Acoustic wave-driven oxide dependant dynamic behavior of liquid metal droplet for inkjet applications

In this paper, we report bouncing and separating dynamic behaviors of a liquid metal droplet with/without the oxide layer in response to the applied acoustic wave. The oxidized liquid metal droplet is readily bounced off from the surface when it is excited by acoustic wave, while the HCl treated liquid metal droplet is fragmented into several small droplets. The bouncing height of the oxidized liquid metal is proportional to the applied acoustic wave amplitude. The number of the fragmented liquid metal droplets for the HCl-treated liquid metal according to time and acoustic wave amplitude was investigated. We also demonstrated the acoustic wave-based inkjet application to generate liquid metal droplets based on the pinch-off and the Rayleigh instability by changing amplitude of the acoustic wave. The probability for the generation of various droplet sizes with different acoustic wave amplitude was also studied.


Introduction
Gallium-based liquid metal alloy including EGaIn [1] (75% gallium and 25% indium) and Galinstan [2] (68.5% gallium, 21.5% indium, and 10% tin) has many useful and favorable material properties such as high electrical and thermal conductivity, low vacuum pressure, low toxicity as compared with Mercury and liquid property of the deformability of the shape [3,4]. Due to these extraordinary material properties, gallium-based liquid metal has been applied to various applications in tunable antennae [5][6][7][8], stretchable devices [9][10][11][12], chemical sensors [13,14], microfluidics actuators [15,16], soft electronics [17,18]. Gallium-based liquid metal alloy easily and rapidly forms a solid thin skin of oxide layer (a few nanometers) on its surface in oxygen environment and it becomes viscoelastic leading to easy-wetting to almost surfaces [19,20]. Although the oxide layer of the liquid metal has a limitation for applicability of various applications due to its wetting property, this oxidized surface of liquid metal has a significant advantage from a physical point of view as well. The oxide layer of the liquid metal allows liquid metal to be stably settled on most surfaces, including glass, metal, and paper, and it can also physically stabilize the liquid metal shape as a state of equilibrium [21].
There have been a few methods to remove the oxide layer to have the non-wetting property recovered or overcome the wetting problem, such as making a lyophobic and non-wettable surface against the oxidized liquid metal [22][23][24][25]. Most representative method to have a non-wetting property of gallium-based liquid metal is to treat Hydrochloric acid (HCl) to the oxide layer of liquid metal [26]. The oxidized liquid metal surface is a combination of Ga 2 O 3 and Ga 2 O. When HCl applies to the oxide layer, the component of the surface is converted to gallium chloride (GaCl 3 ) and indium chloride (InCl 3 ) [27]. The HCl-treated liquid metal behaves like a true liquid and can easily change its shape freely due to a removal of the few nm oxide skin which enclosed the unoxidized liquid metal in it. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
In this paper, we report a study on bouncing and fragmentation behavior of the liquid metal depending on the presence or absence of the surface oxide layer with the applied acoustic wave as an external stimulus. We investigated the physical characteristics of the oxidized liquid metal and HCl-treated liquid metal which was bouncing/fragmenting by applying acoustic wave with varying amplitude. Total number of fragmented liquid metal droplets from the HCl-treated liquid metal droplet according to time was investigated. Acoustic wave amplitude dependant number of the separated liquid metal droplets at a time was studied. In addition, we studied the bouncing height of the oxidized liquid metal droplet dependent on the acoustic wave amplitude. In order to study the feasibility of application using this dynamic characteristic, we demonstrated acoustic wavebased inkjet printing based on the pinch-off and the Rayleigh instability by changing amplitude of the acoustic wave.

Experiment
To compare the dynamic behavior of the liquid metal droplet with an applied acoustic wave, we investigated two different gallium-based liquid metal droplets; Oxidized liquid metal and HCl-treated liquid metal. We utilized the Galinstan ® (Geratherm Medical AG) without any modification as one of the gallium-based liquid metal droplet. Oxidized liquid metal droplet and HCl-treated liquid metal droplet were placed on a non-wettable wrapping paper (Model ES-PR201040425, Evershine CO., Ltd.). We placed a woofer speaker (Peerless, Inc., Model 830990) underneath the non-wettable wrapping paper with a ∼1 mm gap, which was linked to an amplifier (PZD700, Trek Co.) and a function generator (33210A, Agilent Co.).
Once the liquid metal droplet was exposed to air, brightness of the surface of the liquid metal droplet (∼8 μl) was changed to be slightly dim, as the surface was instantly oxidized. The oxidized liquid metal droplet formed a thin (a few nanometers) viscoelastic oxide layer which protected the pure liquid metal enclosed by the oxidized liquid metal surface and stably maintain the shape of the oxidized liquid metal droplet from the external stimulus. When the acoustic wave was applied the oxidized liquid metal droplet was readily bounced off from the surface regardless of the amplitude of acoustic wave ( figure 1(a)). For another set of samples, ∼7 μl HCl solution (37 wt%) was dropped to the oxidized liquid metal droplet for 25 s, which led to a complete removal of the surface oxide layer of the liquid metal droplet. When an acoustic wave was applied to the HCl-treated liquid metal droplet, the HCL-treated liquid metal droplet was also bounced off from the surface but at the same time the shape of the liquid metal was not maintained when the external stimulus was high. The HCl-treated liquid metal droplet was fragmented into several smaller droplets under high amplitude excitation signal ( figure 1(b)).  Figure 2 shows the dynamic characteristics of the oxidized liquid metal droplet and HCl-treated liquid metal droplet in response to varying applied voltages. The acoustic wave with a frequency of 30 Hz was applied with the voltage amplitude varies in the range of 10-30 V. When 10 V was applied, the oxidized liquid metal droplet was started to readily bounce off from the surface. When the excitation voltage was increased from 10 V to 30 V, while the shape of the bounced off oxidized liquid metal droplet slightly changed, the images of the bounced off liquid metal droplet showed that the droplet was not fragmented ( figure 2(a)). This is due to the solid thin (a few nanometers) surface oxide layer protects liquid metal inside the oxide skin intact and maintain true liquid phase.
For the HCl-treated liquid metal droplet, when we applied 10 V, the HCl-treated liquid metal droplet was similarly bounced off like the oxidized liquid metal droplet. Since the oxide layer was removed by treating HCl solution to the surface of the oxidized liquid metal droplet, the HCl-treated liquid metal is expected to have a true liquid property. As expected, the shape of the bounced off HCl-treated liquid metal continually changed its shape in the air due to its unlimited deformability ( figure 2(b1)). When we increased the voltages higher than 10 V amplitude, the HCl-treated liquid metal droplet was started to be separated into smaller droplets. With 20 V amplitude, the HCl-treated liquid metal droplet bounced off the surface and instantaneously separated into several smaller droplets and also re-merged in between smaller liquid metal droplets in near distance ( figure 2(b2)). By increasing the voltage amplitude to 30 V, the droplet was fragmented into countless smaller pieces ( figure 2(b3)). This set of experiments showed that the presence of the surface oxide layer on the galliumbased liquid metal droplet plays an important role in determining the dynamic characteristics of liquid metal droplet under external stimuli. Based on the initial study of the dynamic characteristics of the oxidized liquid metal droplet and HCl-treated liquid metal droplet with applied acoustic waves, we further studied the number of the separated HCl-treated liquid metal droplets at a time and time dependant total number of the separated liquid metal droplets for the HCl-treated liquid metal ( figure 3). The blue-colored dotted line indicated that of the acoustic wave amplitude dependant number of the separated liquid metal droplets at a time and red-colored circle line indicated that of the time dependant total number of the separated liquid metal droplets for the HCl-treated liquid metal. By increasing the acoustic wave amplitude, the number of the separated liquid metal droplet at a time was also increased ( figure 3(a)). The maximum number of the separated liquid metal droplet at a time was ∼6 with an applied voltage of 30 V. When the higher acoustic wave amplitude was applied to the HCl-treated liquid metal droplet, the more numbers of droplets were generated. By increasing the applied acoustic wave amplitude, the number of separated liquid metal at a time was also increased, while the bouncing height of the HCl-treated liquid metal droplet was decreased. This is because some of the acoustic wave energy applied to the liquid metal droplet were used to use to separate the HCl-treated liquid metal droplet into smaller size droplets. Thus, this resulted in the loss of energy used for bouncing from the surface [28]. Additionally, the liquid metal droplet kept being separated into the smaller droplets, as the time of the applied acoustic wave went by ( figure 3(b)). As the time increased with an applied acoustic wave amplitude, the total number of separated liquid metal droplet was rapidly and exponentially increased. With 10 s acoustic wave application, the total number of the separated liquid metal was about 60 and the smallest size of the diameter of the fragmented liquid metal droplet was ∼0.1 mm. Figure 4 shows the bouncing height of the oxidized liquid metal in accordance with an acoustic wave amplitude. When applied voltages were increased, the bouncing height of the oxidized liquid metal droplet was  nearly linearly increased as a function of the applied voltage between 10 V and 30 V. In case of the oxidized liquid metal droplet, since the viscoelastic surface oxide layer protects the pure phase of liquid metal inside and no separation occurs in a droplet, the acoustic wave energy was solely used for bouncing of the droplet [21]. Thus, the oxidized liquid metal droplet showed higher bouncing height than HCl-treated liquid metal droplet with the same applied voltages. The oxidized liquid metal droplet was bounced off up to 88 mm when 30 V was applied. All tests were repeated five times and the average results were plotted and the error bars shows standard deviation.
Based on the study of the dynamic characteristics of the oxidized liquid metal and the HCl-treated liquid metal with applied acoustic waves, we performed a demonstration with in mind of the inkjet application utilizing separation of HCl-treated liquid metal droplet into smaller droplets. Figure 5(a) shows conceptual schematic diagrams of the a train of liquid metal droplet generation from a large HCl-treated liquid metal based on the pinch-off and Rayleigh instability with the different acoustic wave amplitude. An inkjet application device was fabricated with an acryl chamber (horizontal 2.5 cm, length 2 cm, a height of 1.8 cm), which was used to make 2 mm thick acryl parts cut by a laser cutting machine (LaserCut 6.1 Laser Equipment CO. Ltd., Korea) and a diameter of 1 mm orifice was formed at the center of a thin flexible tape attached the top of the acryl chamber. If the diameter of orifice was smaller than 1 mm, there was no ejection of liquid metal droplet regardless of the applied voltages. If the orifice gets larger, the HCl-treated liquid metal naturally flows out by gravitational force without any acoustic excitation. The HCl-treated liquid metal in the amount of 60 μl was injected in the acrylic chamber through the orifice. We turned the woofer speaker upside down so that the bottom plate of the inkjet device can be applied to the acoustic wave to eject the HCl-treated liquid metal from the orifice. The liquid metal was not ejected when acoustic wave amplitude of 10 V was applied. This is the fact the acoustic wave amplitude of 10 V was not strong enough to eject the HCl-treated liquid metal through the orifice. With an applied voltage of 20 V, a train of the liquid metal droplets were ejected out of the chamber ( figure 5(b)). The HCl-treated liquid metal chemically reacted to the HCl solution in the acryl chamber, resulted in the high surface tension of the liquid metal continuously [27]. Due to its high surface tension and the sufficient strong acoustic wave amplitude (20 V) which can eject the liquid metal from the chamber, the inkjet device can pinch off at the end of the orifice as a pendant droplet shape. When the voltage was increased to 30 V, the inkjet device generated a jet stream of liquid metal as shown in figure 5(c). The ejected liquid metal jet stream spontaneously broke up into smaller liquid metal droplets due to the Rayleigh instability [29,30].
The liquid metal droplet was generated in a variety of size at applied 20 V and 30 V. We measured the size of the liquid metal droplets generated from the inkjet device and analyzed droplet size distribution with varying excitation conditions. The size of the generated droplet from the inkjet device was in a range of diameter of 1 to 1,000 μm as shown in figure 5(d). When we applied the voltage of 30 V, smaller liquid metal droplets were generated more than larger size droplets. On the other hand, with an applied voltage of 20 V, the probability of the generating larger droplets was increased. We concluded that the size of the liquid metal droplet ejected from the chamber is controllable by varying the applied acoustic wave amplitudes. Behavior of ejected droplets is based on either pinch off or Rayleigh instability. We notify that the re-oxidation of the liquid metal droplet definitely would be occurred, the dynamic behavior of the re-oxidized droplet would be slightly different from that of the firstly oxidized liquid metal droplet, which was demonstrated in this manuscript.

Conclusion
In this paper, we demonstrated bouncing and separation behavior of the liquid metal droplet with/without the oxide layer in response to varying acoustic wave amplitudes. Acoustic wave-based inkjet application to generate a train of liquid metal droplets was also demonstrated. Depending on amount of excitation, it was found that pinch-off or the Rayleigh instability governs behaviors of the ejected liquid metal droplets. It was found that the size distribution of the liquid metal droplets can be controlled. This may work may be used for further in-depth study on fragmentation behavior of liquid metals and practical liquid metal inkjet developments.