periodic motion. Γ = 3.3, Ω = 0.97. (b) The limping drop, a (2, 2) walking mode. Γ = 2, Ω = 0.42. (c) The mixed walking state, shown here evolving from (2, 1) → (2, 1) → (2, 1) → (2, 1). Γ = 3.4, Ω = 0.72.

Image of FIG. 7.
FIG. 7.

Mixed state walkers observed with the 20 cS-70 Hz combination. Γ = 3.4, Ω = 0.72. (a) The trajectory for a drop in the mixed state, shaded according to the speed. The circular bath domain is indicated. (b) The observed variation of walking speed with arc-length, as normalised by the Faraday wavelength. (c) A Fourier power spectrum of the normalised velocity fluctuations, which indicates that the mode-switching arises periodically, after the droplet has walked a distance of approximately 0.95λ. (d) Trajectory of a mixed mode, shaded according to speed, that destabilises into a (2, 1) walker after collision with the boundary near (, ) = ( − 25, −20) mm.


Generic image for table
Table I.

The walking and bouncing modes observed for the three viscosity-frequency combinations examined. Modes in bold typeface are those for which an associated spatiotemporal diagram is included (see Figs. 4–6 ).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Exotic states of bouncing and walking droplets