Introduction

Rotary motion is fundamental to countless mechanical systems and technologies, from the earliest waterwheels to modern combustion engines. Rotation occurs around a central axis and is described by its rotational speed, often expressed in revolutions per minute (rpm). Despite the diversity and complexity of real-world designs, most rotary motors can be grouped into a few fundamental categories of energy conversion, including electrical (e.g., electromagnetic motors), thermal/chemical (e.g., internal combustion engines), and fluidic (e.g., wind or hydro turbines). Nearly all rely on numerous complex moving parts, and it has been decades since the emergence of a widely adopted new rotary motor concept. Consequently, any structure that introduces a fundamentally different mechanism of rotation is regarded as an important progress in the field.

The emergence of room-temperature liquid metals, such as non-toxic gallium and its alloys, has enabled unconventional approaches to actuation combining electrochemical and fluidic phenomena1. When a liquid metal droplet (LMD), immersed in an electrolyte, is exposed to an electric field, a strong surface motion, so-called Marangoni flows, appears along the droplet’s surface2. This, in turn, creates internal LMD vortices due to the conservation of mass. As an actuator, the resulting hydrodynamic surface flow generates a net force that propels the droplet forward3. At present, most liquid metal-based actuators take advantage of this propulsion effect and translate it into mechanical work and motion4.

The mechanical actuation of LMDs in electrochemical environments can also be exploited for motor concept development5,6. Motors that integrate electrolytes with self-propelling liquid metals have been demonstrated7,8,9,10. Also, LMDs actuated by external magnetic11,12 and acoustic fields13 have been shown. However, a key challenge remains in establishing reliable mechanisms for liquid metal-based mechanical rotation that effectively convert electrical energy into rotary motion. Several designs have been tested to extract the mechanical movement from the electrolyte and liquid metals, e.g. encapsulations for LMDs to provide a functional mechanical access point which can be used to create a moving platform14,15 or a rotating wheel16. Other examples include ‘hamster wheel’-like architectures using the LMD movement inside a wheel to generate rotation17,18,19. However, these liquid metal motors create rotation ‘indirectly’ via the viscous force between the LMD surface Marangoni flows and the surrounding electrolyte. This implies a significant loss of energy due to the smoothness of the LMD/electrolyte interface. Additionally, those motors require intermediate components like a wheel or structural parts to outsource motion from the movement of the LMD. The indirect conversion of LMD Marangoni flows into mechanical motion, particularly rotary motions, is limited by the low energy conversion efficiency and high complexity and thus low reliability in system design. To date, such limitations have restricted the achievable rotational speed to below 60 rpm in previous studies16,17. A promising approach to overcome these challenges is the direct conversion of the LMD vortex motion into mechanical rotation.

Here, we introduce a fundamentally different type of liquid metal-based electrochemical-fluidic motor that eliminates intermediate moving parts (e.g. bearings, structural components) and relies directly on the internal vortices of the liquid metal due to Marangoni convection (Fig. 1a (i)). This motor operates by placing the LMD into an electrolyte and applying a voltage to two electrodes immersed in the solution, which induces vortices inside the LMD without direct contact with the droplet. When the LMD is held in place, avoiding its bulk actuation, internal vortices driven by Marangoni flow can be harnessed to rotate a paddle inserted into the LMD (Fig. 1a (ii)). By placing a copper (Cu) cross-shaped paddle inside the LMD, our motor design functions as a liquid metal droplet rotary paddle motor. The Cu paddle is an integral part of the motor and acts as the rotating motor shaft. It provides peripheral connectivity, separating the system from the electrolytic environment without additional components. This LMD paddle motor is driven by pulsed electric signals which create stronger, and more energy efficient Marangoni flows compared to continuous driving signals.

Fig. 1: A liquid metal-actuated Cu paddle motor driven by pulsed electric signals.
Fig. 1: A liquid metal-actuated Cu paddle motor driven by pulsed electric signals.
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a Illustration of the internal LMD vortices (i) and the Cu paddle inserted inside the LMD (ii). b Schematic of the LMD paddle motor within an alkaline electrolyte showing the sideview (top image) and top view (bottom image). Graphite electrodes on each end create an electric field (gray arrows) across the electrolyte. The top view indicates the electrolyte flow (blue arrows). c Electrolyte flow-field visualization highlighted with food dye. The inset in (i) shows the rotation of the Cu paddle. Scale bar: 10 mm. d PTM-signal with ton = 10 ms, toff = 10 ms and U = 10 V. e Rotational speed measurements for varying U with constant ton = 10 ms and toff = 10 ms. f Rotational speed measurements for varying r with ton = toff = 10 ms and U = 10 V.

Results

Liquid metal droplet rotary paddle motor design

The LMD paddle motor consists of a eutectic gallium-indium (EGaIn) droplet, which is liquid at or near room temperature (EGaIn melting point is 15.7 °C). The droplet is placed inside a 3D-printed container filled with a 2 M sodium hydroxide (NaOH) solution (Fig. 1b). The NaOH concentration is chosen based on past reports regarding the most stable Marangoni flow generation around a LMD20. Two graphite electrodes, positioned at the two ends of the container (width b = 11 mm, height z = 7.4 mm) by a distance a, create an electric field across the electrolyte when a voltage U is applied. EGaIn naturally forms an amphoteric oxide skin when surrounded by an oxygen containing medium21. The alkaline solution continuously dissolves this oxide layer, while forming negatively charged gallate ions. Under the applied external potential gradient, these ions are redistributed, polarizing the LMD and generating a surface tension gradient across its surface22. This gradient induces Marangoni flows along the droplet surface, while simultaneously generating convections in the form of vortices inside the LMD. This is likely due to the high surface tension of the LMD that tends to remain in a spherical shape with minimal surface energy, together with the mass flow conservation, which forces the LMD to form internal vortices with the impact from the outside in. These vortices also cause a hydrodynamic force propelling the LMD toward the anode. Eventually, to immobilize the LMD, the droplet is placed inside a 1.4 mm deep geometrical depression in the housing.

The LMD paddle motor uniquely harnesses the internal LMD vortices by embedding a cross-shaped Cu paddle directly within them (Fig. 1a, Fig. S1). In contrast, most liquid metal-based actuators use the LMD Marangoni flows only indirectly through the viscous force between the moving LMD surface and the surrounding electrolyte15,23. Like a waterwheel, our LMD paddle motor directly translates the internal LMD vortices to create mechanical rotation, as a result of pushing the Cu paddles (Movie S1). To enhance wettability with EGaIn, the Cu paddle is pretreated in an acidic solution24. The Cu paddle sits in two narrow slits in the housing with one end extending outside the motor to enable peripheral connection (Fig. 1c (i)). The small slit spacing (0.6 mm) and the high surface tension of the electrolyte prevent electrolyte leakage.

The positional fixation of the LMD has been commonly employed to create a pumping or mixing effect of the surrounding electrolyte in a closed electrolyte loop25,26. Here similarly to establishing an electrolyte loop, the motor architecture includes a ‘bypass channel’ (created with a ‘wall’) to facilitate electrolyte circulation (Fig. 1b, blue arrows in top view). Without this bypass, the LMD would pump the electrolyte from the anode side (decreasing electrolyte volume) toward the cathode side (increasing electrolyte volume), thereby disrupting the driving electric field force. Flow-field visualization highlights the electrolyte path around the LMD (Fig. 1c (ii)) and through the bypass (Fig. 1c (iii), Movie S2).

Influence of driving signals and motor geometry on performance

In our previous study, we demonstrated that driving LMDs with pulse-time modulated (PTM) signals, compared with direct current (DC) signals, remarkably increases the droplet speed, stability and energy efficiency in operation27. Here, the LMD paddle motor is likewise driven by PTM-signals that are defined by the on-state time ton, off-state time toff and U (Fig. 1d). The initial experiments use PTM-signals with ton and toff at 10 ms at 10 V. The current consumption is 59 mA which is 50% less compared to continuous driving signals. The power consumption is primarily determined by the electrolysis reaction on the electrodes. Results show that by reducing the NaOH concentration to 0.5 M lowers the electrolysis activity and decreases the power consumption by 31% to 41 mA compared to the 2 M NaOH solution (Fig. S2). However, no significant change in rotational motor speed is observed for varied NaOH concentrations (0.5 to 3 M). The LMD paddle motor shows no rotation for PTM-signals with U < 8 V and U > 22 V (Fig. 1e). Within this range, the rotational speed profile shows two local peaks with maxima of 334 rpm at 10 V and 282 rpm at 17 V. The decline after the first peak may result from increased electrolysis at the electrodes inhibiting the electric field. A further increase in U strengthens the electric field, overcoming the electrolysis effect and may explain the rise to the second peak. However, higher U intensifies both the electrolysis and oxide skin formation, which ultimately reduces the Marangoni flow until the Cu paddle stops moving.

The measured rotational speed across different droplet sizes with the LMD radius r shows an overall stable range from 201 to 265 rpm with a minimum r of 2.7 mm and a maximum r of 3.2 mm (Fig. 1f). Within that range of droplet size, the LMD paddle motor drives continuous rotation of the Cu paddle. Outside that range, no or only very hesitant paddle rotation is observed. Since the capillary length of EGaIn is ≈ 3 mm, which is the critical size where surface tension forces and gravitational forces are equal, it is to be expected that the highest rotational speed occurs around this droplet size. Smaller LMDs generate weaker Marangoni flows due to a reduced surface tension gradient, whereas larger LMDs deform into flattened, non-spherical droplet shapes under the influence of gravity. In both cases, the relative vertical Cu paddle position inside the LMD is altered, likely contributing to the decline in rotational speed.

The vertical Cu paddle position z is determined by the slit height, and it is found to be a crucial design criterion for stable motor operation. The optimal motor performance is achieved when the paddle is placed in the upper half of the LMD (z = 2.4 mm) which reaches up to 300 rpm (Fig. 2a, b (i)). Paddle positions at the center (z = 2 mm, Fig. 2b (ii)) and lower half (z = 1.6 mm, Fig. 2b (iii)) of the LMD show no motor rotation. This result further supports the influence of changing droplet sizes (Fig. 1f).

Fig. 2: Cu paddle position and electrode distance analysis.
Fig. 2: Cu paddle position and electrode distance analysis.
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a Rotational speed measurements for different Cu paddle positions in z-direction. b Schematic of the vertical Cu paddle position inside the LMD. c Rotational motor speed measurements for different a. d Schematic of the horizontal LMD position change relative to the Cu paddle. e The voltage field distribution for U = 10 V at a = 40 mm (sideview). f The electric field distribution at a = 40 mm for the side view (i) and top view (ii). g The voltage field distribution for U = 10 V at a = 20 mm (sideview). h The electric field distribution at a = 20 mm for the side view (i) and top view (ii). i Images of the LMD top view at a = 40 mm before motor start (i) and during motor operation (ii). j Images of the LMD top view at a = 20 mm before motor start (i) and during motor operation (ii).

The two electrodes on each end of the motor create the voltage gradient across the electrolyte, which is crucial for generating the LMD vortices. Therefore, the voltage U and the electrode distance a are both relevant to the motor performance. Using a PTM-signal with U = 10 V and ton = toff = 10 ms, the decrease of a, which means an increase of the voltage gradient, shows a decrease of the motor rotational speed (Fig. 2c, Fig. S3, Movie S3). This directly correlates to the observed decrease in rotational speed for increasing U (Fig. 1e). Notably, the results show that when the LMD is manually pushed with a pipette for a = 20 mm, the motor speed drastically increases from 143 rpm to 240 rpm (Fig. 2d (iv), Movie S4). It also indicates the gradual displacement of the LMD with an increasing voltage gradient (Fig. 2d). This observation shows once more the importance of the Cu paddle position but here horizontally within the LMD.

A homogenous and unidirectional voltage gradient is essential for generating strong Marangoni flows. The simulated voltage distribution at a = 40 mm shows an even voltage distribution (Fig. 2e). In contrast, at a = 20 mm, the distribution tilts toward the LMD (indicated with the dashed line), which likely contributes to the decline in rotational speed (Fig. 2f). Similarly, the simulated electric field at a = 20 mm (Fig. 2h) is more concentrated on the LMD surface near the electrodes compared to a = 40 mm (Fig. 2f). For optimal polarization and strong Marangoni flows, the electric field should be evenly distributed on both sides of the LMD. These results suggest that electrode design and spacing can negatively affect the flow behavior of the internal LMD vortices. Additionally, the depression used to hold the LMD may further introduce asymmetry in the driving electric field.

A closer examination of the LMD position during motor operation shows that the housing depression is insufficient to firmly stabilize the droplet in its position at shorter electrode distances (stronger voltage gradients). At a = 40 mm, the LMD remains stable in position (Fig. 2i), whereas at a = 20 mm, the droplet shifts toward the electrode and shows slight deformation from its spherical geometry (Fig. 2j). This observation supports our claim that changes in the relative horizontal position of the Cu paddle within the LMD are likely the primary cause of the reduced rotational speed (Fig. 2d (i-iii)). Although it’s challenging to have direct insights into the internal LMD vortices, these results further emphasize the critical role of both the vertical and horizontal Cu paddle position and the LMD dynamics in the performance of this motor design.

The polarization of the LMD, when exposed to the electric field, promotes the surface oxidation on the anodic side of the LMD. This oxide skin reduces the LMD surface tension and inhibits surface Marangoni flow28. As our previous work showed, PTM-signals are more effective in creating strong LMD motion than DC signals, since they allow the LMD to recover from the oxidation during the toff period27. Here, the electrolyte dissolves the oxide and restores the LMD surface properties. Using PTM-signals with ton = 10 ms at 10 V, while varying toff (Fig. 3a) in the range of 2 to 20 ms, shows average paddle rotation speeds from 216 to 286 rpm (Fig. 3b, red curve), when a is 40 mm. For toff < 2 ms and toff > 20 ms, no or highly unstable paddle rotation is observed. Notably, no paddle motion is seen under DC excitation (toff = 0 ms). Additionally, the ratio of the current consumption under PTM-signals (I) to that under DC-signals (IDC) highlights the reduced power usage with PTM, as no power is consumed during toff (Fig. 3b, green curve). Changing both ton and toff shows high-speed motor operation at 10 and 20 ms, which aligns with results from our previous study (Fig. 3c)27. While the electric field drives Marangoni vortices, it also promotes partial oxide growth on the EGaIn surface, reducing hydrodynamic activity over time. PTM-signals use intermittent resting cycles by switching the signal off, which allows the alkaline environment to dissolve the oxide layer to maintain droplet performance. Nonetheless, prolonged toff reduces the LMD activity and paddle rotational speed due to friction between the EGaIn, electrolyte, and Cu paddle.

Fig. 3: PTM-signal analysis and LMD paddle motor demonstration.
Fig. 3: PTM-signal analysis and LMD paddle motor demonstration.
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a Schematic of PTM-signals with increasing toff. b Rotational speed measurements for varying toff with fixed ton = 10 ms and U = 10 V (red curve). toff = 0 is equal to a DC-signal. The green curve shows the power consumption efficiency of using PTM-signals (fixed ton = 10 ms) in relation to a DC-signal. c Rotational speed measurements for varying ton and toff at U = 10 V. d Photos of the LMD paddle motor demonstrator with a propeller attached to the motor shaft end. Scale bar: 10 mm. e Rotational speed measurement over time for the LMD paddle motor demonstrator from (d).

Propeller motor demonstration

To evaluate the functionality and durability of the LMD paddle motor, a propeller is attached to the external end of the Cu shaft (Fig. 3d). Driven by PTM-signals (ton = toff = 10 ms, U = 10 V), the motor is able to rotate the propeller continuously (Fig. 3d (i-iii), Movie S5). The propeller is isolated from the electrolytic environment, thereby demonstrating peripheral mechanical connectivity. The LMD paddle motor demonstrates continuous operation (80 min is shown in Fig. 3d). The motor torque τ is estimated to be 0.15–25 nNm (Fig. S4). Although the measured torque remains below that of commercial electromagnetic rotary motors, this work establishes a foundational demonstration of liquid metal-based rotary motors, with future work expected to explore procedures for torque improvement. The observed rotational speed gradually declines from 220 to 180 rpm. The electrolysis on the electrodes evaporates the electrolyte and decreases its volume over time, which may interrupt the electric field. Another observation is the decrease in droplet size over time. The perpetual generation and dissolution of the oxide skin shrinks the LMD and raises the relative vertical Cu paddle position inside the LMD, which is crucial for the motor performance (Fig. 2b). It is likely that implementation of future strategies, such as change of electrolyte, and alteration of the design structure, can mitigate this effect.

Discussion

In this work, we demonstrated a liquid metal–based electrochemical-fluidic motor with an inserted paddle. This motor achieved a peak rotational speed of 320 rpm, a substantial improvement over previously reported liquid metal motors, which reached at most 60 rpm17,18. The enhancement arises from directly extracting rotational motion via the paddle inside the LMD, rather than relying on less efficient friction-based strategies.

We further characterized the motor that operates by PTM across varying electrode distances, applied voltages, electrolyte concentrations, droplet sizes, and on/off time ratios of the applied alternating voltage, identifying conditions that optimize performance. Future motor design improvements may include reducing electrolysis by minimizing the electrode distance from the droplet (thereby lowering the required voltage), decreasing the electrolyte concentration, and enhancing motor performance, e.g. through an optimized paddle design.

This unique motor design offers an efficient means of converting electric-field-induced Marangoni flows into mechanical rotation in liquid metal, while remaining compact, self-contained, and free from additional moving parts. The LMD paddle motor represents a fundamentally new type of actuation system, leading to possibilities for micromechanical systems, soft robotics, and biomedical devices, where miniaturization, softness and mechanical simplicity are critical.

Methods

Materials and methods

The liquid metal is EGaIn, prepared by melting 75% gallium and 25% indium at 200 °C. The alkaline electrolyte is a 2 M sodium hydroxide (NaOH) solution. The housing material is 3D printed with polyamide. The paddle design is cut out by a CO2-laser from a Cu plate and consists of two pieces that slide together to form the cross-shaped Cu paddle (Fig. S1). The pulsed signals are timed by an Arduino microcontroller, while U is provided by an external power supply via a relay.

Measurements

The rotational speed of the LMD paddle motor is measured by recording the rotation of the bent Cu paddle end with a 60 Hz camera. The number of video frames for 10 complete paddle revolutions is measured to calculate the mean, minimum, and maximum rotational speed. The torque τ is derived from the measured angular shaft position from the initial acceleration phase of the motor.

Simulation

Numerical simulations of the voltage and electric field distribution in the liquid metal paddle motor are performed using the Electrostatic Module of ANSYS Electronics (ANSYS Inc.). The electric potential is obtained by solving Poisson’s equation, assuming a negligible free charge density in the 2M NaOH electrolyte. The electric field is calculated as the gradient of the potential. The setup includes two 6 mm graphite electrodes at 0 V and 10 V, and a 3 mm liquid metal droplet modeled as a conductive sphere with floating boundary conditions. Simulations are conducted for electrode separations of 20 mm and 40 mm, matching the experimental geometry.