3D-printed Soft Microrobot for Swimming in Biological Fluids* Tian Qiu, Stefano Palagi, and Peer Fischer, Member, IEEE
Abstract— Microscopic artificial swimmers hold the potential to enable novel non-invasive medical procedures. In order to ease their translation towards real biomedical applications, simpler designs as well as cheaper yet more reliable materials and fabrication processes should be adopted, provided that the functionality of the microrobots can be kept. A simple single-hinge design could already enable microswimming in non-Newtonian fluids, which most bodily fluids are. Here, we address the fabrication of such single-hinge microrobots with a 3D-printed soft material. Firstly, a finite element model is developed to investigate the deformability of the 3D-printed microstructure under typical values of the actuating magnetic fields. Then the microstructures are fabricated by direct 3D-printing of a soft material and their swimming performances are evaluated. The speeds achieved with the 3D-printed microrobots are comparable to those obtained in previous work with complex fabrication procedures, thus showing great promise for 3D-printed microrobots to be operated in biological fluids.
I. INTRODUCTION Microscopic robots have attracted a lot of attention in the last decade. Indeed, they hold the potential to reduce the invasiveness of some current medical procedures, as well as to enable new procedures. Artificial microswimmers are particular attractive because they could navigate through bodily fluids to reach specific targets deep in the body, where to perform local diagnosis or therapeutic tasks [1]. However, actuating swimmers at the micro scale presents several challenges. Considering their size and speed, microswimmers experience low Reynolds number (Re) fluid dynamics. For common Newtonian liquids such as water, in this regime kinematic reversibility applies, which means that any reversible actuation cannot give rise to net propulsion. This principle is also known as the ‘scallop theorem’ [2]. Most artificial microswimmers deal with propulsion in homogeneous Newtonian fluids [3]. Two swimming mechanisms that break symmetry and are useful at low Re are therefore often used to propel artificial microswimmers: one is rotating rigid helical flagella, and the rotation is coupled to forward propulsion by a helical shape [4-6]; the other is beating flexible tails, which generates forward propulsion by a propagation wave [7-9]. However, because these schemes need to break the reciprocity, they require either a relatively complex shape and/or a complex actuation scheme. Simpler * This work was supported by the Max Planck Society and the European Research Council under the ERC Grant agreement Chiral MicroBots (278213). T. Qiu, S. Palagi and P. Fischer are with Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany (corresponding author: P. Fischer; +49 711 689-3560; e-mail: [email protected]). T. Qiu is also with Institute of Bioengineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. P. Fischer is also with the Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.
978-1-4244-9270-1/15/$31.00 ©2015 IEEE
designs, as well as cheaper yet more reliable materials and fabrication processes should be adopted to ease the translation of artificial microswimmers towards real applications, provided that their functionality can be kept. In addition, considering that most biological fluids, such as blood, the vitreous of the eye and the synovial fluid in the joints, are non-Newtonian [10], addressing micro-swimming in this kind of complex fluids is a mandatory step on the way to real biomedical applications. Some efforts have indeed been made to experimentally study the propulsion scheme in these fluids. Keim et al. reported an oscillating dumbbell structure that took advantage of fluidic elasticity to propel in viscoelastic fluids [11]. Our group has demonstrated that effective propulsion through viscoelastic hyaluronic acid gels requires the nanostructures to have a diameter that is smaller than the characteristic mesh size of the biological gel, which is in effect a nano-porous medium [12, 13]. Recently, we have shown that by exploiting non-Newtonian fluid dynamics, a microswimmer can be propelled with an actuation scheme as simple as the reversible opening and closing of a single-hinge, clamshell-like micro-structure [14]. The appeal of a single-hinge microrobot is that it is particularly simple to be implemented, and that it could be actuated by a variety of common actuators, even at small scales. Nevertheless, fabricating these microswimmers so far required a lengthy process consisting of several steps. Here, we report that it is possible to build single-hinge microrobots using commercial 3D-printing techniques. In particular, the body of the microrobot is directly 3D-printed out of a soft material, and then two permanent micro-magnets are attached to it. A weak external magnetic field applies a torque on the magnets, causing the deformation of the soft monolithic body, and finally driving the opening and closing of the single-hinge micro-structure. In this way, net forward propulsion of the 3D-printed microrobot in a non-Newtonian fluid is achieved, with swimming performances that are comparable to previously reported ones. The 3D-printing process offers many advantages over traditional fabrication techniques, as it allows complex 3D shapes to be rapidly processed and tested and thus holds enormous potential for the fabrication of soft microrobots. II. MATERIALS AND METHODS A. Microrobots Design and Modelling The schematic and dimension of the microrobot are shown in Fig. 1. The microrobots are designed to have two thick and wide shells connected by one thin and narrow hinge. The two shells are much wider than the hinge to enable a larger contact area with the fluid, which facilitates propulsion. At the same time, although the microrobots’ bodies are monolithic structures printed out of the same material, only the hinge is expected to bend under magnetic
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Israel) has a resolution of 600 dpi, which corresponds to about 42 µm, in the X and Y axes and of 1600 dpi (about 16 µm) in Z axis [15]. Since TangoBlackPlus could not be printed in high quality mode due to its large thermal expansion coefficient, it was printed in digital material mode. The two micro-magnets (⌀200×400 µm) were attached to the shells using cyanoacrylate glue (Ultra Gel, Pattex). The orientation of the magnets was achieved with the help of a bigger magnet under a stereoscope (MZ95, Leica, Germany). Finally, each microrobot was released from the supporting material using tweezers and by gently washed in deionized water.
Figure 1. Schematic and dimensions (µm) of the 3D-printed microrobot: a) top view; b) side view.
actuation, because of its higher compliance, while the deformation of the two shells is expected to be negligible. In order to verify that the designed microrobots actually exhibit this single-hinge motion, and to investigate the deformability of the 3D-printed micro-structures under the action of the weak external magnetic field, a numerical simulation was performed. The coupling with the fluid was not taken into account in the simulation, as the action of the hinge is primarily determined by the magnetic and mechanical aspects of the 3D-printed micro-structures. The simulation was performed with COMSOL Multiphysics 4.4 (AC/DC and Solid mechanics modules). The model consists of the 2D central section of the microrobot, but it also accounts for the out-of-plane thicknesses. The elastomeric 3D-printed structure was modelled as a hyper-elastic neoHookean solid (elastic modulus E set to 0.8 MPa, as reported for TangoBlackPlus). Both the interaction between the two micro-magnets (having a remanent magnetic flux density Br of 1.43 T, with the orientation reported in Fig. 1) and the action of the external magnetic field were considered in the model. The resulting forces and torques acting on each of the micro-magnets, which are treated as rigid bodies, are transferred to the soft structure, which is free to deform. First, the geometry of the microrobot in the absence of any applied external fields was determined. Then, a time-dependent simulation step was carried out, which modelled one actuation period (2 s). The magnetic field was set to increase linearly from zero to its maximum (30 mT) in the first 0.1 s, and to then exponentially decrease back to zero (see Fig. 2(b)).
C. Fluid Preparation and Rheological Measurement Fumed silica suspension is used as a non-Newtonian model fluid because of its shear-thickening property. Indeed, a fumed silica suspension is shear-thickening, because the silica nanoparticles aggregate and jam under shear, which increases the apparent fluid viscosity. As reported in [16], fumed silica powder (Aerosil 150, Evonik, Germany) was mixed with poly(propylene glycol) (PPG, Mw = 725, SigmaAldrich) at a concentration of 8% w/w. After thoroughly mixing, the solution was degassed for 3 h. Glycerol (99.5%, VWR, France) was used as received and served as the Newtonian fluid in the control experiment. A shear rate ramp experiment was carried out on a rheometer (Kinexus Pro, Malven, UK) with a 40 mm-diameter plate-to-plate geometry. The viscosity of the fumed silica suspension was measured in the range of 0.05 – 300 s-1 with a 4-min ramp time under 25 °C. The value of viscosity and its transition shear rate are highly dependent on the concentration, thus can slightly vary in different fluid batches. D. Microrobot Actuation The microrobot was actuated by an external homogeneous magnetic field, which was generated by a pair of Helmholtz coil. Briefly, the signal from a function generator was fed into a power amplifier to drive the Helmholtz pair, which generated a homogeneous (spatial)
B. Microrobots Fabrication The fabrication technique we previously adopted for single-hinge microswimmers [14] consisted of molding their bodies with polydimethylsiloxane (PDMS), which was a lengthy 4-step process including the preparation of the solid mold, liquid PDMS molding, curing followed by a release step. Here, the four steps are replaced with one single 3Dprinting step. The total width of the swimmer was set to 1 mm so that all the features could be printed in sufficiently high resolution. The 3D printer (Objet 260 Connex, Stratasys,
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Figure 2. Numerical simulation results: a) frames from the timedependent simulation; the externally applied magnetic field is represented by the arrows; the color outside the structure show the intensity distribution of the overall magnetic field; the colors inside the structure show the distribution of the mechanical stress; b) imposed magnetic field (dashed curve, right axis) and obtained aperture angle (solid curve, left axis).
deformation takes place only in the hinge, and that the two shells behave like rigid bodies, as clearly shown in Fig. 2. This confirms that the 3D-printed micro-structures, made out of this soft material and in these dimensions, exhibit a fully reciprocal single-hinge-like deformation. B. Microrobots Fabrication The flexible bodies of the microrobots are 1 mm wide in total and have sub-millimeter features, approaching the highest resolution limit of 3D-printing with the adopted soft material. The smallest feature is the middle hinge, which measures only 90 µm × 200 µm. The soft hinge structure is designed to enable movement in the microrobot without the need for a complicated assembly. Moreover, this design choice allows us to adopt a fabrication via direct 3D-printing.
Figure 3. a) A 4-by-4 array of 3D-printed microrobots; b) side view of a microrobot (a ruler with a line spacing of 1 mm is shown for comparison); c) top view.
magnetic field changing as a function of time as schematically depicted in Fig. 2(b). An asymmetric actuation (with maximum amplitude of 30 mT) with a 0.1 s linear rise and a 1.9 s exponential decay, as well as a symmetric sinusoidal wave for control experiments, was utilized. The swimming experiments were carried out in an open fluidic channel made of PDMS bonded to glass. The channel was inverted to avoid the friction between the microrobot and the bottom of the fluidic channel. The weight of the microrobot was balanced by the surface tension of the fluid/air interface. It is important to note that in control experiments we have verified that the meniscus plays no role in the swimming mechanism and that the swimming mechanism also works for a microrobot immersed in the bulk of the fluid [14]. The channel was 5 mm wide and 3 mm high to avoid boundary effects at low Re. The microrobot was imaged under bright field using a stereoscope with a CCD camera (DFC 490, Leica). Each frame of the video was extracted by FFmpeg (http://www.ffmpeg.org). The images were analyzed frame by frame and the coordinates of the midpoint of the microstructure hinge were extracted using a customized Matlab program. III. RESULTS A. Numerical Simulation The simulation shows that, in the absence of an external magnetic field, the compliant hinge bends, causing the angle between the shells to be about 120° at rest (see Fig. 2). This stationary configuration is a balance of the repulsion between the two micro-magnets and the stress in the micro-structure. The simulation also shows that when the magnetic field is applied, the micro-magnets tend to align with the external field, causing a further deformation of the hinge and, consequently, the partial closure of the micro-structure. The angle between the shells for a magnetic field of 30 mT is predicted to be about 40°. The simulation highlights that the
The microrobots are printed such that the direction of the 90 µm height is aligned with the Z axis, which is where the printer has its highest resolution. Multiple micro-structures are printed at the same time (an array of 16 microrobots is shown as an example in Fig. 3(a)). The total fabrication time is shortened from over 4 hours in the previous process [14] to about 10 minutes. Although the final dimensions of the printed structure slightly differ from the target dimensions, because of the use of a soft printing material, the printing result nevertheless reproduces the designed shape of microrobots as seen in the microscope images in Fig. 3. C. Microrobots Actuation and Propulsion The fumed silica suspension used as non-Newtonian, shear-thickening fluid exhibits an almost constant viscosity of about 1 Pa∙s at low shear rate (range from 0.1 – 2 s-1), while it rapidly rises to over 10 Pa∙s at higher shear rates (10 s-1). The transition from 2 to 10 s-1 is almost linear, and follows the power law theory
µ = m γ̇ n‒1
where µ is the apparent viscosity, γ̇ is the shear rate, m and n-1 are two coefficients which are 0.19 and 2.76 respectively. Although many biological fluids exhibit a shear thinning property, they were described by the same power law, for example whole blood [10], synovial fluid [17], mucus [18], and cytoplasm of leukocytes [10]. Therefore, the shearthickening fluid used in this paper is a model fluid resembling a whole class of power law fluids which the microrobot can swim in. In agreement with the simulation, the 3D-printed microrobots are bent at the middle hinge when no field is applied. When a magnetic field is applied the microrobots close their two shells as a function of the field strength. A fast closing and slow opening step is easily achieved by applying
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Figure 4. Fast closing and slow opening of a 3D-printed microrobot under the action of a time-asymmetric magnetic pulse in non-Newtonian fluid (scale bar: 200 µm).
process, thus enables an optimization of the design of the microrobot to reach high propulsion speed in the target fluid. The robot described herein is actuated by an external magnetic field, but the principle of low-Re swimming by means of reciprocal actuation is general. It means that most micro-actuators, e.g. bimetallic strips, shape memory alloys, or heat/light actuated polymer can be used to propel microswimmers in non-Newtonian power-law fluids such as blood, synovial fluid and mucus. Combining 3D-printing with these simple actuation schemes leads to a new class of biomedical microrobots – 3D printed robots that can move at low Reynolds number with symmetric body-shape changes.
Figure 5. Average speed of the microrobot in different conditions. Net propulsion is observed by applying a time-asymmetric magnetic field in the non-Newtonian fluid. As expected, negligible propulsion is observed in the same fluid under time-symmetric actuation, nor in a Newtonian fluid under asymmetric actuation. Each group was repeated five times respectively with the same microrobot.
REFERENCES [1]
a time-asymmetric magnetic field (see Fig. 4). Fig. 5 shows the results from a propulsion test on a 3Dprinted microrobot in the non-Newtonian fluid. The results from two control experiments on the same microrobot are also reported for comparison. A net displacement is achieved when the 3D-printed microrobot is propelled in a shearthickening fluid under time-asymmetric magnetic excitation. The average speed of the 3D-printed microrobot is calculated to be 4.8±1.9 µm/s under asymmetric actuation, which shows a significant difference compared to the two (non-swimming) control groups, where negligible net displacements are observed. The average speed of the 3D-printed microrobot is in a similar range as those obtained with complex fabrication procedures [14]. The mechanism that underlies swimming at low-Re with reciprocal motion is that during the fast-closing half-period, the fluid in between the two shells exhibits a higher shear rate and thus a higher viscosity than the fluid in front of the microrobot; while in the slow opening half-period the viscosity there is no such difference and the fluid in front and at the back of the microrobot has low viscosity, thus it propels further forward than backward. Indeed, the results from the first control experiment show that applying the same asymmetric actuation in a Newtonian fluid (glycerol) results in no net displacement, in accord with Purcell’s scallop theorem [2], while the results from the other control experiment show that, if the actuation in a non-Newtonian fluid is symmetric, then the viscosity does not change and the forward and backward displacements are equal with no net displacement.
[2] [3] [4] [5] [6]
[7] [8] [9]
[10] [11] [12]
[13]
IV. CONCLUSION In this paper, we have reported the development of soft microrobots that are fabricated by direct 3D-printing, for operating in non-Newtonian biological fluids. We showed that, by considering the features of the target fluids, the design of microswimmers can be tailored and simplified, enabling the adoption of faster, cheaper and more flexible fabrication processes. 3D-printing is capable of fabricating microrobots with sub-millimeter resolution, which permits several advantages over traditional fabrication techniques: 1) it permits the use of a variety of materials with different mechanical properties, including soft materials; 2) it allows freely-designed 3D shapes; 3) it speeds up the fabrication
[14] [15] [16] [17] [18]
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B. J. Nelson, I. K. Kaliakatsos, and J. J. Abbott, "Microrobots for Minimally Invasive Medicine," Annual Review of Biomedical Engineering, vol. 12, pp. 55-85, 2010. E. M. Purcell, "Life at Low Reynolds-Number," American Journal of Physics, vol. 45, pp. 3-11, 1977. E. Lauga and T. R. Powers, "The hydrodynamics of swimming microorganisms," Reports on Progress in Physics, vol. 72, pp. 096601, 2009. A. Ghosh and P. Fischer, "Controlled Propulsion of Artificial Magnetic Nanostructured Propellers," Nano Letters, vol. 9, pp. 22432245, Jun 2009. L. Zhang, J. J. Abbott, L. X. Dong, B. E. Kratochvil, D. Bell, and B. J. Nelson, "Artificial bacterial flagella: Fabrication and magnetic control," Applied Physics Letters, vol. 94, pp. 064107, 2009. D. Schamel, M. Pfeifer, J. G. Gibbs, B. Miksch, A. G. Mark, and P. Fischer, "Chiral Colloidal Molecules And Observation of The Propeller Effect," Journal of the American Chemical Society, vol. 135, pp. 12353-12359, 2013. R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone, and J. Bibette, "Microscopic artificial swimmers," Nature, vol. 437, pp. 862865, 2005. O. S. Pak, W. Gao, J. Wang, and E. Lauga, "High-speed propulsion of flexible nanowire motors: Theory and experiments," Soft Matter, vol. 7, pp. 8169-8181, 2011. E. Diller, J. Zhuang, G. Zhan Lum, M. R. Edwards, and M. Sitti, "Continuously distributed magnetization profile for millimeter-scale elastomeric undulatory swimming," Applied Physics Letters, vol. 104, pp. 174101, 2014. R. J. Roselli and K. R. Diller, Biotransport: Principles and Applications: Principles and Applications: Springer Science & Business Media, 2011. N. C. Keim, M. Garcia, and P. E. Arratia, "Fluid elasticity can enable propulsion at low Reynolds number," Physics of Fluids, vol. 24, pp. 081703, 2012. T. Qiu, D. Schamel, A. G. Mark, and P. Fischer, "Active Microrheology of the Vitreous of the Eye Applied to Nanorobot Propulsion," in 2014 IEEE International Conference on Robotics and Automation (ICRA 2014), Hongkong, China, 2014. D. Schamel, A. G. Mark, J. G. Gibbs, C. Miksch, K. I. Morozov, A. M. Leshansky, et al., "Nanopropellers and Their Actuation in Complex Viscoelastic Media," ACS Nano, vol. 8, pp. 8794-8801, 2014. T. Qiu, T.-C. Lee, A. G. Mark, K. I. Morozov, R. Münster, O. Mierka, et al., "Swimming by reciprocal motion at low reynolds number," Nat. Commun., vol. 5, pp. 5119, 2014. Stratasys. Objet260 Connex. Available: http://www.stratasys.com/deDE/3d-printers/design-series/objet260-connex S. R. Raghavan and S. A. Khan, "Shear-thickening response of fumed silica suspensions under steady and oscillatory shear," Journal of Colloid and Interface Science, vol. 185, pp. 57-67, 1997. B. P. Conrad, "The effects of glucosamine and chondroitin on the viscosity of synovial fluid in patients with osteoarthritis," University of Florida, 2001. S. Hsu, K. P. Strohl, M. Haxhiu, and A. M. Jamieson, "Role of viscoelasticity in the tube model of airway reopening. II. NonNewtonian gels and airway simulation," Journal of Applied Physiology, vol. 80, pp. 1649-1659, 1996.
Abstract— Microscopic artificial swimmers hold the potential to enable novel non-invasive medical procedures. In order to ease their translation towards real biomedical applications, simpler designs as well as cheaper yet more reliable materials and fabrication processes should be adopted, provided that the functionality of the microrobots can be kept. A simple single-hinge design could already enable microswimming in non-Newtonian fluids, which most bodily fluids are. Here, we address the fabrication of such single-hinge microrobots with a 3D-printed soft material. Firstly, a finite element model is developed to investigate the deformability of the 3D-printed microstructure under typical values of the actuating magnetic fields. Then the microstructures are fabricated by direct 3D-printing of a soft material and their swimming performances are evaluated. The speeds achieved with the 3D-printed microrobots are comparable to those obtained in previous work with complex fabrication procedures, thus showing great promise for 3D-printed microrobots to be operated in biological fluids.
I. INTRODUCTION Microscopic robots have attracted a lot of attention in the last decade. Indeed, they hold the potential to reduce the invasiveness of some current medical procedures, as well as to enable new procedures. Artificial microswimmers are particular attractive because they could navigate through bodily fluids to reach specific targets deep in the body, where to perform local diagnosis or therapeutic tasks [1]. However, actuating swimmers at the micro scale presents several challenges. Considering their size and speed, microswimmers experience low Reynolds number (Re) fluid dynamics. For common Newtonian liquids such as water, in this regime kinematic reversibility applies, which means that any reversible actuation cannot give rise to net propulsion. This principle is also known as the ‘scallop theorem’ [2]. Most artificial microswimmers deal with propulsion in homogeneous Newtonian fluids [3]. Two swimming mechanisms that break symmetry and are useful at low Re are therefore often used to propel artificial microswimmers: one is rotating rigid helical flagella, and the rotation is coupled to forward propulsion by a helical shape [4-6]; the other is beating flexible tails, which generates forward propulsion by a propagation wave [7-9]. However, because these schemes need to break the reciprocity, they require either a relatively complex shape and/or a complex actuation scheme. Simpler * This work was supported by the Max Planck Society and the European Research Council under the ERC Grant agreement Chiral MicroBots (278213). T. Qiu, S. Palagi and P. Fischer are with Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany (corresponding author: P. Fischer; +49 711 689-3560; e-mail: [email protected]). T. Qiu is also with Institute of Bioengineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. P. Fischer is also with the Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.
978-1-4244-9270-1/15/$31.00 ©2015 IEEE
designs, as well as cheaper yet more reliable materials and fabrication processes should be adopted to ease the translation of artificial microswimmers towards real applications, provided that their functionality can be kept. In addition, considering that most biological fluids, such as blood, the vitreous of the eye and the synovial fluid in the joints, are non-Newtonian [10], addressing micro-swimming in this kind of complex fluids is a mandatory step on the way to real biomedical applications. Some efforts have indeed been made to experimentally study the propulsion scheme in these fluids. Keim et al. reported an oscillating dumbbell structure that took advantage of fluidic elasticity to propel in viscoelastic fluids [11]. Our group has demonstrated that effective propulsion through viscoelastic hyaluronic acid gels requires the nanostructures to have a diameter that is smaller than the characteristic mesh size of the biological gel, which is in effect a nano-porous medium [12, 13]. Recently, we have shown that by exploiting non-Newtonian fluid dynamics, a microswimmer can be propelled with an actuation scheme as simple as the reversible opening and closing of a single-hinge, clamshell-like micro-structure [14]. The appeal of a single-hinge microrobot is that it is particularly simple to be implemented, and that it could be actuated by a variety of common actuators, even at small scales. Nevertheless, fabricating these microswimmers so far required a lengthy process consisting of several steps. Here, we report that it is possible to build single-hinge microrobots using commercial 3D-printing techniques. In particular, the body of the microrobot is directly 3D-printed out of a soft material, and then two permanent micro-magnets are attached to it. A weak external magnetic field applies a torque on the magnets, causing the deformation of the soft monolithic body, and finally driving the opening and closing of the single-hinge micro-structure. In this way, net forward propulsion of the 3D-printed microrobot in a non-Newtonian fluid is achieved, with swimming performances that are comparable to previously reported ones. The 3D-printing process offers many advantages over traditional fabrication techniques, as it allows complex 3D shapes to be rapidly processed and tested and thus holds enormous potential for the fabrication of soft microrobots. II. MATERIALS AND METHODS A. Microrobots Design and Modelling The schematic and dimension of the microrobot are shown in Fig. 1. The microrobots are designed to have two thick and wide shells connected by one thin and narrow hinge. The two shells are much wider than the hinge to enable a larger contact area with the fluid, which facilitates propulsion. At the same time, although the microrobots’ bodies are monolithic structures printed out of the same material, only the hinge is expected to bend under magnetic
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Israel) has a resolution of 600 dpi, which corresponds to about 42 µm, in the X and Y axes and of 1600 dpi (about 16 µm) in Z axis [15]. Since TangoBlackPlus could not be printed in high quality mode due to its large thermal expansion coefficient, it was printed in digital material mode. The two micro-magnets (⌀200×400 µm) were attached to the shells using cyanoacrylate glue (Ultra Gel, Pattex). The orientation of the magnets was achieved with the help of a bigger magnet under a stereoscope (MZ95, Leica, Germany). Finally, each microrobot was released from the supporting material using tweezers and by gently washed in deionized water.
Figure 1. Schematic and dimensions (µm) of the 3D-printed microrobot: a) top view; b) side view.
actuation, because of its higher compliance, while the deformation of the two shells is expected to be negligible. In order to verify that the designed microrobots actually exhibit this single-hinge motion, and to investigate the deformability of the 3D-printed micro-structures under the action of the weak external magnetic field, a numerical simulation was performed. The coupling with the fluid was not taken into account in the simulation, as the action of the hinge is primarily determined by the magnetic and mechanical aspects of the 3D-printed micro-structures. The simulation was performed with COMSOL Multiphysics 4.4 (AC/DC and Solid mechanics modules). The model consists of the 2D central section of the microrobot, but it also accounts for the out-of-plane thicknesses. The elastomeric 3D-printed structure was modelled as a hyper-elastic neoHookean solid (elastic modulus E set to 0.8 MPa, as reported for TangoBlackPlus). Both the interaction between the two micro-magnets (having a remanent magnetic flux density Br of 1.43 T, with the orientation reported in Fig. 1) and the action of the external magnetic field were considered in the model. The resulting forces and torques acting on each of the micro-magnets, which are treated as rigid bodies, are transferred to the soft structure, which is free to deform. First, the geometry of the microrobot in the absence of any applied external fields was determined. Then, a time-dependent simulation step was carried out, which modelled one actuation period (2 s). The magnetic field was set to increase linearly from zero to its maximum (30 mT) in the first 0.1 s, and to then exponentially decrease back to zero (see Fig. 2(b)).
C. Fluid Preparation and Rheological Measurement Fumed silica suspension is used as a non-Newtonian model fluid because of its shear-thickening property. Indeed, a fumed silica suspension is shear-thickening, because the silica nanoparticles aggregate and jam under shear, which increases the apparent fluid viscosity. As reported in [16], fumed silica powder (Aerosil 150, Evonik, Germany) was mixed with poly(propylene glycol) (PPG, Mw = 725, SigmaAldrich) at a concentration of 8% w/w. After thoroughly mixing, the solution was degassed for 3 h. Glycerol (99.5%, VWR, France) was used as received and served as the Newtonian fluid in the control experiment. A shear rate ramp experiment was carried out on a rheometer (Kinexus Pro, Malven, UK) with a 40 mm-diameter plate-to-plate geometry. The viscosity of the fumed silica suspension was measured in the range of 0.05 – 300 s-1 with a 4-min ramp time under 25 °C. The value of viscosity and its transition shear rate are highly dependent on the concentration, thus can slightly vary in different fluid batches. D. Microrobot Actuation The microrobot was actuated by an external homogeneous magnetic field, which was generated by a pair of Helmholtz coil. Briefly, the signal from a function generator was fed into a power amplifier to drive the Helmholtz pair, which generated a homogeneous (spatial)
B. Microrobots Fabrication The fabrication technique we previously adopted for single-hinge microswimmers [14] consisted of molding their bodies with polydimethylsiloxane (PDMS), which was a lengthy 4-step process including the preparation of the solid mold, liquid PDMS molding, curing followed by a release step. Here, the four steps are replaced with one single 3Dprinting step. The total width of the swimmer was set to 1 mm so that all the features could be printed in sufficiently high resolution. The 3D printer (Objet 260 Connex, Stratasys,
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Figure 2. Numerical simulation results: a) frames from the timedependent simulation; the externally applied magnetic field is represented by the arrows; the color outside the structure show the intensity distribution of the overall magnetic field; the colors inside the structure show the distribution of the mechanical stress; b) imposed magnetic field (dashed curve, right axis) and obtained aperture angle (solid curve, left axis).
deformation takes place only in the hinge, and that the two shells behave like rigid bodies, as clearly shown in Fig. 2. This confirms that the 3D-printed micro-structures, made out of this soft material and in these dimensions, exhibit a fully reciprocal single-hinge-like deformation. B. Microrobots Fabrication The flexible bodies of the microrobots are 1 mm wide in total and have sub-millimeter features, approaching the highest resolution limit of 3D-printing with the adopted soft material. The smallest feature is the middle hinge, which measures only 90 µm × 200 µm. The soft hinge structure is designed to enable movement in the microrobot without the need for a complicated assembly. Moreover, this design choice allows us to adopt a fabrication via direct 3D-printing.
Figure 3. a) A 4-by-4 array of 3D-printed microrobots; b) side view of a microrobot (a ruler with a line spacing of 1 mm is shown for comparison); c) top view.
magnetic field changing as a function of time as schematically depicted in Fig. 2(b). An asymmetric actuation (with maximum amplitude of 30 mT) with a 0.1 s linear rise and a 1.9 s exponential decay, as well as a symmetric sinusoidal wave for control experiments, was utilized. The swimming experiments were carried out in an open fluidic channel made of PDMS bonded to glass. The channel was inverted to avoid the friction between the microrobot and the bottom of the fluidic channel. The weight of the microrobot was balanced by the surface tension of the fluid/air interface. It is important to note that in control experiments we have verified that the meniscus plays no role in the swimming mechanism and that the swimming mechanism also works for a microrobot immersed in the bulk of the fluid [14]. The channel was 5 mm wide and 3 mm high to avoid boundary effects at low Re. The microrobot was imaged under bright field using a stereoscope with a CCD camera (DFC 490, Leica). Each frame of the video was extracted by FFmpeg (http://www.ffmpeg.org). The images were analyzed frame by frame and the coordinates of the midpoint of the microstructure hinge were extracted using a customized Matlab program. III. RESULTS A. Numerical Simulation The simulation shows that, in the absence of an external magnetic field, the compliant hinge bends, causing the angle between the shells to be about 120° at rest (see Fig. 2). This stationary configuration is a balance of the repulsion between the two micro-magnets and the stress in the micro-structure. The simulation also shows that when the magnetic field is applied, the micro-magnets tend to align with the external field, causing a further deformation of the hinge and, consequently, the partial closure of the micro-structure. The angle between the shells for a magnetic field of 30 mT is predicted to be about 40°. The simulation highlights that the
The microrobots are printed such that the direction of the 90 µm height is aligned with the Z axis, which is where the printer has its highest resolution. Multiple micro-structures are printed at the same time (an array of 16 microrobots is shown as an example in Fig. 3(a)). The total fabrication time is shortened from over 4 hours in the previous process [14] to about 10 minutes. Although the final dimensions of the printed structure slightly differ from the target dimensions, because of the use of a soft printing material, the printing result nevertheless reproduces the designed shape of microrobots as seen in the microscope images in Fig. 3. C. Microrobots Actuation and Propulsion The fumed silica suspension used as non-Newtonian, shear-thickening fluid exhibits an almost constant viscosity of about 1 Pa∙s at low shear rate (range from 0.1 – 2 s-1), while it rapidly rises to over 10 Pa∙s at higher shear rates (10 s-1). The transition from 2 to 10 s-1 is almost linear, and follows the power law theory
µ = m γ̇ n‒1
where µ is the apparent viscosity, γ̇ is the shear rate, m and n-1 are two coefficients which are 0.19 and 2.76 respectively. Although many biological fluids exhibit a shear thinning property, they were described by the same power law, for example whole blood [10], synovial fluid [17], mucus [18], and cytoplasm of leukocytes [10]. Therefore, the shearthickening fluid used in this paper is a model fluid resembling a whole class of power law fluids which the microrobot can swim in. In agreement with the simulation, the 3D-printed microrobots are bent at the middle hinge when no field is applied. When a magnetic field is applied the microrobots close their two shells as a function of the field strength. A fast closing and slow opening step is easily achieved by applying
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Figure 4. Fast closing and slow opening of a 3D-printed microrobot under the action of a time-asymmetric magnetic pulse in non-Newtonian fluid (scale bar: 200 µm).
process, thus enables an optimization of the design of the microrobot to reach high propulsion speed in the target fluid. The robot described herein is actuated by an external magnetic field, but the principle of low-Re swimming by means of reciprocal actuation is general. It means that most micro-actuators, e.g. bimetallic strips, shape memory alloys, or heat/light actuated polymer can be used to propel microswimmers in non-Newtonian power-law fluids such as blood, synovial fluid and mucus. Combining 3D-printing with these simple actuation schemes leads to a new class of biomedical microrobots – 3D printed robots that can move at low Reynolds number with symmetric body-shape changes.
Figure 5. Average speed of the microrobot in different conditions. Net propulsion is observed by applying a time-asymmetric magnetic field in the non-Newtonian fluid. As expected, negligible propulsion is observed in the same fluid under time-symmetric actuation, nor in a Newtonian fluid under asymmetric actuation. Each group was repeated five times respectively with the same microrobot.
REFERENCES [1]
a time-asymmetric magnetic field (see Fig. 4). Fig. 5 shows the results from a propulsion test on a 3Dprinted microrobot in the non-Newtonian fluid. The results from two control experiments on the same microrobot are also reported for comparison. A net displacement is achieved when the 3D-printed microrobot is propelled in a shearthickening fluid under time-asymmetric magnetic excitation. The average speed of the 3D-printed microrobot is calculated to be 4.8±1.9 µm/s under asymmetric actuation, which shows a significant difference compared to the two (non-swimming) control groups, where negligible net displacements are observed. The average speed of the 3D-printed microrobot is in a similar range as those obtained with complex fabrication procedures [14]. The mechanism that underlies swimming at low-Re with reciprocal motion is that during the fast-closing half-period, the fluid in between the two shells exhibits a higher shear rate and thus a higher viscosity than the fluid in front of the microrobot; while in the slow opening half-period the viscosity there is no such difference and the fluid in front and at the back of the microrobot has low viscosity, thus it propels further forward than backward. Indeed, the results from the first control experiment show that applying the same asymmetric actuation in a Newtonian fluid (glycerol) results in no net displacement, in accord with Purcell’s scallop theorem [2], while the results from the other control experiment show that, if the actuation in a non-Newtonian fluid is symmetric, then the viscosity does not change and the forward and backward displacements are equal with no net displacement.
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IV. CONCLUSION In this paper, we have reported the development of soft microrobots that are fabricated by direct 3D-printing, for operating in non-Newtonian biological fluids. We showed that, by considering the features of the target fluids, the design of microswimmers can be tailored and simplified, enabling the adoption of faster, cheaper and more flexible fabrication processes. 3D-printing is capable of fabricating microrobots with sub-millimeter resolution, which permits several advantages over traditional fabrication techniques: 1) it permits the use of a variety of materials with different mechanical properties, including soft materials; 2) it allows freely-designed 3D shapes; 3) it speeds up the fabrication
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