Introduction

Natural organisms predominantly use soft materials to safely and efficiently interact with the environment and others, which has inspired the development of soft systems1,2,3, including soft robotics, wearable devices, and biomedical equipment, etc., to transform the way we interact with machines and environment1,4. Fluid power has become the most popular power mean for these soft systems due to its inherent flexibility5, allowing for a number of unique benefits such as the simplicity of their design, ease of fabrication, and low cost, etc. However, a critical barrier stems from that existing fluidic soft systems mainly rely on traditional rigid components (pumps and valves, etc.) for fluid power generation and control6,7,8,9,10. These standard universal pumps and valves originally developed for rigid mechatronic systems appear too bulky and redundant for nascent soft systems. Especially more and more rigid pumps or valves are required to achieve multi-circuit actuation and control of soft systems, which greatly increases the weight and volume of soft system and limits their portability. Therefore, how to develop portable, powerful, and standard universal fluid power components for soft systems is a key challenge for their technological advances and widespread applications.

To overcome this barrier, scientists and engineers have made a lot of efforts and contributions to develop flexible and portable fluid power components. A series of innovative flexible valves were explored and embedded into soft systems to greatly reduce the need for external rigid control components and simplify the control logic of multiple fluidic circuits, facilitating the versatility and autonomy of soft robotics and wearable devices7,11,12,13,14. Despite these advantages, the requirement of external power sources to pressurize and depressurize working fluid remains a critical challenge that should be addressed simultaneously before untethered soft systems are widely practical. To achieve flexibility and portability of fluid power source, various novel pumps responsive to external stimuli (e.g., thermal, combustion, chemical reaction, phase transition, electrostatic force, etc.) have also been developed15,16,17,18,19,20. These techniques effectively remove fluidic tether but introduce new challenges like slow response speed, poor controllability, limited output density, etc. Furthermore, existing manufacturing methods of these pumps (e.g., casting and manual assembly, etc.) cannot achieve a trade-off between structural complexity, low cost, labor saving, accuracy repeatability, and mass manufacturing, limiting their generality in soft systems.

As is well known, electronic chips achieve high integration and miniaturization of multiple circuits through the combination of many modular transistors, extensively promoting the portability and versatility of electronic products such as mobile phones and computers, etc. Inspired by the modular design concept of electronic chips as well as their great success in portable electronic products, here we apply this modular design concept of electronic chips to develop multi-circuit flexible electro-hydraulic power chips (EPCs), whose shapes and functions can be programmed through different combinations of multiple electro-hydraulic power “transistor” modules. These “transistor” modules can directly convert electrical energy into hydraulic power without any moving parts. Then, flexible materials in combination with multi-material 3D printing techniques are used to freely fabricate the desired flexible EPCs. These 3D-printed flexible EPCs have several distinctive qualities: (i) Chip-integrated design concept and multi-circuit independent control allow soft systems to achieve as much functionality as possible in extremely compact space; (ii) High output density of electro-hydraulic power “transistor” module has been achieved by combining the structural design of non-uniform strong electric field, the selection of lightweight and flexible materials, and the use of near-net 3D printing technique; (iii) Compared with traditional manufacturing method (e.g., casting and manual assembly, etc.), digital 3D printing technique not only dramatically saves labor and time, but also facilitates personalized customization, precision repeatability and standardized mass-manufacture. Successful applications of flexible EPCs in multi-circuit mass transfer, five-finger selective cooling, bird’s multiple actuation, and jellyfish’s fast swimming illustrate their great potential to be popularized in fluidic soft systems.

Structure and working principle of electro-hydraulic power transistor

It is widely known that transistors are the basic modules of electronic chips. Similarly, we have developed our flexible fluid power transistors—electro-hydraulic power “diode” or “triode” — as the basic elements for EPCs. Figure 1a shows a prototype of flexible electro-hydraulic power “diode”, which consists of a triangular-shaped emitter electrode (Conductive Thermoplastic Polyurethane, TPU), a silt-shaped collector electrode (Conductive TPU), and a channel support shell (Non-conductive TPU). Planar layout and flexible materials allow electro-hydraulic power “diode” to be easily fabricated via multi-material 3D printing (Fig. 1b, c, Supplementary Fig. 1, Supplementary Table 1, and Supplementary Movie 1). A unidirectional jet could be generated from emitter to collector electrodes in electro-hydraulic power “diode” (Supplementary Fig. 2 and Supplementary Movie 2). The smallest electro-hydraulic power “diode” we can print weighs 0.13 g and is about one-third of a thumbnail, exhibits high pressure and flow rate density of 10.77 kPa and 2.15 L/min.

Fig. 1: Design, fabrication, and working principle of flexible electro-hydraulic power transistor.
Fig. 1: Design, fabrication, and working principle of flexible electro-hydraulic power transistor.The alternative text for this image may have been generated using AI.
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a Structure of flexible electro-hydraulic power “diode”. Triangular-shaped emitter electrode and silt-shaped collector electrode are conductive TPU, while the support shell is non-conductive TPU. Define the angle of triangular-shaped emitter electrode as α, the horizontal distance between the tip of the triangular-shaped emitter electrode and the collector electrode as l, and the distance between the two collector electrodes as d. b Conceptual illustration of multi-material 3D printing of electro-hydraulic power “diode” using conductive TPU (black) and non-conductive TPU (white). c Fabrication result of electro-hydraulic power “diode”. d Working principle of electro-hydraulic power “diode”. Strong non-uniform electric field dissociate neutral liquid molecules into free electrons and positive ions. Positive ions move along electric fields to collector electrode, dragging liquid flow. e Structure of flexible electro-hydraulic power “triode”. It is made of two emitter electrodes and a collector electrode. f Demonstration of an electro-hydraulic power “triode” to pump liquid between two tanks, and the pumping direction is reversed. g Demonstration of an electro-hydraulic power “triode” to pump liquid from right to left. h Demonstration of an electro-hydraulic power “triode” to pump liquid from left to right.

The working principle of electro-hydraulic power “diode” is given as follows (Fig. 1d): When the emitter and collector electrodes are respectively connected to high-voltage positive and grounding negative electrodes, a non-uniform strong electric field will be formed between them to cause the dissociation of a small amount of neutral liquid molecules into free electrons with negative charges and positive ions. All free electrons will be absorbed by emitter electrode, while the positive ions will move to collector electrode along the direction of electric field gradient. The rapid and continuous movement of positive ions will directly drag the rest liquid molecules flow to generate a strong jet from emitter to collector electrodes. When the positive ions reach to collector electrode, they will combine with free electrons of collector electrode to reform neutral liquid molecules. As long as applied electric field exists, continuous fluid flow will generate in electro-hydraulic power “diode”. Theoretical results of electro-hydraulic power “diode” are consistent with experimental ones (see Supplementary Materials, Supplementary Fig. 3, and Supplementary Table 2), indicating that the working principle is reasonable and accurate. Two triangular-shaped collector electrodes can be symmetrically distributed on either side of one emitter electrode to form an electro-hydraulic power “triode” (Fig. 1e). This “triode” can achieve reversibly bidirectional pumping when two opposite emitter electrodes are selectively connected to high-voltage positive electrode. Figure 1f–h, and Supplementary Movie 3 demonstrate the rapid, controllable, and fast-switching bidirectional fluid flow processes of the electro-hydraulic power “triode”.

Performances of electro-hydraulic power transistor

The output pressure and flow rate of electro-hydraulic power “diode” are determined by a large number of factors, including fluid materials, voltage range, and electrode configuration, and the measurement devices of output pressure and flow rate is shown in Supplementary Fig. 4. In order to choose electrically responsive fluids, the flow capacities of many electrically responsive fluids are tested. Among them, four fluids with different flow capacities (including the most strongest fluid: Linalyl Acetate) are demonstrated in this work. A Movie comparing the flow capacities of these four fluids is shown in Supplementary Movie 4. Moreover, the resistance measurement of four electrically responsive fluids is conducted to explain the interface resistance between the conductive TPU and different fluids as well as different flow performance of these four fluids (Supplementary Fig. 5). The results show that Linalyl Acetate has a higher current than FC 40, 7100, and 7200 at the same applied voltage, indicating that more electronic motion could pass through the interface between the conductive TPU electrode and fluid, and enter the fluid to produce stronger flow effects. Additionally, we tested the output performances of four different electrically responsive fluids at different voltages (Fig. 2a, b). It is apparent that the output performances of different fluids show an approximately linear increase with the increase of applied voltage, which offers an effective and precise way to control the output performance of electro-hydraulic power “diode” by adjusting input electrical signal.

Fig. 2: Performances of flexible electro-hydraulic power transistor.
Fig. 2: Performances of flexible electro-hydraulic power transistor.The alternative text for this image may have been generated using AI.
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a Pressure versus voltage for four types of liquids. Liquid 1: Linalyl Acetate; Liquid 2: 3 M™ Fluorinert™ FC-40 Electronic Liquid; Liquid 3: 3 M™ Novec™ 7100 Engineered Fluid 4; Liquid 4: 3 M™ Novec™ 7200 Engineered Fluid. b Flow rate versus voltage for four types of liquids. c Pressure versus triangle electrode angle α at the voltage of 12 kV and 15 kV. d Flow rate versus triangle electrode angle α at the voltage of 12 kV and 15 kV. e Pressure versus electrode gap l at the voltage of 12 kV and 15 kV. f Flow rate versus electrode gap l at the voltage of 12 kV and 15 kV. g Pressure versus slit width d at the voltage of 12 kV and 15 kV. h Flow rate versus slit width d at the voltage of 12 kV and 15 kV. i Pressure versus voltage for different series integration use of multiple electro-hydraulic power transistors. j Flow rate versus voltage for different parallel integration use of multiple electro-hydraulic power transistors. k Transient response of electro-hydraulic power transistor at the voltage of 15 kV. l Performance comparison between electro-hydraulic power transistor, commercial rigid pumps, and existing flexible pumps.

Meanwhile, the electrode configuration (i.e., triangular angle of emitter electrode α, slit width of collector electrode d, and electrode gap between emitter and collector electrodes l) have a significant influence on the output performances of electro-hydraulic power “diode”, and their influence law should be explored to provide theoretical guidance for optimization design of electro-hydraulic power toransistor. Figure 2c, d show that the flow rate and pressure of electr-hydraulic power “diode” first increase and then decrease as the triangular angle α of emitter electrode increases. Note that the output performances reach the highest values at a triangular angle α of 60° due to the strongest non-uniform electric field intensity being formed at this angle. Additionally, the small electrode gap l (Fig. 2e, f) and slit width d (Fig. 2g, h) are beneficial to the enhancement of output pressure and flow rate. These phenomena indicate that the smaller, lighter, and more powerful electro-hydraulic power transistors could be fabricated with the advancement of printing accuracy.

Moreover, the output pressure could be linearly raised by series integration use of multiple electro-hydraulic power transistors (Fig. 2i), while output flow rate could be linearly raised by parallel integration use of multiple ones (Fig. 2j). To further validate this stacking rule, we have also measured the output pressure and flow rate of an ECP with four transistors in series and five transistors in parallel (Supplementary Fig. 6). The results show that its output pressure is four times that of one transistor, while its output flow rate is five times that of one transistor. These results are in accord with the series/parallel rules of EPC performance mentioned above. The response time (peak time) of electro-hydraulic power transistor is ~0.67 s, and the switching response time of bidirectional pumping is ~0.83 s (Fig. 2k). We also compare the flow rate and pressure density of electro-hydraulic power transistors with other commercial rigid pumps and existing flexible pumps (Fig. 2l). The special pressure (10.77 kPa/g) and flow rate (2.15 L/min/g) of electro-hydraulic power transistor are far higher than those of commercial rigid pumps21,22,23 and existing flexible pumps19,20,24,25,26,27. When an EPC is applied with a voltage of 15 kV, its power consumption of EPC is about 3.24 W and energy conversion efficiency is about 11.91%. (“Power consumption and energy efficiency of EPC” in Supplementary Materials). Continuous operating experiments of EPC under different voltages are conducted, and the temperatures of both fluid and EPC shell (near electrodes) are measured to know the temperature effects on their performance. The results show that the temperatures of fluid and EPC shell are relatively stable during continuous operation, and there is no obvious temperature increase (“Temperature measurement of EPC fluid and shell” in Supplementary Materials and Supplementary Fig. 7).

Programmable electro-hydraulic power chips

Interestingly, diverse EPCs could be programmatically designed to the desired shape, size, and function through reasonable combination and arrangement of electro-hydraulic power transistor modules, and 3D printed to meet different demands of various soft systems. The design of EPCs can be divided into three levels from simplicity to complexity. (i) Linear single channel: the length and width of a single linear channel can be respectively increased through the series and parallel integration of multiple electro-hydraulic power transistors (Fig. 3a, b), while the height of the channel can be increased directly with the increase of printing height (Fig. 3c). (ii) Plane multiple channels: multiple channels can be integrated into one plane, including interconnected channels with multiple entrances or exits (Fig. 3d, e) and multiple independent channels (Fig. 3f); (iii) Multi-layered layout: the desired shape and size in 3D space can be obtained through multi-layer stacking (Fig. 3g–i, Supplementary Figs. 8 and 9). The detailed wiring and control methods of EPCs are described in Supplementary Materials, Supplementary Figs. 10 and 11, while the interface connection information between interfacing devices and EPCs is also elaborated.

Fig. 3: Diverse design of EPCs.
Fig. 3: Diverse design of EPCs.The alternative text for this image may have been generated using AI.
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a Electro-hydraulic power transistor module, and the length of a single-channel EPC can be increased through series integration of multiple electro-hydraulic power transistors. b The width of a single-channel EPC can be increased through parallel integration of multiple electro-hydraulic power transistors. c The height of a single-channel EPC can be customized directly through 3D printing. d Interconnected-channel EPC with three entrances/exits in one plane. e Interconnected-channel EPC with four entrances/exits in one plane. f EPC with eight independent channels in one plane. g Three-layer stacked EPC with the same shape and size for each layer. h Three-layer stacked EPC with the same shape but different sizes for each layer. i Three-layer stacked EPC with different shapes and sizes for each layer.

Although there are some previous works about modular pumps19,20,24, their structures are relatively complex and mainly manufactured via traditional fabrication techniques such as casting and manual assembly, etc. With the increase in module number and combination complexity, it is difficult to achieve their high precision, miniaturization, and easy manufacturing. The proposed EPCs based on electro-hydraulic power transistors have unique merits in the simplicity of their design and ease of fabrication, allowing designers to move toward this level of structural complexity and compact layout, albeit at a larger scale and with fewer materials.

Soft system applications of electro-hydraulic power chips

Fluidic soft robots or wearable devices always require multiple independent fluidic circuits to achieve their functional operations, such as various crawling behaviors of a quadruped, multimodal grasping of a flexible robotic gripper, wearable tactile feedback of different objects from virtual world, etc. Increasing the number of independently operated fluidic circuits via traditional rigid pumps and valves will greatly increase the burden on soft systems, even exceeding the limits they can withstand. We illustrate the unique merit of flexible EPCs in various multi-circuit soft systems by demonstrating three scenarios of multi-circuit mass transfer, five-finger selective cooling, and bird’s multiple actuation.

We design and print a miniatured square EPC (Fig. 4a, b). There are four fluidic circuits in the EPC, two of which are unidirectional fluidic circuits and the other two are bidirectional fluidic circuits. These four fluidic circuits are independently controllable without interference with each other, and their flow rate and pressure can be adjusted directly by changing input voltage signal. This EPC made of fully flexible materials shows good flexibility and can easily be stretchable and twisted (Fig. 4c), ensuring the security in human-machine interaction process. The EPC selectively and controllably moves liquids with suspended particles of different colors (Supplementary Movie 5) in four independent fluidic circuits (Fig. 4d, g), two independent fluidic circuits (Fig. 4e, h), and one single fluidic circuit (Fig. 4f, i), illustrating their broad potential in wearable drug delivery or screening devices.

Fig. 4: Design, fabrication, and performances of a miniatured square EPC.
Fig. 4: Design, fabrication, and performances of a miniatured square EPC.The alternative text for this image may have been generated using AI.
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a Schematic diagram of square EPC. The chip consists of four independent fluidic circuits, two of which are unidirectional fluidic circuits and the other two are bidirectional fluidic circuits. b Fabrication result of square EPC. c The square EPC can be stretchable and twisted. d Schematic diagram of four-circuit flow. e Schematic diagram of two-circuit flow. f Schematic diagram of one-circuit flow. g Demonstration of four-circuit flow in square EPC. h Demonstration of two-circuit flow in square EPC. i Demonstration of one-circuit flow in square EPC.

We also embed a five-circuit EPC into a wearable glove device to effectively achieve controllable temperature control for selectively cooling different fingers (Fig. 5a). This wearable device mainly consists of a EPC, some flexible tubes, a cooling source (TES1-4903, Zave), an energy supply system, and high-voltage power converter (Supplementary Fig. 12). Five independent flexible tubes are wrapped around five fingers, and connected to a five-circuit EPC (Fig. 5b), thereby forming five independent fluidic circuits. A cooling source is placed on a wearable bracelet to contact a small section of five independent fluid circuits. When the fluid in one or more fluidic circuits of EPC is driven, the fluid flow will pass through the cooling area and bring low-temperature liquid to cool one or more fingers. Figure 5c shows the temperature information of fingers when the EPC is out of work. The five-circuit EPC selectively and controllably moves low-temperature liquid to reduce the temperature of one finger (Fig. 5d), two fingers (Fig. 5e), three fingers (Fig. 5f), four fingers (Fig. 5g), and five fingers (Fig. 5h). These results indicate that the EPC is an advance in promoting the development of wearable devices for human thermal management with lighter weight and higher spatial resolution, illustrating its great potential in future virtual reality applications.

Fig. 5: Thermal regulation of five-circuit EPC.
Fig. 5: Thermal regulation of five-circuit EPC.The alternative text for this image may have been generated using AI.
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a Schematic diagram of a wearable glove device to effectively achieve temperature control for cooling different fingers. The device consists of a five-circuit EPC, some flexible tubes, a cooling source, and an energy supply system. The fluid flow will pass through the cooling area and bring low-temperature liquid to cool one or more fingers. b Fabrication result of a five-circuit EPC. c Temperature information of five fingers when the five-circuit EPC is out of work. d Temperature information of one finger selective cooling state (i.e., little finger). e Temperature information of two fingers selective cooling state (i.e., thumb and forefinger). f Temperature information of three fingers selective cooling state (i.e., thumb, forefinger, and middle finger). g Temperature information of four fingers selective cooling state (i.e., thumb, middle finger, ring finger, and little finger). h Temperature information of all five fingers cooling state.

Except for mass and heat transfer functions for fluidic wearable devices, EPCs could also be embedded into soft robots to achieve versatile motions without bulky and redundant fluid power/control components. A four-circuit fluid power actuator driven by a customized EPC is implanted into a soft robotic bird to achieve independent actuation of different organs, including a mouth, two wings, and a tail (Fig. 6a). The four-circuit fluid power actuators (Fig. 6b and Supplementary Fig. 13) are made of four flexible actuators, four liquid tanks, and a three-layered four-circuit integrated EPC (Fig. 6c). The operating principles of mouth opening and closing motion, wing flapping motion, and tail curling motion are schematically shown in Fig. 6d–f, respectively. The bird’s mouth opens when the corresponding mouth actuator is out of work. As the corresponding mouth actuator is driven by EPC, the fluid flow will cause the soft actuator contract to pull the mouth to close (Fig. 6d and Supplementary Movie 6). Two corresponding wing actuators can be independently controlled by EPC to achieve the wing flapping up and down at different frequencies (Fig. 6e), while the corresponding tail actuator powered by EPC is responsible for the tail curling motion (Fig. 6f). The independent actuation of opening and closing the mouth, flapping the wings, and curling the tail is respectively demonstrated in Fig. 6g–i, and the simultaneous actuation of all these motions are shown in Fig. 6j.

Fig. 6: Structure, operating principle, and experimental results of a soft robotic bird powered by a three-layered four-circuit electro-hydraulic power chip.
Fig. 6: Structure, operating principle, and experimental results of a soft robotic bird powered by a three-layered four-circuit electro-hydraulic power chip.The alternative text for this image may have been generated using AI.
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a Structure of a soft robotic bird. It consists of a mouth, two wings, a tail, an embedded four-circuit fluid power actuator, and a flexible shell. b A four-circuit fluid power actuator. c A three-layered four-circuit integrated electro-hydraulic power chip. d Operating principle of mouth opening and closing motion. e Operating principle of wing flapping motion. f Operating principle of tail curling motion. g Demonstration of mouth opening and closing motion. h Demonstration of wing flapping motion. i Demonstration of tail curling motion. j Demonstration of mouth opening and closing motion, wing flapping motion, tail curling motion at the same time.

In addition, we designed and manufactured a jellyfish-like robot propelled by four paddling actuators, of which the paddling actuators are driven by EPCs (Fig. 7a). Each paddling actuator consists of an EPC sealed by elastic film, electrically responsive fluid, and PET sheet (Fig. 7b). When the EPC is not applied with voltage, the pre-deformed PET sheet is initially in a bent state. As the EPC is applied with high voltage, the jet generated by the EPC drives the liquid to flow from EPC tank into PET sheet. This process will cause the rapid extension of the initially bent PET sheet, thereby achieving the paddling action of jellyfish robot to propel itself swim forward. Once the voltage is removed, the elastic potential energy of the PET sheet will drive the polymer film to return to its initial bend state accompanied by liquid reflux (Fig. 7c). By applying periodic high voltage, jellyfish robot can achieve fast swimming (Fig. 7d). Figure 7e shows the actual swimming process of jellyfish robot (Fig. 7e and Supplementary Movie 7), which can reach a swimming speed of ~ 0.87 body lengths per second that is obviously faster than other flexible jellyfish robots28,29,30,31,32,33,34 (Fig. 7f).

Fig. 7: Structure, operating principle, and swimming performance of EPC-driven flexible jellyfish robot.
Fig. 7: Structure, operating principle, and swimming performance of EPC-driven flexible jellyfish robot.The alternative text for this image may have been generated using AI.
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a Structure of EPC-driven flexible jellyfish robot. It consists of a flexible shell, EPCs, and PET sheets. b Structure of a paddling actuator. c Operating principle of paddling actuator. The PET sheet is initially in a bent state. As the EPC is applied with high voltage, the jet drives the liquid to flow from EPC tank into PET feet. This process causes the rapid extension of bent PET sheet, achieving the paddling action of jellyfish robot to propel itself swim forward. Once the voltage is removed, the elastic potential energy of the PET sheet will drive the polymer film to return to its initial bend state. d Schematic of 2-cycle swimming of jellyfish robot. e Demonstration of the periodic swimming of jelleyfish robot. f Swimming performance comparison between EPC-driven jellyfish robot and other flexible jellyfish robot28,29,30,31,32,33,34.

Discussion

In summary, we have proposed a strategy of flexible EPCs that can achieve multi-circuit independent pumping and control of fluidic soft systems in an extremely simple and lightweight form that is not possible with existing technologies. The multi-material 3D printing shows great advantages for the monolithic fabrication of complex, multi-circuit EPCs with high repeatability, few materials, and low manual labor requirements, while previous fluid power components have been mainly fabricated in multiple steps using a silicone molding process followed by manual assembly of subsystems. The demonstration of multi-circuit mass transfer, five-finger selective cooling, and bird’s multiple actuation illustrate the great potential of EPCs as mass-manufactured, low-cost, and standard universal fluid power components for fluidic soft systems.

Except for stacking method, there are also several methods to further improve the output pressure or flow rate of EPC. Actually, the out pressure or flow rate of EPC is also determined by fluid materials and electrode types, etc. The output pressure or flow rate of EPC could significantly be improved by discovering or developing new electrically responsive fluid materials with stronger flow performance. For example, doping other materials into the electrically responsive fluids is a feasible way to enhance their output pressure or flow rate. Electrode types (including materials and size) can also affect the output pressure or flow rate. Firstly, developing flexible electrode materials with better conductivity could also improve output pressure or flow rate. Secondly, it is found from Fig. 2e–h that the smaller the electrode size and electrode spacing, the higher the output pressure or flow rate. This indicates that the smaller, lighter, and more powerful EPCs could be fabricated with the high printing accuracy. The development of 3D printing techniques with higher printing resolution and accuracy or new printing technologies could reduce the size of EPCs, thereby increasing output pressure or flow rate.

Except for unidirectional or bidirectional flow function, developing the devices driven by EPCs to prevent fluid flow is an important and meaningful research direction, which could add more functions to soft systems. Moreover, the EPCs could be fully integrated and printed with soft robots and wearable devices themselves, making these soft systems lighter and more compact, simpler to manufacture, and more reliable in fluidic sealing. In addition, flexible high-voltage circuits should also be developed and integrated with EPCs for printing together. This strategy of EPCs has great potential to be popularized as the standard universal fluid power components for autonomous soft systems.

Methods

Materials and fabrication of electro-hydraulic power “diode”

Electro-hydraulic power “diode” consists of a triangular-shaped emitter electrode, a silt-shaped collector electrode, and a channel-shaped supporting shell. All these parts are made of flexible thermoplastic polyurethane elastomers (TPUs), in which the triangular-shaped emitter electrode and the silt-shaped collector electrode are made of conductive TPU material, and the supporting shell is made of the non-conductive TPU material. The triangular-shaped emitter electrode and the silt-shaped collector electrode are kept centered to form an electrode pair, and the supporting shell is mainly used to construct the flow channel and fix the electrodes.

The electro-hydraulic power “diode” is 3D-printed by conductive TPU and non-conductive TPU in a 3D-printing machine (Raise 3D E2). The one printer nozzle is used to print the electrodes by conductive TPU, while the other one is responsible for the supporting shell by non-conductive TPU. Two nozzles are interleaved and printed circularly to achieve the monolithic fabrication mold of electro-hydraulic power “diode”, as shown in Supplementary Fig. 1. During the printing process, the detailed 3D printing parameters of EPC are illustrated in Supplementary Table 1. After printing, the printed components are refined processing.

Experimental demonstration of electro-hydraulic flow

A semi-circular flow channel with an electro-hydraulic power “diode” is designed and printed, as shown in Supplementary Fig. 2a. The detailed size of this semi-circular flow channel is as follows: The width of the channel is 6 mm, the inner radius of the channel is 19 mm, the outer radius of the channel is 25 mm, the wall thickness is 1 mm, and the depth of the channel is 5 mm. The electrodes are fully submerged with the electrically responsive fluid of Linalyl Acetate. When the emitter electrode and collector electrode are respectively connected to high-voltage positive electrode (10 kV) and grounding negative electrode (0 kV), a non-uniform strong electric field will be formed between them to generate a strong flow. Because the liquid is transparent, its flow effect could not be directly observed. Thus, we use a red tracer to track the liquid flow. The demonstration process is shown in the Supplementary Movie 2 and Supplementary Fig. 2b. It can be seen that the total time of flow in half a circle is 0.48 s.

Theoretical models and simulation of electro-hydraulic flow

The theoretical model is built to obtain the distributions of electric potential, charge density and flow velocity in an electro-hydraulic power “diode”35,36. Since the electrically responsive fluid is incompressible, its continuity equation is:

$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0$$
(1)

where \(u\) and \(v\) are the components of the flow velocity in the x and y directions, respectively.

For two-dimensional constant flow, the N-S equation is:

$$u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}={f}_{x}-\frac{1}{\rho }\frac{\partial p}{\partial x}+\frac{\eta }{\rho }\left(\frac{{\partial }^{2}u}{{\partial }^{2}x}+\frac{{\partial }^{2}u}{{\partial }^{2}y}\right)$$
(2)
$$u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}={f}_{y}-\frac{1}{\rho }\frac{\partial p}{\partial y}+\frac{\eta }{\rho }\left(\frac{{\partial }^{2}v}{{\partial }^{2}x}+\frac{{\partial }^{2}v}{{\partial }^{2}y}\right)$$
(3)

where \({f}_{x}\) and \({f}_{y}\) are the components of the force f per unit mass volume in the x and y directions, respectively, p is the pressure,\(\,\rho \) is the density of the electrically responsive fluids, and \(\eta \) is the viscosity of the electrically responsive fluid.

Since there is no dielectric constant gradient in the electrically responsive fluid, the electric bulk force density acting on the dielectric fluid can be expressed as37:

$${f}_{x}=\frac{q}{\rho }{E}_{x}$$
(4)
$${f}_{y}=\frac{q}{\rho }{E}_{y}$$
(5)

where \(q\) is the charge density and \({E}_{x}\)、\({E}_{y}\) are the components of the electric field strength in the x and y directions. The potential distribution in the electrically responsive fluid is:

$${\nabla }^{2}\phi=-\frac{q}{{\varepsilon }_{0}{\varepsilon }_{r}}$$
(6)

where \(\phi \) is the electric potential, \({\varepsilon }_{0}\) is the vacuum dielectric constant, \({\varepsilon }_{r}\) is the relative dielectric constant of the electrically responsive fluid. The electric field distribution in the electrically responsive fluid is:

$$E=-\nabla \phi $$
(7)

The current density in the electrically responsive fluid is calculated as follows:

$${\bf{j}}=q{\mu }_{i}{\bf{E}}+q{\bf{u}}-{D}_{i}\nabla q+\sigma {\bf{E}}$$
(8)

where \(j\) is the current density, \({\mu }_{i}\) is the ion mobility, \({D}_{i}\) is the charge diffusion parameter, and \(\sigma \) is the conductivity of the fluid. The law of conservation of charge is:

$$\nabla \cdot {\bf{j}}=0$$
(9)

The injected charge density is:

$${q}_{e}=k({E}_{static}-{E}_{thres})$$
(10)

where \(k\) is a constant of proportionality of the injected charge density, \({E}_{{static}}\) is the electric field on the surface of the electrode, and \({E}_{{thres}}\) is the threshold electric field strength at which the electric field on the surface of the electrode generates flow.

As shown in the Supplementary Fig. 3a, the boundary ① is the fluid inlet, the initial velocity is, the boundary ② is the fluid outlet, the triangular electrode is connected to the positive high voltage V, the slit electrode is grounded, and there is no slip phenomenon on the flow wall of the electrically responsive fluid, so the boundary conditions from ① to ⑥ are respectively:

$$u={U}_{in},v=0,\frac{\partial \phi }{\partial x}=0$$
(11)
$$\frac{\partial u}{\partial x}=0,\frac{\partial v}{\partial x}=0,\frac{\partial q}{\partial x}=0,\frac{\partial \phi }{\partial x}=0$$
(12)
$$u=0,v=0,\frac{\partial \phi }{\partial y}=0$$
(13)
$$u=0,v=0,q={q}_{e},\phi=V$$
(14)
$$u=0,v=0,\phi=V$$
(15)
$$u=0,v=0,q=0,\phi=0$$
(16)

Based on the above theoretical model, the simulation of electro-hydraulic flow is carried out in the software of COMSOL Multiphysics. The boundary conditions of ①-⑥ are shown in Supplementary Fig. 3a. The electrically responsive fluid is Linalyl Acetate, and its basic parameters are shown in Supplementary Table 2. The input voltage is set as 15 kV, the calculated potential distribution and electric field are shown in Supplementary Fig. 3b. It can be seen that the potential decreases gradually from triangular electrode to slit electrode. Supplementary Fig. 3c demonstrates the velocity distribution cloud and velocity field when the input voltage is 15 kV. It can be seen that the numerical simulation can better simulate the fluid flow under the electric field. The simulated flow rate of the electro-hydraulic power “diode” at a voltage of 15 kV is about 260 ml/min, while the experimentally measured flow rate of this electro-hydraulic power “diode” at a voltage of 15 kV is 287 ml/min. The error between the simulated and experimental values is only 9.4%, indicating the theoretical results are in good agreement with the experimental one. Thus, it can be concluded that the working principle is reasonable and accurate.

Performance test of electro-hydraulic power “diode”

The performance test of electro-hydraulic power “diode” mainly includes pressure test and flow test. The pressure testing device is shown in the Supplementary Fig. 4a, which mainly consists of a liquid reservoir, connecting tubes, electro-hydraulic power “diode”. The output pressure is measured by a piezometer. In order to prevent the difference of liquid level height from affecting pressure measurement results, we keep the liquid level in the reservoir at the same level as the liquid level at the front end of the pressure gauge. When a high voltage power supply (Model 20 C, Trek) is used to apply high-voltage to an electro-hydraulic power “diode”, the value of the output pressure can be read on a piezometer. The flow test device shown in the Supplementary Fig. 4b consists of the reservoir, connecting tube, electro-hydraulic power “diode” and measuring cylinder. The output flow rate can be obtained from the liquid volume measured by the measuring cylinder within a period of time.

Power consumption and energy efficiency of EPC

A test device is used to know the useful work\(\,{W}_{F}\) and useful power \({P}_{F}\) of an EPC, while the applied voltage is set as 15 kV and the electrically responsive fluid is Linalyl Acetate. During the work process, the useful work\(\,{{\rm{W}}}_{{\rm{F}}}\) and useful power \({P}_{F}\) of EPC can be expressed respectively as:

$${W}_{F}={\int }_{0}^{{t}_{1}}{P}_{a}(t)\cdot Q(t){dt}\,{and}\,{P}_{F}=\frac{{W}_{F}}{{t}_{1}}$$
(17)

where \({P}_{a}\) represents the output pressure of EPC, and \(Q\) represents output flow rate of EPC, \({t}_{1}\) represents the duration of stable pumping.

The input electric energy \({W}_{E}\) and input power \({P}_{E}\) can be expressed respectively as:

$${W}_{E}={\int }_{0}^{{t}_{1}}U\cdot i(t){dt}\,{and}\,{P}_{E}=\frac{{W}_{E}}{{t}_{1}}$$
(18)

Hence, the energy efficiency η could be calculated by the ratio of useful work (\({W}_{F}\)) to input electric energy (\({W}_{E}\)):

$$\eta=\frac{{W}_{F}}{{W}_{E}}\times 100\%=\frac{{\int }_{0}^{{t}_{1}}{P}_{a}(t)\cdot Q(t){dt}}{{\int }_{0}^{{t}_{1}}U{{\cdot }}i(t){dt}}\times 100\%=\frac{{P}_{F}}{{P}_{E}}\times 100\%$$
(19)

In this case, the average output power \({P}_{F}\) during the pumping processes was measured as ~0.386 W, while the average input power \({P}_{E}\) during the pumping processes was measured as ~3.24 W. Thus, the energy efficiency during the pumping process was ~11.91%.

Resistance measurement of different electrically responsive fluids

The device used to measure the resistances of electrically responsive fluids consists of a DC voltage, a voltage amplifier, a safety resistor, an ammeter (M1252), several wires, a semi-circular flow channel, and an EPC. Two conducting wires are linked to positive electrode and negative electrode respectively, and the minimum measurement resolution of the ammeter is 1 nA. When the applied voltages are set as 3 kV, 5 kV, 9 kV, 12 kV, and 15 kV respectively, the corresponding currents under these voltages can be obtained. The obvious linear relationship between voltages and currents for four different electrically responsive fluids is shown in Supplementary Fig. 5. It is apparent that the Linalyl Acetate has the minimum resistance among four liquids.

Temperature measurement of EPC liquid and shell during continuous operation

The temperature measurement of EPC liquid and shell during continuous operation is shown in Supplementary Fig. 7. The temperatures of the liquid and the outer shell (near the electrodes) were respectively measured by a two-channel thermometer (YET-620L) with two K-type thermocouples (KPS-ZT-K-2000-SMPZ). The sampling frequency of the thermometer is set as 1 Hz. The EPC was continuously operating for 10 min at different voltages of 6 kV, 10 kV, and 15 kV, and the temperatures of both liquid and the outer shell (near the electrodes) could be obtained and shown in Supplementary Fig. 7b–d. The results of temperature measurement show that the temperatures of the liquid and the outer shell are almost constant during continuous use, and there is no obvious temperature increase.

Wiring and control methods of EPCs

The wiring principle of EPC is that: (i) Linear single channel: As schematically shown in Supplementary Fig. 10a, all positive electrodes with the same directions are connected in series to form a conducting TPU wire for power supply and control, while all negative electrodes are also connected in series to form another TPU wire. All these conducting wires are printed and wrapped in the non-conducting TPU at the bottom shell of EPC, which can achieve effective insulation protection. The thickness of the conducting TPU wire is 1 mm, while the thickness of the bottom shell is 2 mm. Thus, as for EPC with a single channel, only one-way positive electrode input and one-way negative electrode output is needed to supply power and achieve control of the EPC; (ii) Plane multiple channels: When there are multiple channels in a plane, each flow channel has its own wires. For example, Supplementary Fig. 10b shows four interconnected channels connected to four entrances or exits. These four channels have the independent wiring, and thus four independent wires are required for power supply and control of four channels in the EPC. The same wiring principle is used for the four independent channels in Supplementary Fig. 10c; (iii) Multi-layered layout: For the multi-layer EPC, different layer has its independent wire and the wiring method is the same as that used for multiple channels. In summary, one channel needs one-way electricity input and output, while each channel or each layer has independent electricity input and output.

Based on the number of wiring lines, we set the corresponding number of control lines. For example, the control logic of an EPC with four channels is shown in Supplementary Fig. 11. This control logic consists a DV voltage source, a voltage amplifier, a microcontroller, and four high-voltage relay modules. Each high-voltage relay module has three relay units, which is controlled by a microcontroller (Arduino Mega2560). For each channel, there are two positive wires and one negative wire. Thus, in each high-voltage relay module, two relay units are used to control two positive wires, and one relay unit is used to control the negative wire. By controlling the opening and closing of different relay units, different flow functions of four-channel EPC can be achieved.

The detailed interface connection information between interfacing devices and EPCs is that there are two connections between interfacing devices and EPCs: electrical connection and flow channel connection. Firstly, high-voltage resistant wires is used to connect the printed electrodes of EPCs to provide the input voltage, and then the K-407 silicone sealant at the connection position is used to achieve sealing treatment while maintaining the adhesion between theses two through curing treatment. Secondly, the flow channel interface of EPCs will be printed to match the shape and size of the flexible flow channel to be connected. Then, we use gap fitting to achieve the fit between the flow hole and the pipeline, and use silicone sealant at the joint to achieve sealing treatment.

High voltage power converter

The miniature and lightweight high-voltage power converter was designed and fabricated to power the electro-hydraulic power “diode” or EPC, thereby achieving rapid pumping when the electro-hydraulic power “diode” or EPC is embedded into different soft systems. The high-voltage power converter adopted a conventional topology that consisted of pulse oscillating circuit, inverter circuit, high-frequency transformer, and voltage doubling rectifying circuit38. The pulse oscillating circuit was mainly made of a timer NE 555 to output a pulse of a certain pulse width for driving the MOSFET. The inverter circuit was mainly made of a MOSFET IRF 540 N to form a fly-back topology drive circuit, converting the input DC power into high-frequency square wave pulse. After that, the high-frequency square wave pulse was boosted by a high-frequency transformer and then converted into a required DC high voltage by a voltage doubler rectifier circuit. This high voltage power converter can boost the input voltage of 3.7 V supplied by button cell to 15 kV. When multiple fluidic circuits in the EPCs are needed to be driven, multiple high-voltage power converters are applied to achieve independent drive and control of each circuit.

Thermal regulation of five-circuit EPC

A wearable glove device powered by a five-circuit EPC is used to achieve selective cooling of five fingers. This wearable device consists of a five-circuit EPC, some flexible tubes, a cooling source, and the energy supply system. The five-circuit EPC is 3D-printed, and the process is the same to that of electro-hydraulic power transistor mentioned above. The cooling source is a semiconductor cooler (Zave TES1-4903) capable of rapid cooling of liquid. Inner diameter of the flexible tubes is 3 mm, while the outer diameter of the flexible tubes is 4 mm. The energy supply system will be described in the next section. Five independent flexible tubes are wrapped around five fingers, and connected to a five-circuit EPC, thereby forming five independent fluidic circuits. When the fluid in each fluidic circuit is driven, the fluid flow will pass through the cooling area and bring low-temperature liquid to the corresponding finger. As a result, five fingers can be selectively cooled by the selective actuation of different circuits in the five-circuit EPC.

Soft robotic bird powered by EPC

Different organs of a soft robotic bird are actuated by a four-circuit fluid power actuator powered by a customized EPC. The soft robotic bird consists of a flexible shell, a mouth, two wings, a tail, and an implanted four-circuit fluid power actuator (Supplementary Fig. 13a). Among these, the flexible shell, mouth, wings, and tail are all printed by flexible PLA in the machine of TL-D3 Pro. The four-circuit fluid power actuator are made of four flexible actuators, four liquid tanks, and a three-layered four-circuit integrated EPC (Supplementary Fig. 13c). These four flexible actuators and liquid tanks are all made by using soft silicone materials, and fabricated by traditional casting method (Supplementary Fig. 13b). The detailed casting process is as follows: (i) Make silicone rubber. Mix silicone rubber part A and part B in a ratio of 1:1, stir well, and then degas in a vacuum dryer for about 3 min to remove air bubbles; (ii) Pouring silicone rubber. Pour the uncured silicone rubber into the mold and cure at room temperature for about 6 h; (iii) Demolding. After casting, silicone demolding is performed and the finished linearly deformed executive structure is obtained. The independent actuation of opening and closing the mouth, flapping the wings, and curling the tail can be successfully achieved by selectively driving different circuits in the EPC.

Jellyfish-like soft robot powered by EPC

The jellyfish-like soft robot consists of a flexible shell, four EPCs sealed with elastic films, and four leg actuators with PET sheets. The black shell of the jellyfish-like soft robot is flexible PET sheet. The elastic films are all made by using soft silicone materials, and the casting method of this film is same as Supplementary Fig. 13b. The leg actuator is made of two polymer films, a pre-deformed PET sheet, and electrically responsive fluid. Two polymer films are heat sealed with a liquid reservoir, and the electrically responsive fluid was injected into the reservoir. The pre-deformed PET sheet was glued on the leg actuator to make it be bent. When the EPCs in jellyfish robot are applied with 15 kV and the frequency of the input signal is set as 1 Hz, the jellyfish robot could achieve a swimming speed of ~0.87 body lengths per second (Fig. 7e and Supplementary Movie 7).