Rapid swimmer using explosive boiling due to electrical discharge in water

A strong micro heat engine that can be used in the untethered state is essential for next-generation microrobots and microswimmers.^1–3 In particular, the boiling phenomenon is promising to produce large mechanical energy from heat energy. Thus, various studies have been devoted to this issue.^4–14 For example, by using a Leidenfrost phenomenon [which is a kind of film boiling phenomenon^5,15–21], Hashmi et al.⁶ demonstrated that a solid cart having water droplets on the bottom can move at the velocity of ∼0.16 m/s on a hot ratchet surface, while Wells et al.⁷ demonstrated that levitating dry-ice blocks rotate on hot turbine-like surfaces. Furthermore, Xu et al.⁸ demonstrated that a paper-made rotor can rotate at the angular velocities of more than 30 rad/s due to the Leidenfrost phenomenon, while Dodd et al.⁹ demonstrated that micropatterned electrode heaters can provide a motion of a droplet through the Leidenfrost phenomenon. Moreover, Li et al.¹⁰ demonstrated that the segmented film cut by a Z-shaped pattern can spin a drop. However, the above-mentioned devices receive heat energy from a high-temperature surface, and thus, they are difficult to apply directly to microrobots or microswimmers that move freely in water or on the surface of the water.

Numerous swimmers^1–3,22 have been proposed ranging from micro- to centimeter-scale (or meter-scale), and some of them have been analyzed from the viewpoint of the fluid dynamics extensively. In particular, the swimming problem related to the scallop theorem^23,24 has been studied extensively for micro-scale swimmers at a low-Reynolds-number region because of the expectation of various biomedical applications, while the flopping problem^25–28 has been studied extensively for centimeter-scale (or meter-scale) swimmers at a relatively large-Reynolds-number region to develop autonomous underwater vehicles (AUVs) based on aquatic animals' swimming, which can be applied mainly to underwater research or exploration. For example, for the small-Reynolds-number problem, Felderhof²³ mathematically clarified that the velocity of a three-sphere chain swimmer increases slightly in syrup compared to that in water, while Eberhard et al.²⁴ investigated an oscillating two-sphere swimmer in a weakly viscoelastic fluid and numerically showed that the swimmer moves toward the smaller sphere. Furthermore, for the relatively large-Reynolds-number problem, Wu et al.²⁷ investigated the hydrodynamic performance of a self-propelled carangiform swimmer with a flexible caudal fin and numerically clarified that moderate rigidity increases the hydrodynamic performance, while Pourfarzan and Wong²⁸ showed the effect of the amplitude ratio on the propulsive performance of in-line tandem pitching foils inspired by the plesiosaur flippers. These studies reveal the importance of controlling the flow around swimmers. However, a method to control the flow around the swimmer using explosive vaporization with underwater electrical discharge has not been explored yet in spite of the possibility that it provides an untethered powerful thermal propulsion method that can be used across a wide range of device sizes from micro to centimeter scale.

Underwater electrical discharge^29–33 accompanies a generation of bubbles with shock waves, and it is often used for the disintegration of kidney stones,³⁴ water treatment³⁵ (which decomposes a variety of harmful organic compounds), pretreatment,³⁶ and synthesis of materials.³⁷ For example, Merciris et al.³⁷ reported the synthesis of nanoparticles by pulsed underwater discharges, while Ueda et al.³⁶ reported shock wave effects on underwater discharge as a pretreatment for enzymatic saccharification. Moreover, electrical discharge in the gas phase is widely used in many applications; e.g., plasma spray³⁸ using electrical discharge is well known as a typical surface coating method in the industry, while electrical discharge machining is very common.³⁹ Furthermore, in the field of fluid engineering (especially, aeronautical engineering), discharge plasma actuators are important to prevent damage to the body, noise, and vibration due to the shock wave and boundary layer interaction (SWBLI), and thus, there exist many studies on this issue.^40–45 For example, Ma et al.⁴³ numerically clarified the control effect of the pulsed arc discharge plasma on the impinging shock wave and SWBLI in a Mach 2.5 flow, while Chen et al.⁴⁰ reported the detailed characteristics of a nanosecond dielectric barrier discharge plasma actuator to explore the engineering potential for flow control.

In this context, we previously demonstrated that a hot object having a ratchet structure under the body can move at the velocity of ∼0.2 m/s on a shallow water layer through the Leidenfrost phenomenon.⁴⁶ Furthermore, we demonstrated that by using an electrical discharge in water, a centimeter-scale object can be launched into the air with an initial velocity ∼4 m/s.¹⁴ However, how to supply energy to the untethered devices that utilize such boiling phenomena remained an important issue. To overcome this problem, we here consider using an antenna to receive energy from a pair of the parallel electrodes, and then, we drive our swimmer by using an explosive evaporation due to an electrical discharge in water. Therefore, in this study, we focus on the development of the rapid swimmer using explosive boiling due to electrical discharge in water and elucidate its design concept. In particular, we demonstrated that by applying direct current (DC) high-voltage pulses repeatedly between a pair of parallel electrodes, the water-repellent swimmer that has an aluminum discharge antenna in the rear part can swim with the maximum velocity of ∼14 cm/s on the water surface in a shallow water pool, like a water strider.

Figure 1 shows a schematic view of a rapid swimmer using explosive boiling due to electrical discharge in water. Specifically, Fig. 1(a) is a plan view of the measurement system. As shown in Fig. 1(a), by placing plural slide glass plates on a (vinyl chloride) flat plate with a thickness of 1 mm, we fabricated a rectangular shallow pool of width l₁ (=15 mm), length l₂ (=76 mm), and depth of 2 mm. Furthermore, we set a copper (Cu) tape of length 60 mm (thickness 18 to 30 μm) in an L-shape manner along the upper and lower walls as a pair of parallel electrodes. After injecting water (distilled water) into the pool to depth h_w (=1 to 2 mm), we applied high-voltage pulses intermittently by a high-voltage pulse power supply (peak voltage: ∼70 kV, peak current: ∼40 A, typical pulse width of the current: ∼70 μs), and observed the motion of the device (swimmer) with a video camera (Panasonic Co., LUMIX DC-TZ90 or Sony Co., DSC-RX100M4). Figures 1(b) and 1(c) are the plan and side views of the swimmer, respectively, while Fig. 1(d) shows the photograph of the swimmer. As shown in these figures, the swimmer was made by sandwiching aluminum (Al) foil [of thickness 11 μm, width d (= 1 to 5 mm), and length w₄ (=2.5 mm)] to a pair of polyethylene terephthalate (PET) flat plates (of thickness 0.1 mm) with double-sided tape (of thickness 0.1 mm). Here, the shape of the PET body was selected to an isosceles triangle shape with base w₁ (= 8 mm) and height w₂ (= 8 mm), to reduce the flow resistance. Furthermore, the protruding part (of size $d × w 5$⁠) of the Al foil was used as a discharge antenna to accept external energy and to generate electrical discharges at the upper and lower edge of the Al foil. In other words, by providing this antenna, we made it possible to keep moving between parallel electrodes by repeated pulses. In addition, we set the condition that $d < w 1$ so that the pressure (caused by the explosive boiling phenomenon generated by the underwater discharge) becomes the driving force of the swimmer. In other words, we designed it so that the boiling due to discharge occurs in the space sandwiched between the rear wall of the swimmer and the antenna. Moreover, by applying a water-repellent treatment to the back side of the device using a water-repellent agent (CCI Co., smart view), we designed it so that the swimmer floats on the surface of the water due to surface tension. In other words, we devised to reduce the flow resistance by making it move on the surface of the water-like Gerridae (water striders). Furthermore, the green and red vinyl tapes of size $1.5 × 1.5$ mm² were used to detect the azimuth angle θ and position (x_p, y_p) of the device at a time t by using the functions of the open-source computer vision library (OpenCV). Furthermore, the motion route length of the swimmer was defined as $s ( t ) = ∫ 0 t d s$⁠, while the velocity of the swimmer was defined as $U ( t ) = d s d t$⁠. Here, we approximate ds as $d s ≃ ( x p ( t ) − x p ( t − Δ t ) ) 2 + ( y p ( t ) − y p ( t − Δ t ) ) 2$⁠, where $Δ t = 1 / 240$ s (or 1/960 s) is a time interval of the measurement.

Figures 2(a), 2(b), 2(c), and 2(d) (Multimedia view) show photographs of the motion of the swimmer at t = 0/240, 4/240, 28/240, 112/240, and 580/240 s, respectively. Here, Figs. 2(a) and 2(d) show the photographs of the first and second discharges, respectively, while Fig. 2(e) shows the photograph of the final state after the fifth discharge. From these figures, we find that electrical discharge in water occurs repeatedly at the Al discharge antenna, almost vertically symmetrically, and this repeated discharge causes the swimmer to move to the right. Furthermore, from Fig. 2(e), we find that the swimmer moves from $x ≃ 20$ to 50 mm by the five times discharges. Moreover, Fig. 2(f) shows the typical dependence of the applied voltage V₀ and current I₀ on t. From Fig. 2(f), we find that the peak voltage is ∼70 kV, while the peak current is ∼40 A. Furthermore, from Fig. 2(f), we find that although the width of the peak current (or the peak voltage) is ∼70 μs, the voltage of ∼20 kV continues for ∼5 ms after the peak voltage.

Figure 3 shows the quantification of the motion of the rapid swimmer. Specifically, Fig. 3(a) shows the trajectories of the green and red tape positions, while Figs. 3(b) and 3(c) show the dependence of the route length s and azimuth angle θ on t, respectively. Here, arrows 1 to 5 show the points at the first to fifth electrical discharges for N = 1, where N = 1 to 3 is the trial number. In particular, in Fig. 3(a), arrows 1 to 5 (1b to 5b) show the green (red) positions. From Figs. 3(a) and 3(b), we find that the swimmer moves greatly due to the discharges. Furthermore, from Fig. 3(c), we find that the swimmer tends to move slightly diagonally downward immediately after the discharge, and returns to the stable position of $θ ≃ 0$ when the propulsive force subsides. Here, we consider that $θ ∼ 0$ is stable because the water surface in the center between the electrodes is concave due to the hydrophilic meniscus of the electrode walls. Moreover, Fig. 3(d) shows the dependence of U on t. Here, the peaks correspond to the electrical discharges. From Fig. 3(d), we find that the velocity U of the swimmer decreases exponentially with time.

Figure 4 shows the characteristics of the rapid swimmer. Specifically, Figs. 4(a) and 4(b) are the dependence of $s total$ and $U max$ on the water depth h_w, respectively. Here, $s total$ shows the final route length after the five times discharges, while $U max$ shows the maximum velocity during the measurement using the five times discharges. From these figures, we find that $s total$ and $U max$ approximately increase with h_w linearly. This is probably because the flow resistance under the swimmer becomes smaller as h_w increases. Figure 4(c) shows the dependence of s on t at the antenna width d = 1 to 5 at N = 1, while Fig. 4(d) shows the dependence of $U max$ on d. From these figures, we find that $s total$ and $U max$ approximately decrease with d linearly. This is probably because the propulsive force is only produced by the rear wall of the swimmer. In other words, the driving force is considered to be proportional to the length from the antenna's upper (lower) edge to the upper (lower) edge of the rear wall of the swimmer.

Figure 5 (Multimedia view) shows the generation of an asymmetrical wave that occurs immediately after the electrical discharge. Specifically, we found that by the electrical discharge at t = 0/960 s [Fig. 5(a)], the large wave occurred especially behind the rear part of the rapid swimmer [Fig. 5(b)]. This is probably due to the explosive boiling due to electrical discharge in water. In other words, we consider that the bubble having high pressure was generated due to the large heat energy of the electrical discharge between the Al discharge antenna and the electrodes; then, the bubble pushed the left-side water and the right-side body of the swimmer. Consequently, as shown in Figs. 5(c)–5(f), we found that the left-side wave moved in the left direction, while the swimmer moved in the right direction with the right-side wave.

Figure 6 shows the model of the mechanism of the propulsion of the swimmer due to the asymmetrical wave resulting from the high pressure due to the initial bubble expansion. Specifically, Fig. 6(a) shows that, in the initial state, the swimmer with a water-repellent bottom surface floats on the surface of the water due to surface tension. Then, by the Joule heat of the electrical discharge in water, the high-pressure bubble is generated behind the rear part of the body of the swimmer, as shown in Fig. 6(b). Consequently, because of the initial pressure of the bubble, the left-side wave moves to the left, while the swimmer moves to the right with the right-side wave, as shown in Fig. 6(c). Furthermore, because of the motion of the swimmer, the flow velocity under the swimmer becomes the Couette flow, as shown in Figs. 6(a) and 6(b). Consequently, we consider that $s total$ and $U max$ increase with h_w [as shown in Figs. 4(a) and 4(b)] because the shear stress of the Couette flow is inversely proportional to the water depth h_w. Moreover, this model tells us that the propulsion force is proportional to the length of $w 1 − d$⁠. Thus, it explains the results of Figs. 5(c) and 5(d) to some extent.

Figure 7 shows the comparison between the theoretical and experimental results. Specifically, Figs. 7(a) and 7(b) show the dependence of U and s on t, respectively, at h_w = 2 mm and d = 3 mm. Here, the experimental data of U and s correspond to the motion of the first discharge at N = 2 in Figs. 3(b) and 3(d). From the fitting between the experimental and theoretical results in Fig. 7(a), we obtain that $η = 10 5$⁠, A = 60 Hz, and $f 0 = 1.5$ N; i.e., we assume a large apparent viscosity $μ *$ with a relatively large f₀. This is because, in a relatively narrow pool, the entire surface of the water must be moved in an instant against the front wall in order to move the boat instantly. Furthermore, from Fig. 7(b), we find that although the theoretical value of s agrees with the experimental result at $0 < t ≤ 0.05$ s, the theoretical value does not agree with the experimental value at t > 0.05 s; i.e., s continues to increase experimentally even at t > 0.05 s although it becomes constant theoretically at t > 0.05 s. This is because the swimmer continues to move by advection even at t > 0.05 s because the background flow does not stop. Note that there is a large fluctuation for f₀ due to the fluctuation of $U max$⁠; e.g., we need to assume $f 0 = 3.0$ N to fit the experimental data at N = 1.

Figures 7(c) and 7(d) show the dependence of $U max$ on h_w and d, respectively. From these figures, we find that the experimental dependence of $U max$ on h_w and d can be explained well by our simple theory. Here, there is a tendency that the theoretical values are smaller than the experimental values in spite of that the prediction (⁠ $U max ≃ f 0 h w μ * A 0$⁠) should overestimate the maximum value U [as shown in Figs. 7(a) and 7(b)]. This is because the experimental values of $U max$ in Figs. 7(c) and 7(c) are the average values of the maximum values for the five discharge events in each N.

The average electric field E₀ between the parallel electrodes is written as $E 0 = V 0 l 1 = 4.0$ MV/m, while the superficial discharge electric field $E 1 * ≃ V 0 l 1 − d = 4.3$ to 5.0 MV/m at d = 1 to 5 mm, i.e., $E 1 * / E 0 ≃ 1.075$ to 1.25. Here, if there is no device between the parallel electrodes, the discharge will occur at the edge of the parallel electrodes. However, more importantly, due to the shape effect of the antenna, the electric field concentration occurs locally; as a result, a strong local electric field $E 1 local$⁠, which is two to three times larger than E₀, occurs. Thus, if the device with an antenna of length d is placed between the electrodes, a discharge will occur reliably at the antenna part; i.e., discharges always occur where the local electric field is strongest. Therefore, the distance l₁ between the parallel electrodes, which is the width of the pool, should be selected so that discharge occurs when the strong electric field is generated locally. For example, since Buogo and Cannelli⁴⁷ reported an underwater spark-generated bubble at $E 0 = 1.175$ MV/m, we consider that we can expand l₁ from 15 to 51 mm (⁠ $∼ 15 × 4 / 1.175$ mm) at least in the future, and probably, we can expand it 100 to 150 mm because of the shape effect of the antenna part. However, since there exists a downwardly convex meniscus between the electrodes, the swimmer now can move approximately in the x direction even if the direction of propulsion by the electric discharge fluctuates. Therefore, if l₁ becomes large and the influence of the meniscus weakens, the swimmer might not move in a straight manner; in other words, the condition that $l 1 ∼ w 1$ plays an important role to propel the swimmer in the x direction.

One of the important factors that determine $F 0 * = f 0 e A t$ in our model represented by Eq. (1) is the intensity of the electrical discharge. Here, the electrical discharge we are observing is considered to be a spark discharge because the high voltage (⁠ $V 0 ∼ 70$ kV) causes a large current (⁠ $I 0 ∼ 40$ A) only for a short period (⁠ $Δ t ∼ 70$ μs). That is, the instantaneous power $P 0 = V 0 I 0$ is 2.8 MW, and the thermal energy released during the period $Δ t ∼ 70$ μs is 196 J. Now it is not fully known how much water evaporates instantaneously. However, if we assume that a cylindrical region with a diameter $ϕ$ of 0.1 mm and a length l₁ of 15 mm becomes a conductive path in the average sense, the surface area S₀ is to be 4.695 mm², and thus, the instantaneous heat flux q₀ is estimated to be about 0.596 TW/m². Here, 0.596 TW/m² is an incredibly large heat flux compared to the heat flux $∼ 1$ GW/m² of the ordinary film boiling. Thus, we consider that this extremely large instantaneous heat flux is the origin of the explosive evaporation and the origin of the strong propulsion force of our swimmer.

Our swimmer can move with a high velocity (∼14 cm/s) on water. Thus, in microfluidic systems, our swimmer can be used as a sample carrier (or belt conveyor and batch processing tool) using the surface of the swimmer as a substrate. That is, as shown in Fig. 8(a), various treatments can be applied to the substrate surface while moving the swimmer at high speed. Of course, it is expected that a method of forming a substrate holder on the swimmer and carrying a small substrate is also possible. Furthermore, in the future, not only the manufacturing process but also applying reagents and inspecting with light will probably be possible.

By providing electrodes outside and inside the circular channel, our swimmer can continue to move within the circular channel. Furthermore, underwater electrical discharge is often used for water treatment. Thus, by making an inlet and an outlet in the circular channel and introducing the water to be treated, we can apply our swimmer to water treatment, bio-application pretreatment, virus removal, and sterilization systems, as shown in Fig. 8(b). Here, we can expect that water agitation and mixing will occur effectively because a large wave (in Fig. 5) is generated near the swimmer due to the underwater discharge.

From our findings, if we introduce rotational asymmetry into the antenna part, we may realize a device that continues to rotate between the electrodes in the future. This rotational motion probably enhances the agitation and mixing function further along with the sterilization function. In other words, our swimmer can be applied to a rotary mixer with a sterilization function. Furthermore, by making inlet and outlet parts with check valves, we may realize a mixer with pumping and sterilizing functions, as shown in Fig. 8(c). Therefore, we consider that our presented results are important.

Our presented results at least showed that powerful heat engines can be driven without the need for large batteries. In other words, we showed that enough energy can be supplied from the outside without wires to drive the heat engine. In particular, selective discharge due to an antenna has opened a way to the untethered microrobots. In fact, the above-mentioned applications will be realized based on the selective discharge technique. However, to develop navigatable microrobots and microswimmers that can move freely between electrodes, it is necessary to clarify how to control the direction of motion in the future.

We previously demonstrated that the launcher using the explosive boiling in water can launch the centimeter-scale object of mass 60 mg can be launched into the air to the height of $∼ 12$ cm with the maximum velocity $∼ 1.5$ m/s.¹⁴ Thus, the provided kinetic energy (for the previous study) by the explosive boiling is approximately 70 μJ. Here, the provided kinetic energy E_k for the current device is approximately 0.18 μJ because $m p ∼ 9$ mg, $U max ∼ 0.2$ m/s; i.e., E_k of the current device is 389 (= 70/0.18) times smaller than that of the launcher using the explosive boiling. This is mainly because the current device moves the entire water (∼2.3 g) of the pool with a velocity ∼0.2 m/s; i.e., the kinetic energy of the entire water is ∼47 μs. Therefore, we consider that our current device has a lot of room for improvement.

Hashimi et al.⁶ demonstrated that the Leidenfrost cart on the droplet on a hot ratchet moves with a velocity ∼0.16 m/s. However, this device requires the hot ratchet at more than ∼ $150$ °C as a working plain. For this problem, we previously demonstrated that the glider (mass: 1.8 g) using the Leidenfrost phenomenon (a kind of film boiling) with the ratchet structure under the device⁴⁶ moves on shallow water with a velocity ∼0.2 m/s; i.e., the provided kinetic energy is 36  $μ J$⁠, which is 20 (=36/0.18) times larger than that of the current swimmer. However, different from the current device, the glider cannot move for a long time because the previous device moves while releasing the thermal energy stored in the device. Therefore, our device is important because it can continue to move by supplying energy from the outside with an untethered state.

Piñan Basualdo et al.⁴⁸ demonstrated a microrobotic platform actuated by thermocapillary flows for manipulation at the air–water interface. Specifically, they showed that 500-μm-diameter steel spheres can be manipulated precisely with a velocity of ∼11 mm/s for a laser power of 150 mW. Their fabrication system is innovative. However, it needs to control the laser irradiation position precisely according to the motion of the objects and the moving speed of the object is approximately 1/10 times smaller than that of our swimmer. Okawa et al.⁴⁹ showed that a boat using a carbon nanotube-dimethylpolysiloxane (PDMS) composite can be driven by the laser beam of 450 mW with a velocity of ∼16 mm/s due to the thermo-capillary flow. Therefore, although the swimmer using a thermo-capillary flow with a laser beam is promising to control the objects in an untethered state, we find that the velocity of those swimmers is much smaller than our swimmer using an explosive boiling phenomenon.

Although we previously demonstrated a solid-object launcher¹⁴ using an electrical discharge in water, we have first shown a rapid swimmer using explosive boiling due to electrical discharge in water. In particular, by using an antenna structure, we succeed in selectively inducing a discharge at a specific position (rear part) of the device. In addition, this makes it possible to realize a swimmer with a strong propulsive force capable of moving between parallel electrodes. Moreover, by applying a water-repellent treatment to the device body and making the device float on the water surface by surface tension, we realize a device that can glide on the water surface like a water strider. Furthermore, although we here demonstrate one-dimensional driving, we may realize a device that can move between parallel electrodes two-dimensionally or three-dimensionally in the future. In addition, although we previously demonstrated a Leidenfrost glider⁴⁶ having a ratchet structure under the device on shallow water, in the future, we may continue to drive the Leidenfrost layer by using our technology using an antenna with an electrical discharge. In other words, our finding may contribute to solving the untethered problem of the other devices using boiling phenomena. Therefore, we consider that our technology is expansive and important.

In conclusion, we have proposed a rapid swimmer using explosive boiling due to electrical discharge in water. In particular, (1) we have demonstrated that the water-repellent swimmer that has an aluminum discharge antenna in the rear part can swim with the maximum velocity of ∼14 cm/s on the water surface like a water strider between a pair of parallel electrodes in a shallow water pool by applying DC high-voltage pulses repeatedly. (2) We have discussed the analytical model for the motion of the swimmer and showed that the analytical model [which considers the flow resistance of the Couette flow and the apparent force that is proportional to the length (⁠ $w 1 − d$⁠) of the asymmetrical boiling region at the rear of the swimmer] explains the dependence of U on d and h_w well. (3) We have discussed the practical importance of the presented results by showing three examples, namely, applications to microfluidic sample carriers, water treatment, and rotary pumps with sterilization function. Our findings should contribute to next-generation microrobots in the future.

This work was supported by JSPS KAKENHI Grant No. JP21K18698.

The authors have no conflicts to disclose.

Hideyuki Sugioka: Conceptualization (lead); Funding acquisition (lead); Methodology (equal); Supervision (lead); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead). Yuki Arai: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Software (lead); Visualization (lead).

The data that support the findings of this study are available within the article.