Electrically switchable surface waves and bouncing droplets excited on a liquid metal bath

Metallic fluids may contain rather rich unconventional surface wave behaviors when subjected to specific forcing conditions. Here we introduce a high-surface-tension liquid metal–solution bilayer to the Faraday system and investigate its wave evolution under cylindrical confinement. Beyond the Faraday threshold, we observe the formation of highly symmetric wave patterns when the acceleration remains below an upper threshold value ${\mathrm{\Gamma }}_{\mathrm{D}}$, exceeding which gives rise to disordered wave patterns. By varying the driving frequency from 20 to 80 Hz, diverse wave patterns with fold symmetry from 2 to 10 are excited. We further show that noncoalescent droplets of the same liquid metal can be sustained on the structured wave patterns. Distant droplets can be confined at the antinodes of the wavy surface and self-assemble the corresponding wave structures. Besides outlining some major differences between the current system and conventional ones, we also demonstrate a simple yet fast method to switch the surface waves between different states by electrically altering the liquid metal surface tension.

Figure 1

(a) Schematic experimental setups; (b) droplets bouncing on the wavy liquid metal surface when the acceleration is beyond the Faraday threshold (see Video 1 of the Supplemental Material [36]).

Figure 2

Surface wave patterns formed when (a) $\mathrm{\Gamma }<{\mathrm{\Gamma }}_{\mathrm{F}}$; (b) ${\mathrm{\Gamma }}_{\mathrm{F}}<\mathrm{\Gamma }<{\mathrm{\Gamma }}_{\mathrm{D}}$; (c) $\mathrm{\Gamma }>{\mathrm{\Gamma }}_{\mathrm{D}}$; (d) snapshots showing the evolution of a pentagonal wave pattern during one wave period $(f=30\mathrm{Hz},\mathrm{\Gamma }=2.7$; see Video 2 in the Supplemental Material [36]); (e) stability curves of ${\mathrm{\Gamma }}_{\mathrm{F}}\text{−}f$ and ${\mathrm{\Gamma }}_{\mathrm{D}}\text{−}f$. The scatters represent the measured values while the solid lines in black and red are fitting curves of ${\mathrm{\Gamma }}_{\mathrm{F}}$ and ${\mathrm{\Gamma }}_{\mathrm{D}}$, respectively. Note that both curves are fitted by a 5/3 power law and we exclude the wave competition cases during ${\mathrm{\Gamma }}_{\mathrm{D}}$ fitting; (f) representative tongue-shape stability curves of ${\mathrm{\Gamma }}_{\mathrm{F}}\text{−}f$ near the eigenfrequency $f_{\mathrm{E}}$. Typical measurement uncertainties of acceleration are shown as error bars.

Figure 3

(a) Faraday wave patterns with fold symmetry number $N$ from 2 to 10 (see Video 3 in the Supplemental Material [36]); (b) plot of the fold symmetry number $N$ against the driving frequency $f$. The parallel dashed lines are a guide for the eyes to show the repeat of $N\text{−}f$ development; (c) four groups of Faraday wave patterns with the same $N$ at different frequencies. Each group is identified by color in (b) (see Video 4 in the Supplemental Material [36]).

Figure 4

(a) Regime diagram of liquid metal bouncing droplets; the driving frequency is fixed at 55 Hz. Typical measurement uncertainties of acceleration and droplet diameter are shown as error bars; (b) representative spatiotemporal diagrams showing the vertical trajectory of a liquid metal droplet in correspondence to the three stable bouncing states in (a): simple bouncing, period doubling, and Faraday bouncing (see Video 5 in the Supplemental Material [36]).

Figure 5

Bouncing droplets on the vibrating liquid metal bath. (a) Droplets being locked at the wave antinodes and adjacent droplets bouncing in antiphase at the Faraday frequency $f_{\mathrm{F}}$ (equals half the driving frequency $f)$ (see Video 6 in the Supplemental Material [36]); (b) Self-assemblies of liquid metal droplets at their Faraday bouncing state when the bath is vibrating with different fold symmetry number $N$ (see Video 7 in the Supplemental Material [36]); (c) change of the diameter range of Faraday bouncing droplets that can be sustained as a function of $f$. The area filled in blue indicates the Faraday bouncing region. $\mathrm{\Gamma }$ is the driving acceleration corresponding to each surveyed driving frequency $f$, which is chosen from the acceleration range ${\mathrm{\Gamma }}_{\mathrm{F}}<\mathrm{\Gamma }<{\mathrm{\Gamma }}_{\mathrm{C}}$ to maintain the stable Faraday bouncing state of liquid metal droplets. Typical measurement uncertainties of acceleration and droplet diameter are shown as error bars.

Figure 6

Switchable manipulation of surface waves between different states with a dc voltage $\left(U_{\mathrm{dc}}=5\mathrm{V},f=30\mathrm{Hz},\mathrm{\Gamma }=2.7\right)$. The cathode and the anode are inserted into the liquid metal layer and the NaOH solution layer, respectively (see Video 8 in the Supplemental Material [36]).