Rapid electrocapillary deformation of liquid metal with reversible shape retention
© Gough et al.; licensee Springer. 2015
Received: 31 December 2014
Accepted: 11 March 2015
Published: 28 April 2015
A low-voltage, low-power method of electrically deforming a liquid-metal droplet via the direct manipulation of its surface tension is presented. By imposing a quasi-planar geometry on the liquid metal, its sensitivity to electrocapillary actuation is increased by more than a factor of 40. This heightened responsiveness allows the liquid metal to be deformed at rates exceeding 120 mm/s, greater than an order of magnitude faster than existing techniques for electrical deformation. Significantly, it is demonstrated how this process can be combined with voltage-controlled oxide growth on the surface of non-toxic, gallium-based liquid metals to reversibly form and maintain arbitrary, high-energy shapes.
Liquid metals are an attractive material choice for designers wishing to combine the advantages of metals, such as high electrical conductivity, thermal conductivity, and reflectivity, with the inherently dynamic nature of fluids. Liquid metals have been utilized for a wide variety of applications, including reconfigurable antennas  and filters , optical switches , and wearable electronics , among others.
While many of these devices require hydraulic pressure to actuate the liquid metal, there are size, power, and cost advantages in replacing pumps with electrokinetic actuation. Electrowetting on dielectric (EWOD) can create modest deformations in liquid metal by applying electrostatic fringing fields around the edges of the droplet, but at the cost of high actuation voltages . Surface-tension-based actuation techniques such as continuous electrowetting (CEW) are effective at transporting finite volumes of liquid metal with low-voltage, low-power signals , although they have not been shown to effectively manipulate the shape of the liquid metal. Liquid gallium and gallium-based alloys have demonstrated large-scale deformation when subjected to small oxidative voltages  in what has recently been demonstrated to be an electrochemical reaction , but this process generates gallium oxide that can leave residue on channel walls.
Here, we introduce a novel method of electrical surface-tension manipulation that can quickly and dramatically deform a liquid-metal droplet via electrocapillary actuation (ECA). The liquid metal (Galinstan, a non-toxic gallium alloy ) is immersed in an electrolyte and enclosed in a reservoir whose width is much greater than its height. This maximizes the surface area of the liquid-metal droplet relative to its volume, making it more responsive to surface-tension-based actuation. Variations in the liquid-metal surface tension are created by applying a small DC bias (referenced to the liquid metal) across the interface between the liquid metal and a surrounding electrolyte. Direct electrical surface-tension manipulation has been previously used to actuate liquid metal, but with modest deformation . Here, it is shown that the sensitivity of the liquid metal to electrical manipulation can be greatly heightened by imposing a quasi-planar geometry, which substantially decreases the excess surface energy required for actuation and increases responsiveness by over an order of magnitude. The authors have previously used this technique to tune the passband of a coupled-line bandpass filter by elongating the liquid-metal central resonator .
Electrocapillary actuation requires low voltage and low power, is immediately reversible, results in a greater deformation than EWOD, and is capable of moving liquid metal at speeds of over 120 mm/s. Furthermore, when gallium-based alloys such as Galinstan are used, the application of oxidative potentials results in oxide growth  that can be used as a reversible means of maintaining the liquid-metal surface deformation created by ECA. It was previously shown that the natural oxidation of gallium alloys can be leveraged as mechanical support in the creation of 3D structures . Here, we propose using voltage-controlled oxidation to create mechanical support for induced deformations that can be turned on and off like a switch. The technique described in this paper follows this process: first, Galinstan is rapidly deformed with ECA. Second, the deformed Galinstan is held in place by the sudden application of an oxidative potential. Finally, the liquid metal remains in this deformed state until the oxidative potential is replaced by a reductive voltage that removes the oxide layer, allowing the Galinstan to return to its minimum-energy geometry (an application of “recapillarity” ).
where γ o is the surface tension minus electrical influence, C is the capacitance per unit area of the EDL, and V EDL is the voltage across the EDL . This phenomenon, where surface tension is influenced by electrical conditions at the liquid-liquid boundary, is known as electrocapillarity .
where R 1 and R 2 are the principal curvature radii . Liquid metal in an electrolyte-filled channel has a near-180° contact angle with the channel walls , so the pressure is higher within the liquid metal relative to the electrolyte. CEW actuation takes advantage of this relationship by creating a surface-tension gradient across the length of a liquid-metal slug, resulting in a pressure imbalance from one end of the slug to the other and inducing motion , .
In ECA, the EDL voltage is altered by directly applying a DC bias between the liquid metal and electrolyte. This has the same low-voltage and low-power advantages as CEW, but allows for the liquid metal to be deformed and shaped instead of simply moved from point to point. Previous attempts at utilizing this technique resulted in only minor deformation  due to the low surface-area-to-volume ratio of the liquid metal. Here we show how these deformations can be greatly increased by maximizing this ratio.
Using this prolate spheroid approximation, the deformation of the liquid metal can be characterized as a change to the length of the semi-major axis a, and the resulting increase in the surface area of the spheroid can be calculated.
The majority of the surface area of the cylinder is comprised of the circular faces at each of the two planar boundaries. Furthermore, if h is held constant and the deformation of the liquid metal is limited such that the equivalent semi-minor spheroid axis b is always much greater than h, then the area of these faces remains constant. That is, deformation of the liquid metal transforms these circles into ellipses and increases the perimeter length P, but does not alter the area of the liquid metal in contact with each plate.
At the end of the primary channel opposite the reservoir, a positive voltage is applied to the electrolyte relative to the liquid metal. As the electrolyte is semi-conductive, a potential gradient is established within the channel and along the interface between the electrolyte and liquid metal. This creates a surface-tension gradient along the interfacial boundary as described by (1), with the lowest surface tension at the channel entrance. Marangoni forces (F Mar ) that develop along this interface generate a flow of the electrolyte away from the channel entrance, and exert negative displacement pressure on the liquid metal, pulling it flush across the channel entrance. Entrance of the liquid metal into the channel is opposed by the capillary pressure of the channel; this additional pressure threshold must be overcome if flow is to be initiated.
The reservoir and channels are filled with a solution of 1% NaOH, after which the reservoir is filled with Galinstan. The Galinstan wets to a 1-mm-wide embedded copper strip that extends approximately 3 mm into the reservoir, and connects to an external probe point. The probe, along with a graphite probe at the opposite end of each channel, is used to apply an electrical bias directly across the interface between the electrolyte and liquid metal.
A negative DC bias relative to the Galinstan droplet leads to oxide growth on the surface of the liquid metal . The oxide growth is primarily located on the surface facing the channel opening, where the oxidative potential relative to the electrolyte is greatest. The hydrophilic nature of this oxide leads it to increase its contact area with the electrolyte , and the liquid metal begins spreading outwards into the channel at speeds on the order of 2 to 3 mm/s.
Removing the DC bias reasserts the ambient conditions in the channel; the electrolyte reduces the oxidation at the leading edge and, without the mechanical support provided by the oxide layer, the liquid metal retracts back to its minimum-energy position . The time required for this reduction can vary from tens of seconds to several minutes, depending on how thick the oxide layer has become, which in turn dictates how far into the channel the liquid metal has progressed.
A positive voltage applied to the electrolyte relative to the liquid metal (Figure 2) does not result in an oxidizing reaction, and instead generates a buildup of electrocapillary pressure at the channel entrance. When this pressure exceeds the opposing capillary pressure of the channel, rapid flow of the liquid metal into the channel is initiated. The velocity of this flow is a function of both the channel geometry as well as the induced pressure drop caused by the actuation voltage. Thus, the flow velocity can be controlled either by raising the DC potential or by altering the channel dimensions.
For all measured channel widths, a minimum applied voltage of 4 VDC was required to initiate reliable liquid metal flow. As the actuation voltages increase, the flow velocities also increase, with a general trend of faster flow rates in wider channels. Wider channels have reduced capillary force opposing the flow of liquid metal into the channel, resulting in faster liquid-metal flow rates as the channel width increases. As the liquid metal travels further into the channel, its progress is opposed by the hydraulic resistance of the channel as well as the contractile force imposed by its own surface tension. These forces slow the liquid metal continuously so that by the time its leading edge has neared the end of the channel, the speed of the liquid metal has generally decreased from 100 mm/s to 40 to 50 mm/s. However, these speeds still mean that the liquid metal is moving at a rate that is greater than an order of magnitude faster than is possible with electrochemical actuation, allowing for electrically controlled deformations that are much more sensitive to electrical stimuli.
ECA and electrochemical actuation are both unique in their ability to dramatically distort and re-form liquid metal using the direct application of low-voltage and low-power signals. Electrochemical actuation is not dependent on channel geometry and thus enjoys a much wider range of possible deformation, but within the quasi-planar geometries described here ECA is a much more rapid process. Furthermore, the relationship between actuation voltage and oxide formation shown in Figure 6 implies that a sufficiently oxidative voltage can result in oxide growth capable of halting liquid-metal flow in a capillary channel. Since the oxide also wets to the walls of the channel, the liquid metal is trapped in the position in which the strong oxidizing voltage was applied. This is a potentially powerful way of combining ECA with electrochemical oxide deposition; ECA is used to rapidly deform the liquid metal before an oxide layer is developed that provides the mechanical support to maintain the deformation. Reversing the process is achieved by re-applying a small positive bias across the electrolyte relative to the liquid metal (“recapillarity” ).
The liquid metal will remain in this position as long as the adhesive force between the oxide and the channel walls is sufficient to overcome the contracting force of the liquid metal. The prolonged application of the oxidizing voltage will continuously grow the oxide layer, and while this can increase the mechanical stability of the liquid metal it also increases the time required to eventually reverse the deformation by removing the oxide. In the example shown in Figure 8 the oxidizing voltage was removed after approximately 800 ms, and although the NaOH solution immediately begins to dissolve the oxide layer this process can take anywhere from tens of seconds to several minutes before the mechanical stability is compromised. To maintain the deformation for longer periods of time, the oxidizing bias can be periodically applied in short bursts to restore the oxide that has been removed by the electrolyte.
To reverse the process, a small positive voltage is applied, which rapidly reduces the oxide layer at the leading edge and defeats the mechanical stability provided by the oxide . This voltage also restores ECA conditions in the channel, which re-initiates flow for the bulk liquid metal even before the oxide layer has been fully reduced. For this reason the positive bias must be applied in short (tens of milliseconds) bursts to prevent the liquid metal from exiting the channel or stretching to the point of breaking before the oxide has been completely removed. The length of time required for this process varies depending on the thickness of the oxide layer and the extent of liquid metal intrusion into the channel, but in our tests was generally on the order of 4 to 5 seconds (recapillarity for the example shown in Figure 8 took approximately 2 seconds).
Electrocapillary actuation is demonstrated to be an effective means of inducing motion in a liquid-metal droplet trapped in a quasi-planar (w > > h) configuration. The channel geometry maximizes the ratio of surface-area-to-volume of the liquid metal, increasing its sensitivity to surface-tension manipulation. The shape of the liquid metal can be distorted with low-voltage, low-power (~1 to 2 mW) signals that generate pressure by creating surface-tension minima on the face of the liquid metal. Once the liquid metal is distorted, voltage-controlled oxide formation can be used as a switch to maintain the shape of the liquid metal. This process can be quickly and completely reversed by reducing the oxide with a small DC bias of opposite polarity .
We believe this method can be used as a low-power means of controlling the shape of a liquid-metal droplet, and has applications for microfluidics, DC and RF switching, optics, and tunable RF devices, such as an RF filter with a tunable passband .
This work was supported by the National Science Foundation under Grant ECCS-1101936.
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