Abstract
Electrohydrodynamic (EHD) pumps noiselessly generate fluid flow in dielectric liquids using high electric fields to create, accelerate, and neutralize ions. Such pumps find applications in wearable actuators, soft robotics, and active thermal management. The influence of fluid properties on pressure and flow rate remains poorly understood. We present a systematic comparison of EHD pumping across 11 fluids, including 8 previously unidentified candidates, spanning viscosities from 0.5 to 19 millipascal seconds and dielectric constants from 2.3 to 64. Tests with more than 30 flexible fiber pumps show that low-viscosity and high–dielectric constant liquids markedly enhance pumping performance. For 1.2-millimeter–inner-diameter fiber pumps, replacing the commonly used Novec 7100 with propylene carbonate increased fluidic power density fivefold, reaching 495 milliwatts per cubic centimeter at 4.4 kilovolts. This study identifies key fluid properties for pumping, expands the EHD fluid library, and establishes a rigorous benchmark for performance evaluation, providing guidance for future EHD pump designs.
Fluid viscosity and permittivity govern EHD pumping, boosting fluidic power output fivefold.
INTRODUCTION
Portable and ideally flexible pumps are key components for fluid pressurization and transport in medical, wearable actuation, on-body thermal management, and soft robotic scenarios. Small conventional pumps driven by compressors, diaphragms, and peristaltic mechanisms can deliver several watts of fluidic power, but their noise and vibration are not suited for integration in compact and especially wearable systems. Electrohydrodynamic (EHD) pumps generate fluidic power through ion formation and ion motion in some dielectric fluids when a high dc voltage is applied (1–5). Compared to conventional pumps, EHD pumps have no moving parts and are completely silent but only work with a limited class of fluids. EHD pumps can be made flexible (4–6), holding great promise to replace rigid pumps in applications including untethered soft robotics (7–9), fluidically powered wearable actuators for exosuits (10–12), active thermal management (13), and haptics (14, 15).
One can distinguish two major configurations of EHD pumps. The first configuration involves interdigitated electrodes with asymmetric spacing, with a high electric field and strong forward pumping in the smaller interelectrode gaps and weaker backward pumping in the larger gaps. The pumping direction is reversible, set by the polarity of the applied voltage (4, 5, 16–20). The second design uses a sharp emitter electrode and a smooth receiver electrode to create an asymmetric electric field in the fluid, thereby producing a preferred pumping direction regardless of polarity (6, 21–23). Considerable progress has been achieved in pump fabrication methods, materials, and geometries. Fabricating EHD pumps from compliant materials (4–6) and improving reliability (16, 19) allow powering fluidic actuators for wearable active devices or for soft robotics. Recently, EHD pumps in fiber format, referred to as “fiber pumps,” have been fabricated via thread winding or dip coating (5, 18, 20). Such fiber pumps are inherently compatible with textiles and thus well suited for integration in fluidic wearables. Three-dimensionally (3D) printed EHD pumps offer a high degree of material versatility, allowing self-healing (6, 21) or swell-resistance functions (22). Researchers have integrated triboelectric nanogenerators with EHD pumps to enable self-powered pumping systems (23).
Despite these advances, the influence of fluid properties on EHD pump performance is poorly understood. EHD fluids can be categorized into three main types. Fluorinated organic fluids, designed for thermal management applications such as HCFC-123 (24), HT-110 (25), and Novec 7100 (4, 5, 13, 18, 26), have been widely used as they offer good pumping performance. A second type is nonfluorinated organic fluids, mainly esters, including dibutyl sebacate (6, 27) and linalyl acetate (21, 23). The third category is organosilicon fluids, primarily used when visualizing EHD flow patterns using particle image velocimetry (28). Fluids vary in physical properties, such as viscosity, dielectric constant, conductivity, boiling point, and surface tension, and in chemical properties, e.g., reactivity, electronegativity, or acidity.
The liquids reported in the EHD literature were used in pumps with different designs and measured using different test methods. The absence of a direct comparison makes it unclear which fluid parameters are critical to pumping performance and whether there exist thresholds values for liquids to be suitable for EHD pumping. This knowledge gap hinders fluid selection and the discovery of previously unidentified candidates. What is the ultimate limit of EHD pumping? Is there a method to design liquids that allow for higher pumping performance? The current understanding of ion species and ion formation mechanisms is inferred from macroscopic pumping behavior. Although two main possible ion formation mechanisms have been proposed, namely, charge injection (29–31) and dissociation and recombination (25, 32–34), it remains unclear which mechanism dominates for any specific fluid. Electrochemical reactions between the electrodes and the fluid have been suggested (35), underscoring the limited understanding of ion formation in EHD systems.
Another challenge in comparing EHD pumps and liquids stems from a lack of robust benchmarks to systematically characterize and investigate EHD pumps. Pressure and flow rate are the two primary performance metrics, typically measured under varying applied voltages. Ideally, one uses a continuously variable flow impedance to record a “pump curve” (36), a plot of generated pressure versus flow rate, showing the continuous relationship between flow rate and pressure. However, many studies report only maximum pressure and flow rate using separate setups without continuous control of flow impedance. Maximum fluidic power output and the maximum efficiency typically occur near the middle of the pump curve (6, 23) and are thus not reported. Moreover, the methods to measure pressure and flow rate vary across studies. For pressure, some groups rely on tracking the height of a liquid column (23), while others use pressure sensors (5, 18, 37). Similarly, in some studies, flow rate is calculated as the volumetric change over time, yielding an average value over a given period (6, 23), whereas others use flow rate sensors to record real-time measurements (5, 18, 37). There is still no unified testing protocol to ensure consistent sampling durations and experimental conditions, which can introduce substantial variability in the reported results, making it particularly challenging to compare the performance of different EHD pumps.
In this study, we leveraged the broad chemical compatibility of polypropylene (PP)–based fiber pumps to systematically compare the EHD pumping performance of 11 representative fluids drawn from the three major categories of EHD liquids, including eight previously unexplored candidates. We used fiber pumps made by winding as they allow high reproducible EHD pumping and provided very high EHD performance (5).
The fluids cover a wide range of viscosity μ (from 0.5 to 19 mPa·s) and dielectric constant εr (from 2.3 to 64). We find that low-viscosity and high–dielectric constant fluids markedly improve pumping performance. For example, replacing a high-viscosity and low–dielectric constant fluid, Belsil 20 PDM silicone oil (μ = 19 mPa·s, εr = 2.7), with a low-viscosity and high–dielectric constant, 3-methoxybutyl acetate (μ = 0.7 mPa·s, εr = 8), increases the maximum fluidic power at 6.4 kV from 0.2 to 97 mW/m. We report pressures and fluidic power for fiber pumps in pressure and power per meter, because the pressure and power scale linearly with pump length (5).
With a fluid with even higher dielectric constant, propylene carbonate (εr = 64), we can further increase the maximum fluidic power output to 560 mW/m at an applied voltage of 4.4 kV. This fluidic power is equivalent to a volumetric power density of 495 kW/m3 (only internal pump volume) or 178 kW/m3 (total volume including fiber walls) and a specific power of 347 W/kg (pump mass without liquid) or 188 W/kg (pump mass including liquid). The fluidic power output using propylene carbonate is 5 times that of fiber pumps using Novec 7100 in this work and 30 times that of previously reported fiber pump using Novec 7100 (5). The higher performance is enabled both by changing the working fluid and by applying a bias pressure to allow operating at higher voltages (38). This performance enables an 18-cm-long fiber pump (mass of 0.3 g) to match the fluidic power of a miniature diaphragm pump (mass of 65 g) (39) and a 2-m fiber pump (mass of 3.4 g) to deliver fluidic power equivalent to a compact gear pump (mass of 500 g) (40).
For reproducible and repeatable testing of over 30 pumps, we developed an automated testbench to capture complete pump curves at different voltages, along with a robust testing methodology. To confirm the generality of the viscosity and dielectric constant trend observed in fiber pumps, we fabricated a copper-electrode needle-ring pump and obtained the same effect on EHD pumping of viscosity and dielectric constant. This work reports fluid selection criteria, greatly expands the usable EHD fluid options, and provides a robust guideline for evaluating and optimizing EHD pump performance.
RESULTS
EHD fiber pumps and performance overview
EHD fiber pumps, as reported in our previous work (5), are thin polymer tubes with two parallel helically wound electrode wires embedded inside so as to be in contact with the fluid. The helical structure is formed by a thread-winding process on a metallic rod, followed by fusing in an oven (see fig. S1). This fabrication method allows flexible material selection. In this study, PP is chosen as the polymer shell layer due to its excellent chemical resistance, allowing us to compare a wide range of liquids. In contrast, thermoplastic polyurethane (TPU) used in our previous work (5) is more mechanically compliant but is not compatible with a wide range of fluid chemistries. As shown in fig. S2, changing the shell material from TPU to PP negligibly affects pumping performance. Both Cu and Au wires are used for their high electrical conductivity and good mechanical compliance, making them well suited for the winding fabrication method.
For this study, we fabricated and tested in total 32 EHD fiber pumps for a highly repeatable and systematic exploration of the interplay between liquid properties and pump pressure, flow rate, fluidic power, and efficiency. The repeatability of our fiber pumps is illustrated in fig. S3, where pressure versus voltage and flow rate versus voltage data are overlaid for 14 fiber pumps, each 18 cm long, using Novec 7100 as the working liquid. To further validate the generality of the observed trend, we also fabricated and tested a Cu-electrode needle-ring pump, which features a markedly different geometry from fiber pumps.
Figure 1A is a schematic view of the charge injection EHD pumping mechanism in a fiber pump. When several kilovolts are applied between the two electrodes, neutral molecules are ionized at the negative electrode. These ions are then driven by the Coulomb force along the electric field lines to the positive electrode, where they are neutralized. The motion of the ions induces local motion of the fluid via viscous drag. The asymmetric spacing between the electrodes introduces directional asymmetry, generating bulk flow in the pump, i.e., there are small gaps with high electric fields pumping strongly in one direction and large gaps with lower electric fields pumping weakly in the opposite direction.
Fig. 1. EHD fiber pump and comparison of pumping performance of different dielectric fluids and pump designs.
(A) The working principle of charge injection EHD for a fiber pump. (B) The EHD fiber pump used in this study has helically wound electrodes partially embedded inside a thermoplastic shell, with wire spacings of 0.8 and 1.6 mm. The inner and outer fiber diameters are 1.2 and 2 mm. (C) Pump curves for three working fluids, at the maximum applicable voltage for each individual fluid, illustrating the strong dependence of pressure and flow rate on the fluid. (D) Pump performance as a function of fluids for Cu-electrode fiber pumps at 6.4 kV showing that both (a) pressure drop and (b) flow rate are higher for liquids with lower viscosity and with higher dielectric constant. Propylene carbonate is not included in this figure as its maximum operating voltage is below 6.4 kV. (E) Performance comparison of the EHD pumps used in this work with literature values (4, 16, 18–23); each point was evaluated at the highest operating voltage. The fiber pumps with propylene carbonate and Novec 7100 stand out for their high performance. Two phase spaces are plotted: (a) maximum flow velocity versus maximum normalized pressure drop and (b) maximum power density versus maximum efficiency. (F) Using an 18-cm-long EHD fiber pump to drive a hydraulic piston to raise a 1.5-kg pumpkin (movie S1), comparing (a) Novec 7100 with (b) propylene carbonate.
Figure 1B shows images of a fiber pump with copper wire electrodes. All fiber pumps in this study share the same geometry: 18 cm long, with asymmetric electrode gaps of 0.8 and 1.6 mm, 1.2-mm inner diameter and 2-mm outer diameter, hence a wall thickness of 400 μm. We compare the pumping performance of 11 different EHD fluids spanning three major categories with a broad range of physical properties.
Given the coupling of fluid dynamics and electrostatics in EHD pumping, we focus on viscosity and dielectric constant as the key fluid properties to investigate. We record pump pressure, flow rate, and fluidic power, allowing us to compare EHD pumps with conventional pumps. Figure 1C plots pump curves for three representative EHD fluids, silicone oil (εr = 2.7, μ = 19 mPa·s), Novec 7100 (εr = 6.8, μ = 0.58 mPa·s), and propylene carbonate (εr = 64, μ = 2.5 mPa·s). The different working fluids exhibit different pumping performance. We also monitor electric current and can hence report the conversion efficiency from electrical power input to fluidic power output.
Figure 1D (a and b) presents the maximum pressure drop and flow rate of various working fluids in our Cu-electrode fiber pumps at 6.4 kV, plotted against the dynamic viscosity μ and the dielectric constant εr of these fluids as a 3D plot. The 3D representation helps visualize how viscosity and permittivity shape the performance landscape in a coupled manner. We observe a clear trend that lower viscosity and higher dielectric constant lead to considerably better performance. For instance, at the same applied voltage of 6.4 kV, from PDM 20 silicone oil (μ = 18.9 mPa·s, εr = 2.7) to 3-methoxybutyl acetate (μ = 0.7 mPa·s, εr = 8), pressure increased from 23 to 227 kPa/m (~10 times), and flow rate increased from 1 to 68 ml/min (more than 60 times). This can be intuitively explained as: Lower viscosity means lower frictional losses, while a higher dielectric constant increases electrostatic forces. However, lower viscosity could also entail reduced drag of ions on neutral molecules. Thus, tuning viscosity might involve a trade-off between fluidic impedance and viscous drag. Within the viscosity range covered in this work, the change in fluidic impedance due to viscosity is the dominant factor. A different trend might emerge at even lower viscosities, i.e., substantially lower than 0.5 mPa·s, but such liquids would likely be too volatile to remain in the liquid phase for stable EHD pumping.
We compare the performance of our fiber pumps with different working fluids with previously reported EHD pumps in two performance phase spaces, as shown in Fig. 1E: (a) maximum flow velocity versus maximum normalized pressure drop and (b) maximum volumetric power density (considering internal pump volume) versus maximum efficiency. This representation allows us to directly visualize how pump geometry and fluid choice jointly determine the attainable performance envelope. In these maps, fiber pumps (filled circles for data from this work; filled squares for literature data), planar pumps (open triangles), and needle-ring pumps (filled triangles) form three distinct clusters. Colors denote the working fluids, highlighting the coupled influence of liquid selection and pump design on overall EHD performance. Across the fluids used in this work, fiber pumps span an order-of-magnitude in maximum pressure and flow. Pumping propylene carbonate extends the fiber-format pump cluster toward the top-right region of both performance spaces, considerably expanding the attainable boundaries in pressure drop, flow velocity, and volumetric power density. The detailed calculations for EHD pumps from literature (4, 16, 18–23) are provided in table S1 and in the Supplementary Text. Data for the fiber pumps in this work using different EHD fluids are listed in table S2.
We illustrate the fluidic power output of an 18-cm fiber pump by using it to drive a hydraulic piston to raise loads. In Fig. 1F, we compare the performance of Novec 7100 and propylene carbonate as the working fluid. When 8.8 kV is applied for 9 s, an 18-cm fiber pump using Novec 7100 raises the 1.5-kg pumpkin by 6.6 mm, corresponding to a fluidic power of 10 mW. With propylene carbonate at 4.4 kV, an 18-cm fiber pump raises the pumpkin by 23.4 mm, for a fluidic power of 38.4 mW, approximately four times that of Novec 7100. For a 3.75- or 5-kg load, only using propylene carbonate does the fiber pump generate sufficient pressure to raise the weight. A detailed description of the demonstration setup and related experimental results is provided in the “Hydraulic piston driven by an 18-cm-long fiber pump” section.
Testbench and testing protocol
All measurements here were taken using a fiber pump testbench using a rigorously defined protocol, allowing consistent comparison of more than 32 fiber pumps. As depicted in Fig. 2A, the testbench features a closed-loop fluidic circuit integrating an EHD fiber pump. Two pressure sensors measure the pressure drop across the pump, and the flow rate sensor captures the flow. A pinch valve controls the fluidic impedance. The pump is powered by a high-voltage power supply (HVPS) with built-in voltage and current monitors (see Materials and Methods). The pump generates clockwise flow in the loop for the polarity shown in Fig. 2A. A pressure regulator and a compressed air source allow applying an overall bias pressure of up to 100 kPa, which allows operation at slightly higher voltages by delaying bubble formation (fig. S2) (38). An optical image of the setup is shown in fig. S4.
Fig. 2. Fiber pump testbench and test protocol.
(A) A schematic diagram of the testbench. (B) Example of process to obtain a pump curve for one voltage value. Time evolution of applied voltage, measured flow rate, and measured pressure drop. After 30 s of stabilization, the pinch valve is closed in eight steps to increase flow impedance. (C) Measured pump curves for different applied voltages. (D) Fluidic power versus flow rate for different applied voltages. (E) Efficiency versus flow rate. The working fluid is Novec 7100. A 100-kPa bias pressure is applied during the test. The data are acquired from a Cu-electrode fiber pump.
Before pump curve data acquisition, the pump’s performance must be allowed to stabilize. This is an important and often underreported step as the high-performance pumping occurs after a “conditioning” phase during which the pump performance changes before stabilizing. For each new pump, with the pinch valve fully open, we gradually increase the voltage in steps while monitoring pressure, flow rate, and current to assess pumping stability. In some cases, an activation process is observed before stabilizing, during which the pump performance gradually improves over time (see fig. S5 for Novec 7100 and fig. S6 for 3-methoxybutyl acetate). All data here are recorded after reaching stable pumping.
Once the pump performance has stabilized, we ramp up the voltage in steps to measure “pump curves” for different voltages. Pump curves are plots of pressure versus flow rate at a fixed voltage, taken by varying the flow impedance. These curves allow determining maximum pressure, flow rate, and fluidic power. Figure 2B illustrates a representative measurement methodology. A detailed description of the measurement protocol can be found in Materials and Methods. An example of the complete pump characterization test of a Cu-electrode fiber pump is shown in fig. S7.
By closing the pinch valve in steps for different settings of the voltage, pump curves for different voltages are obtained (Fig. 2C). The fluidic power output is the product of flow rate Q and pressure drop ∆p, giving us the fluidic power curve (Fig. 2D). The electrical input power , determined from the voltage and current monitors of the HVPS, allows us to compute the pump’s efficiency in converting electrical power to fluidic power, resulting in the efficiency curve shown in Fig. 2E.
As shown in Fig. 2 (D and E), both the maximum fluidic power output and maximum efficiency occur at intermediate flow conditions, rather than at the extremes of pressure or flow rate. This comprehensive characterization process provides a full evaluation of EHD pump behavior, which is essential for applications, as some will call for maximum fluidic power, but others for high pressure and others for high flow rate.
EHD fluid comparison in fiber pumps
We measured the pumping performance of both Cu- and Au-electrode fiber pump with 11 dielectric liquids, spanning a wide range of viscosities and dielectric constants (see Table 1). Because fluorinated liquids are generally not environmentally friendly, Novec 7100 is the only fluorinated fluid involved in our comparison, serving as the performance benchmark because it is the prevalent fluids for interdigitated-electrode EHD pumps (4, 5, 16, 18). We also included two other esters commonly used in needle-ring pumps, linalyl acetate (6, 23), and dibutyl sebacate (37). To expand the list, we selected two esters with viscosity and dielectric constant similar to Novec 7100: 3-methoxybutyl acetate and diethyl malonate. We also included propylene carbonate, an ester with a much higher dielectric constant of 64, and a low-voltage dc conductivity approximately two orders of magnitude higher than that of Novec 7100 (41, 42), to investigate whether there is an upper limit of dielectric constant for pumpable fluids. Five silicone oils were further added as they share similar dielectric constants (2.3 to 2.8) but span a wide viscosity range, making them suitable for isolating the effect of viscosity on EHD pumping. In this work, we focused on silicone oils ranging from ultralow [1.5 centistokes (cSt)] to moderate viscosity (20 cSt).
Table 1. Properties of the 11 fluids used in this research.
| Fluid category | Fluid name | Viscosity (mPa·s) | Dielectric constant | Molecular formula |
|---|---|---|---|---|
| Fluorinated organic fluids | Novec 7100 | 0.58 | 6.8 | C5H3F9O |
| Nonfluorinated organic fluids | 3-Methoxybutyl acetate | 0.7 | 8 | C7H14O3 |
| Diethyl malonate | 1.9 | 7.9 | C7H12O4 | |
| Linalyl acetate | 2.16 | 2.4 | C12H20O2 | |
| Propylene carbonate | 2.5 | 64 | C4H6O3 | |
| Dibutyl sebacate | 7.4 | 4.56 | C18H34O4 | |
| Organosilicon fluids | 1.5 cSt silicone oil | 1.27 | 2.36 | C10H30O3Si4 |
| 5 cSt silicone oil | 4.56 | 2.6 | [─Si (CH3)2O─]n | |
| 10 cSt silicone oil | 9.35 | 2.68 | [─Si (CH3)2O─]n | |
| PDM 20 silicone oil | 18.9 | 2.7 | [─SiC6H5O1.5─]m[─Si (CH3)2O-]n | |
| 20 cSt silicone oil | 19 | 2.72 | [─Si (CH3)2O─]n |
Among the 11 fluids, 10 could be stably pumped in Cu-electrode fiber pumps, while propylene carbonate led to rapid electrochemical erosion of the copper electrodes (fig. S30). To probe the role of electrochemical reactions in EHD pumping, a subset of five fluids from the 10 Cu-compatible ones was tested using Au-electrode pumps. By using Au electrodes, electrochemical reactions with propylene carbonate were delayed, enabling stable pumping of this more conductive and reactive fluid compared to Novec 7100. Among the 11 fluids, only 3, including Novec 7100, linalyl acetate, and dibutyl sebacate, have been previously reported for EHD pumping, while the remaining 8 are reported here.
Pump performance data for Cu-electrode pumps are shown in Fig. 3 (A to E). All 10 fluids, including the 7 previously unidentified ones, showed strong EHD pumping, at a level where they can be used for a wide range of applications.
Fig. 3. Performance of selected dielectric liquids in EHD fiber pumps as a function of voltage.
(A to E) Cu-electrode fiber pumps. (A) Pressure drop, (B) flow rate, (C) current, (D) efficiency, and (E) fluidic power as functions of applied voltage for different working fluids. (F to J) Au-electrode fiber pumps. (F) Pressure drop, (G) flow rate, (H) current, (I) efficiency, and (J) fluidic power as functions of applied voltage for different working fluids. Error bars indicate SDs across three pumps with three trials for each pump.
Key metrics, including pressure drop (here, normalized by the length of the electrode), flow rate, current, efficiency, and fluidic power (normalized by the length of the electrode), were measured at different voltages. As shown in Fig. 3 (A, B, and E), all fluids show higher pressure drop, flow rate, and fluidic power with rising voltage. Detailed performance data of these 10 Cu-compatible fluids, obtained from three Cu-electrode fiber pumps per fluid, are provided in figs. S8 to S17. Note that the pump IDs used for different fluids differ. This is because, in general, we used newly fabricated fiber pumps to avoid possible aging effects. When multiple fluids are scheduled to be tested within a few days, however, the same fiber pump may be reused after a thorough cleaning procedure, as described in Materials and Methods. We verified the consistency of our fiber pumps’ performance by benchmarking using Novec 7100, as shown in fig. S3 with data from 14 Cu-electrode fiber pumps. This consistency allows us to confidently use newly fabricated fiber pumps for each fluid.
Novec 7100 exhibits the best overall performance of the 10 Cu-compatible fluids, generating the second-highest pressure drop (268 kPa/m), the highest flow rate (73 ml/min), and the highest fluidic power output (107 mW/m) although at 8.8 kV, alongside the highest efficiency (2.3%).
Among nonfluorinated organic fluids category, two newly used esters for EHD also deliver competitive results. 3-Methoxybutyl acetate achieves a pressure drop of 227 kPa/m and a flow rate of 68 ml/min, yielding a peak fluidic power output of 97 mW/m at 6.4 kV, comparable to Novec 7100 at much higher voltages. Diethyl malonate reaches the highest pressure drop (290 kPa/m) among all the candidates at 9.6 kV. Despite its higher viscosity and conductivity, which limit flow rate (48 ml/min) and efficiency (0.4%), diethyl malonate achieves a high fluidic power (100 mW/m) on par with Novec 7100 and 3-methoxybutyl acetate. Among the two esters used in prior work for EHD, linalyl acetate leads to a pressure drop of 118 kPa/m, a flow rate of 28 ml/min, and 0.6% efficiency at 8 kV, while dibutyl sebacate yields 124 kPa/m and 11 ml/min at 8.8 kV, both performing well below the two newly used esters in Cu-electrode fiber pumps.
Among all the silicone oils, 1.5 cSt silicone oil shows the best performance, delivering a pressure drop of 160 kPa/m, a flow rate of 49 ml/min, and a fluidic power of 43 mW/m at 8.8 kV. Despite the slightly lower (0.6 times) performance of benchmark fluid Novec 7100, its relatively low current (64 μA) enables an efficiency of 1.4%, as the second highest among all the fluids in Cu-electrode fiber pumps.
To explore the possible role of electrochemistry in Cu-electrode fiber pumps, Au-electrode fiber pumps were tested with Novec 7100, 3-methoxybutyl acetate, linalyl acetate, dibutyl sebacate, and 1.5 cSt silicone oil as a subset of 10 Cu-compatible fluids (Fig. 3, F to J). The overall performance trends match closely those of Cu-electrode fiber pumps. 3-Methoxybutyl acetate and linalyl acetate show nearly identical results in both Au- and Cu-electrode fiber pumps (figs. S19 and S21). For Novec 7100, the Au-electrode fiber pump has lower performance at voltages below 6.4 kV. However, their performance converges at 8.8 kV (fig. S18). For 1.5 cSt silicone oil and dibutyl sebacate, the Au-electrode fiber pump delivers 0.5 to 0.6 times of the pressure and flow rate of Cu-electrode fiber pumps (figs. S20 and S22). These differences may arise from sample-to-sample variation. Alternatively, they could also suggest that electrochemical effects, while not necessarily dominant, could be involved and contribute differently in EHD pumping—and in some cases, positively, such as through enhanced ion formation—to EHD pumping in certain fluids.
We tested propylene carbonate in Au-electrode fiber pumps. This liquid is stable in Au-electrode fiber pumps but leads to rapid degradation of copper electrode fiber pumps at several kilovolts. At 4.4 kV, Au-electrode fiber pumps with propylene carbonate generated a pressure of 892 kPa/m and a flow rate of 128 ml/min, corresponding to a maximum fluidic power output of 560 mW/m (using internal volume). This fluidic power is equivalent to a specific power of 347 W/kg (empty pump mass), ~30 times higher than the specific power of 11 W/kg previously reported for fiber pumps using Novec 7100 (5). The efficiency is 1.1%, comparable in order of magnitude to those of the other tested liquids. The current is 2.1 mA, an order of magnitude higher than for Novec 7100. This higher current correlates with the higher low-voltage dc conductivity of propylene carbonate. The strongly nonlinear current-voltage characteristics of EHD pumps, however, indicate nonohmic electrical conduction. The conductivities at high electric fields are likely very different from those at low voltages. Detailed performance data of propylene carbonate in three different Au-electrode fiber pumps are provided in fig. S23.
Unlike other liquids, whose performance is limited by electrical breakdown at high voltages, propylene carbonate pumping is instead limited by the high pressures that it generates in fiber pumps. At voltages beyond 4.4 kV, the pressure (greater than 200 kPa for an 18-cm fiber pump) becomes high enough to start deforming the pump walls, posing a risk of mechanical failure. Hence, we limited the maximum applied voltage to 4.4 kV (fig. S24). In future work, enhancing the mechanical strength of the fiber pump through fiber reinforcement or increasing the wall thickness or changing wall materials could enable operation at higher voltages with propylene carbonate and further improve performance.
EHD fluid comparison in a needle-ring pump
To assess whether the trend that low-viscosity and high-permittivity liquids lead to higher EHD performance also applies to a nonsymmetrical EHD structure, we fabricated a copper needle-ring EHD pump encapsulated in a 3D printed enclosure. A detailed illustration of the structure, fabrication process, and dimensions of this pump can be found in Materials and Methods and in fig. S25. We selected the same five representative fluids for the Au-electrode fiber pump test: Novec 7100, 3-methoxybutyl acetate, linalyl acetate, dibutyl sebacate, and 1.5 cSt silicone oil. All five fluids were pumpable in the Cu-electrode needle-ring pump, with Novec 7100 and 3-methoxybutyl acetate exhibiting the highest performance (fig. S26). All tests in the needle-ring pump were conducted without bias pressure. Each fluid was tested on the same needle-ring pump with three trials.
In the needle-ring pump, the preferred polarity of the electrodes for pumping depends on the fluid. We observed polarity-independent flow direction for both 3-methoxybutyl acetate and linalyl acetate, always from the needle-electrode to the ring-electrode (figs. S27 and 28). Such polarity-independent pumping in needle-ring pumps has been reported in previous work with linalyl acetate (22). For dibutyl sebacate, consistent with previous research (6, 23), pumping only occurs when the needle serves as positive electrode. In contrast, Novec 7100 and 1.5 cSt silicone oil both required a negatively biased needle to enable pumping.
Effect of fluid viscosity effect on EHD pumping in fiber pumps
To compare how fluid viscosity affects pumping, we compared pump performance for all liquids at 6.4 kV, which is the highest voltage applicable to all liquids except propylene carbonate. Some liquids can be operated at higher voltages, with higher pressure and flow rate. These maximum performance points were used in Fig. 1D.
Figure 4 (A to E) shows a clear decrease with increasing viscosity of key performance metrics for all tested fluids in fiber pumps, at 6.4 kV for both Cu and Au electrodes. Pressure drop (Fig. 4A), flow rate (Fig. 4B), efficiency (Fig. 4D), and fluidic power output (Fig. 4E) all drop as viscosity increases. A sharp drop in performance is observed in the moderate-to-low viscosity range, particularly around 3 to 5 mPa·s. Fluids with viscosities below this threshold, such as Novec 7100, 3-methoxybutyl acetate, and 1.5 cSt silicone oil, deliver higher output across all metrics. Beyond 5 mPa·s, further increases in viscosity result in only marginal additional performance loss, suggesting a plateauing effect where viscous resistance has already become the dominant limiting factor.
Fig. 4. Effect of viscosity on EHD pumping performance in fiber pumps at 6.4 kV for both Cu and Au electrodes.
Lower viscosity improves all pump metrics. (A) Maximum pressure drop, (B) maximum flow rate, (C) maximum current, (D) efficiency, and (E) maximum fluidic power with respect to the viscosities of 10 different EHD fluids. For Cu-electrode fiber pumps, the data are an average of three pumps with three repeats for each pump. For the Au-electrode fiber pump, the data are an average of a single pump with three repetitive tests. The error bars represent the SD.
The relationship between current and viscosity, by contrast, is not strictly monotonic (Fig. 4C). For instance, diethyl malonate and linalyl acetate exhibit nearly identical viscosities (2 mPa·s), yet diethyl malonate generates a pump current approximately five times higher. Despite this large current difference, the two fluids exhibit comparable pressure drop, flow rate, and fluidic power output (Fig. 4, A, B, and E).
Dielectric constant’s effect on EHD pumping in fiber pumps
As shown in Fig. 5 (A to E), fluids with higher dielectric constants generally exhibit better performance, particularly in pressure drop, flow rate, and fluidic power. The same trend is observed in both Au- and Cu-electrode fiber pumps. For example, 3-methoxybutyl acetate (εr = 8) and Novec 7100 (εr = 6.8) show consistently strong performance across all metrics, outperforming liquids with lower dielectric constants, including all silicone oils and linalyl acetate. However, despite the similar dielectric constant, diethyl malonate (εr = 7.9) underperforms Novec 7100 and 3-methoxybutyl acetate, especially in flow rate and fluidic power output. This difference can be attributed to its higher viscosity (1.9 mPa·s), approximately three times that of 3-methoxybutyl acetate (0.7 mPa·s).
Fig. 5. Effect of dielectric constant on EHD pumping performance in EHD fiber pumps at 6.4 kV both Cu and Au electrodes.
Higher dielectric constant generally improves pump metrics. (A) Maximum pressure drop, (B) maximum flow rate, (C) maximum current, (D) efficiency, and (E) maximum fluidic power with respect to the dielectric constants of 10 different EHD fluids. For Cu-electrode fiber pumps, the data are an average of three pumps with three repeats for each pump. For the Au-electrode fiber pump, the data are an average of a single pump with three repetitive tests. The error bars represent the SD.
A similar interplay is observed in the low–dielectric constant range (εr < 3). With a slight increase in dielectric constant, pumping performance drops. This is likely because these fluids share close dielectric constants but differ largely in viscosity, resulting in a local trend dominated by viscosity change. This highlights the coupling effect of the two physical properties.
The two fluids with the highest dielectric constants (3-methoxybutyl acetate and diethyl malonate) exhibit the highest pump currents, both in the several-hundred-μA range (Fig. 5C). However, no clear monotonic trend is observed between dielectric constant and current in other fluids. For example, Novec 7100, despite having a high dielectric constant (6.8), generates a much lower current (43 μA) than diethyl malonate. In addition, 1.5 cSt silicone oil, with a much lower permittivity (εr = 2.3), exhibits a comparable current (26 μA) to dibutyl sebacate (εr = 4.5) with a current of 23 μA.
Viscosity and dielectric constant’s effect on EHD pumping in a needle-ring pump
Given the different breakdown voltages of the selected fluids (fig. S26), we used the data at 8 kV to compare fluids in the needle-ring pump. Figure 6A depicts a clear trend of pressure, flow rate, and efficiency, all dropping with increasing viscosity. Similarly, Fig. 6B shows performance increase with increasing dielectric constant. These results show that the trend observed in fiber pumps, where low-viscosity and high–dielectric constant fluids deliver better performance, also holds in a structurally distinct needle-ring configuration. This consistency across pump geometries supports the generality of the observation.
Fig. 6. Effect of physical properties of working fluids on EHD pumping performance in the needle-ring pump at 8 kV.
(A) Effect of viscosity on EHD pumping performance, including (a) pressure drop, (b) flow rate, and (c) efficiency. (B) Effect of dielectric constant on EHD pumping performance, including (a) pressure drop, (b) flow rate, and (c) efficiency. The same trend of increased pump performance with lower viscosity and with higher permittivity as seen as with fiber pumps. W/O, without.
Hydraulic piston driven by an 18-cm-long fiber pump
To provide an intuitive visualization of how two different working fluids affect the performance of an EHD fiber pump and to illustrate how fiber pumps can deliver fluidic power outside the testbench, we designed a hydraulic system driven by one 18-cm fiber pump. Figure 7A schematically illustrates the setup: a fiber pump drives fluid from a reservoir to a hydraulic piston, raising the load.
Fig. 7. Hydraulic piston driven by an 18-cm-long fiber pump.
(A) Schematic representation of the hydraulic system. (B) Average raising velocity and (C) average fluidic power during 9 s for propylene carbonate (at 4.4 kV) and Novec 7100 (at 8.8 kV) as working fluids. Under a 5-kg net load, (D) Novec 7100 fails to generate measurable displacement, whereas (E) propylene carbonate reaches 10-mm displacement in 9 s.
Novec 7100 and propylene carbonate were selected as the representative fluids. Novec 7100 was operated at 8.8 kV and propylene carbonate at 4.4 kV. To limit maximum piston motion, the pumps were operated for 9 s. A 50-kPa bias pressure was applied to suppress electrical breakdown; it does not contribute to piston motion because the platform was carefully preloaded to cancel this force. Details of the setup are provided in Materials and Methods and fig. S31. We evaluated the fluidic power output using a 1.5-kg pumpkin (movie S1) and metal plates from 1.25 to 5 kg (movie S2).
Figure 7 (B and C) presents the average velocity and fluidic power for the tested loads. With no external net load, the pump using Novec 7100 raises the piston by 17.3 mm in 9 s, whereas using propylene carbonate raises it by 29.4 mm. At a 1.25-kg net load, Novec 7100 raises the piston by 9.2 mm (1.0 mm/s, 12.6 mW), while propylene carbonate raises it by 24.5 mm (2.7 mm/s, 33.4 mW). At 3.75 and 5 kg, pumping Novec 7100 produces no measurable displacement (Fig. 7D), whereas pumping propylene carbonate raises the platform: 15.9 mm at 3.75 kg (1.8 mm/s, 64.8 mW) and 10.0 mm at 5 kg (1.1 mm/s, 54.7 mW), as shown in (Fig. 7E).
There is a mass for which output power is maximized, because speed decreases with increasing load (the pump is working against a higher pressure head), but the exerted force increases linearly with load. The peak fluidic power of 65 mW that we observed in the piston setup is lower than the 100 mW that we measured in the testbench likely due to loss from the extra tubing and fluidic connectors, friction in the piston, and the sliders on the rail.
DISCUSSION
This work presents a systematic and quantitative framework to investigate how fluid properties influence EHD pumping performance. Using this framework, we compared 11 dielectric liquids, including 8 previously unstudied nonfluorinated candidates under identical conditions, considerably expanding the list of viable EHD working fluids and identifying the highest performing liquid to date.
We observe that low viscosity and high dielectric constant are critical factors for increasing pump pressure, flow rate, and pumping efficiency. These trends are consistent across multiple pump configurations, including Cu-electrode and Au-electrode fiber pumps and a Cu-electrode needle-ring pump, suggesting the generality of observed trends. Among all the fluids investigated, propylene carbonate, not reported before for EHD pumping, enables a high volumetric fluidic power density of 495 mW/cm3, or, equivalently, a specific power of 347 W/kg in Au-electrode fiber pumps, ~30 times that of the previously reported EHD pump’s performance (5).
Using propylene carbonate as the working fluid, our 18-cm-long fiber pump (mass of 0.3 g) can generate a maximum of 100 mW of fluidic power, comparable to a miniature diaphragm pump (125 mW, mass of 65 g) (39). Because pressure scales linearly with pump length while flow rate is nearly length independent, a 2-m fiber pump (1 W of fluidic power, mass of 3.4 g) is expected to deliver fluidic power surpassing a compact gear pump (0.9 W of fluidic power, mass of 500 g) (40). The HVPS needs to be accounted for but can be miniaturized. For instance, Cacucciolo et al. (4) reported a 16-g and 5-kV supply, including rechargeable battery, to drive an EHD pump.
The combination of exceptionally high fluidic power density, negligible mass, and a highly integrable fiber form factor unlocks application spaces that are challenging to access with conventional pumps. For instance, a few meters of fiber pumps can supply sufficient pressure and fluidic power to drive fluidic actuators in soft robots (7–9, 43), haptic devices (14, 15), rehabilitation systems (11, 44, 45), and lightweight exosuits (10, 46) in an untethered and fully wearable format. In these systems, traditional pumps with passive connection tubing would impose considerable mass penalties and introduce disturbing noise and vibration, whereas our EHD fiber pumps provide a silent, lightweight, and highly integrable alternative. Beyond these advantages, the fiber form factor also offers unique integration flexibility in wearables: The pumps can be seamlessly woven into textiles and distributed across different regions of the body. Using electrically controlled microvalves, the flow from multiple pumps can be selectively redirected to specific actuators adaptively, allowing the output force of targeted actuators to be substantially enhanced when needed.
In this work, we also introduced a comprehensive and robust pump characterization methodology, enabling reliable and reproducible comparison of EHD pumps. Such a protocol and methodology provide support for rational EHD fluid selection and optimization, advancing the future application of EHD pumps. We hope that other groups can adopt a similar method for easier comparison of different EHD pump architectures.
While this study identifies low viscosity and high dielectric constant as critical factors influencing EHD pumping performance, the choice of working fluid is also constrained by practical considerations. Low-viscosity fluids are generally more volatile and flammable than high-viscosity ones, which may pose safety risks. For example, 0.65 cSt silicone oil has a lower viscosity than the silicone oils investigated in this work, yet it is difficult to adopt in EHD pumping due to its high volatility and flammability. Conversely, although a higher dielectric constant can lead to higher fluidic power output, it is also often associated with increased conductivity and hence pump current that might limit pumping efficiency. A more detailed understanding of the trade-offs between fluid properties and their interplay is necessary.
The mechanisms of ion formation and transport in EHD systems also require deeper investigation, beyond the scope of this paper. The fluid-dependent performance differences between Cu- and Au-electrode fiber pumps suggest that electrochemistry is involved in ion generation for some liquids but not for others and that different mechanisms might dominate at different voltage levels.
For some fluids with similar viscosities, such as diethyl malonate and linalyl acetate, the pump electrical currents differ by nearly a factor of 5, yet their resulting pressure drop, flow rate, and fluidic power remain comparable. This suggests that, in certain liquids, a considerable fraction of ion transport may not effectively contribute to bulk fluid motion, perhaps linked to the size of the ions.
The highest pump currents are observed in fluids with the largest dielectric constants, such as propylene carbonate, 3-methoxybutyl acetate, and diethyl malonate, but, beyond these cases, we observe no clear trend between dielectric constant and pump current. These phenomena indicate that the magnitude of ion migration, reflected by pump current, is influenced not only by dielectric constant but could also involve other mechanisms, further underscoring the complexity of ion transport in EHD pumping systems.
These findings question whether all ion formation and transportation processes are beneficial for pumping performance, efficiency, and lifetime. Future studies may explore how electrode materials can be used to selectively promote or suppress specific ion pathways to optimize both output and durability.
In this work, with a symmetric electrode geometry in fiber pumps and an asymmetric electrode spacing, the net flow of all 11 fluids is from the negative to the positive electrode. However, in the needle-ring pump, with its nonsymmetrical geometry, the flow direction and flow rate are liquid dependent. These fluid- and geometry-dependent varying pumping directions suggest a potential complex coupling effect of the ionization of different fluids and the fluid dynamics in certain pump designs. Further efforts to clarify ion formation and ion transport mechanisms and to visualize the EHD flow (e.g., if there are periodic vortices that could lead to lower efficiency) are essential.
Last, this work demonstrates that several working fluids in EHD fiber pumps can stably achieve a fluidic power output of ~0.1 W/m. Using propylene carbonate, the pumps deliver pressure of up to 890 kPa/m, flow rate of 128 ml/min, and a maximum fluidic power output close to 0.6 W/m. This level of performance means that fiber pumps only a few meters in length can reliably leverage the many well-established fluidic actuators while getting rid of passive tubing and rigid compressors that can tether the system in numerous application scenarios. The low energy conversion efficiency remains the primary bottleneck. In future work, we aim to improve the energy efficiency of EHD fiber pumps to enable operation with compact, lightweight power supplies, paving the way for fully untethered and seamlessly integrated soft robotic systems and wearable devices.
MATERIALS AND METHODS
Fabrication of EHD fiber pumps
The fabrication process of EHD fiber pumps, including the preparation of the threads and the winding process, is illustrated in fig. S1. We follow closely the methods that we reported in our previous work (5) but use PP rather than TPU for the shell of the fiber, due to its much better chemical compatibility. We start with a PP filament with a 1.75-mm diameter (Purefil clear PP filament) and extrude it at 240°C from a 400-μm nozzle to create 400-μm-diameter PP threads (fig. S1A). Following extrusion, to achieve the electrode spacings of 0.8 and 1.6 mm (see Fig. 1B), a total of six polymer threads and two electrode wires are mounted on the threads clamp, which is affixed to a linear stage, and held in place by the thread holder at the bottom, which is mounted on a rotational stage (see fig. S1B). To ensure correct tension, weights are attached to the threads and electrode wires. During the winding process, the threads are wound around a steel rod by simultaneously raising the linear stage and rotating the rotational stage. By controlling the ratio of the speeds of the linear stage and rotational stage, the threads are tightly wound onto the rod. Before winding, the rod was spray coated with a mold-release agent (Ease Release 200, Mann-release) for easy removal after fabrication. A detailed winding fabrication process of PP fiber pumps can be found in fig. S1C.
Fabrication of the needle-ring pump
The fabrication process of the copper needle-ring pump is depicted in fig. S25A. First, a pump box and a pump cap are printed using a 3D printer (Prusa MK4) with PP filaments (Centaur PP Natural, FormFutura). A pair of needle-ring electrodes are computer numerical control (CNC) manufactured from a copper block. Wires are soldered for electrical connections. Next, the electrodes are placed inside the pump box, closed with the 3D printed PP cap. Epoxy is applied to seal the pump. Dimension of the pump are given in fig. S25B. The pump has two Luer connections on both sides, which will be further connected to two Luer-barb adapters to be connected to soft tubing, as shown in the optical image in fig. S25C.
Fluid comparison testbench
Sensors and valve
The fluid comparison testbench integrates two pressure sensors (PA-750-352G-R2, Nidec Components Corporation), one large-measurement-range flow rate sensor for propylene carbonate (EK-SLF3S-4000B, Sensirion AG) and another mid-measurement-range flow rate sensor for the rest of the fluids (EK-SLF3C-1300F, Sensirion AG), and a pinch valve (MPPV-4, Resolution Air). The pressure sensors are connected to a data acquisition device (DAQ, NI USB-6001, National Instruments). The flow rate sensor is connected to a computer via USB for data readout.
Flow rate sensor calibration
This is an essential step as the Sensirion flow meter calibration is strongly liquid dependent due to the wide range of viscosity and thermal conductivities of fluids that we used. The flow rate sensors were calibrated in water mode before experiments using a syringe pump (NEM-B101-02 C, CETONI GmbH). For the EK-SLF3S-4000B sensor, flow rates from 1 to 160 ml/min were imposed with a 50-ml syringe in discrete steps; for the EK-SLF3C-1300F sensor, 1 to 100 ml/min were imposed with a 30-ml syringe in discrete steps. Each step was maintained for 10 s to average the output. The raw sensor signals were recorded and fitted to the imposed flow rates by spline interpolation, and the resulting calibration functions were embedded in the testbench code for consistent flow rate readout in all tests.
Single-channel HVPS
The single-channel HVPS is driven by a 15-W dc-dc converter (Ultravolt 10A24-P15-15, Advanced Energy), which steps up an input of 24-V dc from a power adapter (GST60A12-P1J, MEANWELL) to an output of up to 10 kV with a maximum current of 1.5 mA. The HVPS includes built-in voltage and current monitors, which are connected to the DAQ for real-time acquisition of electrical power supplied to the pumps. An optical image of the single-channel HVPS can be found in fig. S29.
Three-channel HVPS
The three-channel HVPS is driven by three 15-W dc-dc converters (Ultravolt 10A24-P15-15, Advanced Energy), which steps up a 24-V dc input from a power adapter (GST120A12-P1J, MEANWELL) to an output of up to 10 kV with a maximum current of 4.5 mA. The system includes built-in voltage and current monitors, which are connected to the DAQ for real-time acquisition of electrical power input for the pumps. This power supply with higher current capacity is used only for testing fiber pumps with propylene carbonate.
Testbench cleaning
To prevent cross-contamination between different working fluids, all components are thoroughly cleaned between tests. The pressure and flow rate sensors are disconnected, rinsed with isopropanol (IPA), and dried using compressed air for 1 min.
Pump reusing and cleaning
After testing a pump with one fluid, to be reused for another fluid, the pump was thoroughly cleaned to avoid cross-contamination. We flush the pump with IPA and then gently dry with flowing nitrogen inside a fume hood overnight.
Pump characterization measurement protocol
We characterize pump’s performance at different applied voltages. At each voltage level, we hold the voltage for Tvoltagestabilization = 30 s to ensure the performance remains stable. The pinch valve is closed in steps to obtain the pump curves, including pressure, power, and efficiency as functions of flow rate. For each valve position, the pump is stabilized for Tvalvestabilization = 2 s, followed by a measurement period as Tmeasurement = 5 s. The average over the 5 s is taken as one data point. Figure 2B shows a representative test at 8.8 kV with Novec 7100, resulting in eight data points (blue scatter in Fig. 2C). The full voltage sweep from 1.6 to 8.8 kV is also shown in fig. S7.
Hydraulic piston
An 18-cm-long fiber pump is connected between a reservoir and a hydraulic piston (details in fig. S31). The piston is a 50-ml glass syringe with a 28-mm diameter (Eterna Matic glass syringe, Sanitex SA) mounted in a 3D printed holder and enclosed within an aluminum rail cage with poly(methyl methacrylate) side panels. The syringe piston has a low-friction coating that maintains a liquid seal while enabling smooth motion. A bias pressure of 50 kPa is applied to the reservoir using a compressed air source and is balanced by 3-kg preloaded weights on the piston. This value is selected to ensure that the total pressure, including the pressure required to lift the maximum net loads of 5 kg, remains below the typical working pressure limit (150 kPa) of the glass syringe. The plate is guided along the rails by four adapters, with grease applied to minimize friction. A flow rate sensor is used to monitor pump performance during operation. The liquid is initially pumped in a closed loop within the testbench, with no flow to the piston. Once stable EHD flow is confirmed, the flow is redirected to the piston to raise the load. The actuation duration (9 s) is chosen so that the piston maximum displacement remains within 40% of the syringe volume, thereby avoiding piston-tilting or leaks.
Acknowledgments
We thank M. Smith for valuable discussions and all EPFL-LMTS group members for help.
Funding:
This work was supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number 22.00180 (recipient H.S.), and by the Novo Nordisk Foundation under grant no. NNF22OC0071130 (Project WeArAble, recipient H.S.).
Author contributions:
Conceptualization: Y.L., H.S., and M.S. Methodology: Y.L., H.S., and M.S. Investigation: Y.L. Data curation: Y.L. Validation: Y.L. and M.S. Formal analysis: Y.L. Software: Y.L. and M.S. Visualization: Y.L. Supervision: H.S. and M.S. Project administration: H.S. Funding acquisition: H.S. Writing—original draft: Y.L. Writing—review and editing: Y.L., H.S., and M.S.
Competing interests:
The authors declare that they have no competing interests.
Data, code, and materials availability:
All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials.
Supplementary Materials
The PDF file includes:
Supplementary Text
Figs. S1 to S31
Tables S1 and S2
Legends for movies S1 and S2
Other Supplementary Material for this manuscript includes the following:
Movies S1 and S2
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Supplementary Text
Figs. S1 to S31
Tables S1 and S2
Legends for movies S1 and S2
Movies S1 and S2
Data Availability Statement
All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials.







