Recently, the Joint Research Group from the Technical Institute of Physics and Chemistry of the Chinese Academy of Sciences and Tsinghua University reported for the first time the vibration induced Faraday wave phenomenon and bouncing droplet effect of the liquid metal in the journal ‘Physical Review Fluids’, with the paper title as “Electrically switchable surface waves and bouncing droplets excited on a liquid metal bath" (Xi Zhao, Jianbo Tang, Jing Liu, Physical Review Fluids, 3: 124804, 2018). 

Faraday waves are nonlinear subharmonic standing waves that appear on liquid enclosed by a vibrating container. When the vibration acceleration exceeds a critical value (the Faraday threshold), the flat hydrostatic surface instantaneously becomes unstable. This is known as the Faraday instability, a classic hydrodynamic instability problem. Study on surface wave modes and Faraday wave patterns is of great scientific significance for the development of complex nonlinear dynamics and pattern formation theory of hydrodynamic systems, such as Rayleigh-Bénard convection, Taylor-Couette flow and nonlinear optics. More interestingly, the vertically vibrating liquid surface can be used as a soft platform to sustain bouncing droplets of the same fluid. The mechanism of non-coalescence lies in that there is a thin layer of flowing fluid between the two parts of the fluid, which provides a lifting force (Reynolds lubrication theory) and avoids their direct contact. In addition, the wave excited by the droplet impact will couple to the bouncing droplet itself, this hydrodynamic ‘wave-particle duality’ enables the droplet to exhibit incredible quantum-like properties. Due to the above reasons, the Faraday wave system has attracted great attention in recent years. 

There are many parameters that affect the Faraday wave mode, including driving conditions (frequency, acceleration), boundary conditions (container shape, fluid meniscus) and working fluid properties. Among them, fluid density, viscosity, surface tension and the like play a fundamental role. Previous studies on Faraday waves and bouncing droplets have been carried out in conventional fluids such as water and oils due to their moderate density and low surface tension. In contrast, liquid metal is a new class of emerging functional fluid materials with a high density (6 times that of water), large surface tension (about 10 times that of water) and excellent electric conductivity. The combined effect of gravity and surface tension usually makes the liquid metal droplets coalesce with the same metal bath at once. So far, there is no research on the vibration response of the liquid metal. This study reveals rich phenomena of Faraday instability in the liquid metal system, such as unique surface wave characteristics, bouncing droplet behaviors, as well as electrical switching effect that cannot be achieved on non-conductive fluids.  

It has been found that through adjusting the driving frequency and acceleration, the liquid metal surface will exhibit a series of highly symmetric surface wave patterns (Fig. 1a). As the driving frequency increases, the surface wave pattern becomes more complicated, and the fold symmetry number generally increases (Fig. 1b). However, patterns of the same fold symmetry number can also be formed at different frequencies, while the patterns are different in details (Fig. 1b corresponds to the color squares in 1c). The article further explores the quantitative relationship between the surface wave states and the driving parameters, and points out the stable working range of different surface wave modes. These highly symmetrical surface wave patterns excited on the liquid metal surface have never been observed in a single conventional fluid system. The main reason is that the large surface tension of liquid metal will make its dissipation length much higher than that of traditional fluids, so the surface wave is greatly affected by the shape of the fluid boundary (meniscus). The experimentally observed surface wave patterns are actually the result of the superposition of the nonlinear standing waves excited by the vibration and the boundary transmitting waves. 

Furthermore, the authors studied the bouncing behavior of liquid metal droplets on the same metal bath. For conventional fluids, the study of bouncing droplets can only be conducted below the Faraday threshold. Once the driving acceleration exceeds the Faraday threshold, the entire surface will suddenly become turbulent so that is can no longer sustain bouncing droplets. While for the liquid metal system where highly symmetric Faraday wave patterns can be formed, liquid metal droplets can bounce stably on the same metal bath surface even above the Faraday threshold. In this Faraday bouncing regime, the droplets are locked at the antinode position of the surface wave, and collide with the bath surface at the lowest point to obtain stable jumping energy in the vertical direction. Droplets located at adjacent antinodes bounce in opposite phases (Figure 2a). Moreover, multiple droplets automatically assemble into lattice-like structures corresponding to the surface wave patterns (Fig. 2b) due to the locking effect. The paper also finds that for higher frequencies, the range of droplet diameters that can be stably suspended is gradually reduced (Fig. 2c). 

Unlike traditional non-conductive fluids, liquid metal benefits from the excellent electrical conductivity of the inherent nature of metal materials, allowing it to flexibly change its properties by applying an electric field. The authors thus proposed a method for flexibly and rapidly regulating the surface wave states of liquid metal by an applied electric field (Fig. 3). Analysis of the electro-capillary curve of liquid metal reveals that a small applied voltage (below 5 V) can quickly change the surface tension of the liquid metal, which has a great influence on the Faraday threshold and thus change the surface wave states. It is worth noting that adjusting the surface wave states through an applied electric field is reversible. When the electric field is removed, the surface wave can automatically return to its original state. Therefore, this electric switching effect makes the liquid metal system more controllable, which is of great significance for studying the Faraday instability problem. 

In general, the liquid metal Faraday wave system exhibits abundant surface wave modes, which can be excited on demand through adjusting the external driving parameters. The surface wave states can be quickly and effectively adjusted by an applied electric field. And bouncing liquid metal droplets can self-assemble into lattice-like structures. Therefore, the system is well suited for studying pattern formation, mode transition, and droplet self-assembly theory. Furthermore, bouncing liquid metal droplets possess higher degrees of freedom and are not affected by the substrate material. These are of great scientific significance and application value for the study of liquid metal robots, intelligent motors, flexible pumps and vascular robots. The vibration method to realize non-coalescent droplet established in this work also provides a new non-contact technical approach for studying the motion of liquid metal on a soft substrate. Compared to traditional methods such as applying an electric field and changing the chemical field, the application of vibration does not change the chemical composition and properties of the liquid metal and the solution, so this method has extremely high stability and feasibility. In addition, due to the close relationship between the Faraday instability and the working fluid nature, the investigation of the response of the liquid metal fluid to the vibration has a profound and fundamental significance for the improvement of the relevant scientific system of fluid mechanics. 

The above research was supported by the Dean’s Research Funding, the Frontier Project of the Chinese Academy of Sciences, and the NSFC Key Project. 

Article and video source:  

1. https://doi.org/10.1103/PhysRevFluids.3.124804 

2. https://v.youku.com/v_show/id_XMzk4NTIzOTYyOA==.html?spm=a2h0k.11417342.soresults.dtitle 

FIG. 1. Frequency-dependent surface wave structures on the liquid metal surface. (a) Faraday wave patterns with fold symmetry number N from 2 to 10; (b) Plot of the fold symmetry number N against the driving frequency f. The parallel dash lines are a guide for the eyes to show the repeat of N - f development; (c) Four groups of Faraday wave patterns with the same N at different f. Each group is identified by color in figure b. 

FIG. 2. 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 (equals to half the driving frequency)；(b) Self-assemblies of liquid metal droplets at their Faraday bouncing state when the bath is vibrating with different N; (c) Change of the diameter range of Faraday bouncing droplets that can be sustained as a function of f. The blue-color filled area indicates the Faraday bouncing region. Γ is the driving acceleration corresponding to each surveyed f. 

FIG. 3. Switchable manipulation of surface waves between different states with a DC voltage (UDC = 5 V, f = 30 Hz, Γ=2.7). The cathode and the anode are inserted into the liquid metal layer and the solution layer, respectively.