High-performance Marangoni hydrogel rotors with asymmetric porosity and drag reduction profile

Miniaturized rotors based on Marangoni effect have attracted great attentions due to their promising applications in propulsion and power generation. Despite intensive studies, the development of Marangoni rotors with high rotation output and fuel economy remains challenging. To address this challenge, we introduce an asymmetric porosity strategy to fabricate Marangoni rotor composed of thermoresponsive hydrogel and low surface tension anesthetic metabolite. Combining enhanced Marangoni propulsion of asymmetric porosity with drag reduction of well-designed profile, our rotor precedes previous studies in rotation output (~15 times) and fuel economy (~34% higher). Utilizing thermoresponsive hydrogel, the rotor realizes rapid refueling within 33 s. Moreover, iron-powder dopant further imparts the rotors with individual-specific locomotion in group under magnetic stimuli. Significantly, diverse functionalities including kinetic energy transmission, mini-generator and environmental remediation are demonstrated, which open new perspectives for designing miniaturized rotating machineries and inspire researchers in robotics, energy, and environment.

. The changes in shape and weight of hydrogel rotor under different states. By comparing the weight of hydrogel rotor when it is full of fuel and completely dried, we can obtain wHFIP/wmotor = 76.6%. By comparing the geometric sizes of hydrogel rotor when it is full of fuel and full of water, it can be demonstrated that PNIPAm has similar swelling behavior in HFIP and water. When the rotor is transferred into HFIP for fuel filling, some green dyes in the rotor diffuse into HFIP, which makes the color of the rotor fade.

Supplementary Note 1. Biocompatibility of HFIP fuel
HFIP is a metabolite of sevoflurane, which is approved by the Food and Drug Administration (FDA) and widely used in inhaled general anesthesia [1,2] . Approximately ~5% of the sevoflurane dose is metabolized into HFIP, which is then rapidly conjugated with glucuronic acid and excreted in urine [1] . In addition, some clinical studies have proved that intravenous administration of HFIP can reduce inflammation and improve survival in murine septic peritonitis [3,4] . According to the median lethal dose (LD50, 0.18 mg/g in mice when administered intravenously, reported by U.S. Army Armament Research & Development Command, Chemical Systems Laboratory, NIOSH Exchange Chemicals. Vol. NX#03623), an adult mouse (~20 g) is injected with 3.6 mg of HFIP intravenously to achieve median lethality. The mass of HFIP in a certain rotor (r=250 µm, h=474 µm and c=8) is only ~0.2 mg, which is significantly below the intravenous lethal dose. Figure 8. Surface tension characterization of HFIP at different concentrations. The surface tension of HFIP was measured by optical contact angle measuring instrument (Theta Flex, Biolin Scientific, Finland) using the pendant drop method. As HFIP concentration increases from 0% to 100% (v/v), the surface tension decreases from 72.82 mN/m to 14.53 mN/m. Error bars denote the standard deviation of the measurements. Table 1: Different Chemical fuels in hydrogel motors. Density, surface tension, boiling point, maximum rotate speed, and maximum lifetime. The geometric parameters of hydrogel rotors for the test of maximum rotation speed: r=250 µm, h=474 µm and c=8. The geometric parameters of hydrogel rotors for the test of lifetime: r=1000 µm, h=790 µm and c=8. Supplementary Figure 10. The relationships between the time ts to reach maximum rotation speed and geometric parameters of hydrogel rotor. The thickness h and teeth number n remain unchanged at 474 µm and 8 in (a), respectively. The radius r and teeth number n remain unchanged at 1000 µm and 8 in (b), respectively. The radius r and thickness h remain unchanged at 1000 µm and 551 µm in (c), respectively. Error bars denote the standard deviation of the measurements.

Supplementary Note 2. HFIP diffusion coefficients at different surface porosity
Through Einstein's equation of Brownian motion and semi-empirical pore-structure equations, the diffusion coefficient De of HFIP fuel in hydrogel can be expressed as [5,6] where Dw is the diffusion coefficient of HFIP in water (3.2×10 -9 m 2 /s), φ is the surface porosity, and c is a structural parameter that depends on the cross section of the hydrogel. The pores in the cross section of the hydrogel can be approximately considered as circular ( Supplementary Fig. S4), so c = 2 [6] . When the surface porosity of the hydrogel is 40.8% and 78.8%, the corresponding diffusion coefficients of HFIP are 1.47×10 -9 m 2 /s and 2.25×10 -9 m 2 /s, respectively. Figure 11. Comparison between asymmetric rotor and symmetric rotor. (a) Surface porosity distribution of asymmetric rotor fabricated by grayscale digital light processing. (b) Simulation of surface tension distribution after asymmetric rotor is placed at the air-water interface for 43 ms. (c) Surface porosity of symmetric rotor. (d) Simulation of surface tension distribution after symmetric rotor is placed at the air-water interface for 43 ms. (e) Surface tension distribution along profile on one tooth of asymmetric rotor. Based on the simulation result, the surface tension torque Ms of asymmetric rotor is 1.62×10 -9 N·m through numerical integration. (f) Surface tension distribution along profile on one tooth of symmetric rotor. Based on the simulation result, the surface tension torque Ms of symmetric rotor is 0.99×10 -9 N·m through numerical integration.

Supplementary Note 3. Method for evaluating drag reduction effect
For the influence of the shape on drag reduction in a specific flow field, the commonly used method in the industry is the combination of experiments and computational fluid dynamics (CFD). By keeping the flow field unchanged, the shape is modified through experiments and theoretical calculations to obtain the optimized drag reduction effect. This method is widely used in shape design of automobiles, airplanes, ships, missiles and so on [7][8][9][10] . We use this method to optimize the shape design of the rotor and realize drag reduction. First of all, a target rotation speed needs to be assumed to determine the flow field in order to continue the simulation and theoretical calculation, so that the theoretical resultant resistance torque under a specific rotor shape can be obtained. Herein, we specifically studied the theoretical resistance torques of the rotor at 5000 rpm. When the rotor rotates at the interface of water and air, it is mainly subjected to two resistances: the viscous resistance on the bottom surface and the pressure resistance on the side. Since the movement form of the rotor is rotation, it is necessary to further calculate the resistance torques (viscous resistance torque Mv and pressure resistance torque Mp) caused by these two resistances.

◼ Viscous resistance torque Mv
If edge effect and the influence of any other boundaries are neglected, the resistance torque for one side of a disc is given by [11,12] where ρ is the density of the fluid, a is the radius of the disc, ω is the angular velocity of the disc and Re is the Reynolds number.The Reynolds number can be obtained by where ν is the kinematic viscosity of the fluid. Because our rotor is not a complete disc, we introduce a coefficient η to modify Equation(S1) and obtain = 0 (S3) The coefficient η is related to the rotor shape. By numerical integration, coefficients η for different rotor shapes are obtained, as shown in Supplementary Table 3. According to geometric definition of the rotor shape (Fig. 1c), a is replaced by 2r. Finally, the viscous resistance torque Mv of the rotor during the rotation can be evaluated by For pressure resistance torque, it is caused by the pressure of water on the submerged side wall of rotor during the rotation. Pressure resistance torque Mp can be evaluated by where L is the profile of rotor, P is pressure of water at differentiation element dl on rotor profile, h is the depth to which the rotor is immersed in water (approximately equal to the thickness of the rotor), Dp is the length from the differentiation element to the rotor center, β is the angle between P and its component P′. P′ is perpendicular to the straight line connected to the rotor center.
Based on the simulation results, we can get the resultant resistance torque Mr (sum of Mv and Mp) under different shapes by numerical integration. The smaller the resultant resistance torque, the better the drag reduction effect. Table 3: Influence of rotor shape on resistance torques. Under the same type of curve, the curve shape is adjusted by changing parameters: Type Ⅰ: Circular arc by changing radius, Type Ⅱ: Spline curve by changing the position of control points, Type Ⅲ: Parabola and Type Ⅳ: Sine curve by changing the expression, Type Ⅴ: Evolvent by changing the radius of the base circle.  Figure 12. Influence of the ratio (r1/r2) of inner circle radius to tooth length on rotor performance. The geometric parameters of the rotor are as follows: r=250 µm, h=474 µm and c=8. When the ratio decreases, the maximum rotation speed increases and the lifetime decreases. Compared to the increase of the maximum rotation speed, the decrease in lifetime is very small. Therefore, r1/r2 = 1 is chosen as the shape of the rotor. Error bars denote the standard deviation of the measurements.  Figure 18. (a) A cylindrical magnet (diameter of 50 mm, height of 10 mm) is placed 15 mm below the magnetic hydrogel rotor to switch it from rotation to revolution. (b) Simulation of magnetic field formed in the plane of the rotor. The black arrow and gray arrows represent the direction of Fe3O4 nanoparticle chains and the direction of the magnetic field, respectively. The magnetic hydrogel rotor is subjected to a force Fm towards the center due to the magnetic field gradient. Since Fe3O4 nanoparticle chains inside the rotor tend to be consistent with the direction of magnetic induction line, the rotor is also subjected to a torque Mm from the magnetic field during motion. In addition, the rotor is subjected to surface tension torque Ms and resistance torque Mr (refer to Fig. 2 for details). Among them, the force Fm contributes to the centripetal force required for the revolution of the rotor, and the three torques (Mm, Ms and Mr) contribute to the rotation of the rotor during revolution. Combined with the force and torques mentioned above, the magnetic hydrogel rotor can be switched from in situ rotation to revolution under the magnetic field of the cylindrical magnet. When the magnet is removed, the rotor resumes in situ rotation. The switching operation is repeatable and reversible.