Collective Behavior of Reconfigurable Magnetic Droplets via Dynamic

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Collective Behavior of Reconfigurable Magnetic Droplets via Dynamic Self-assembly Qianqian Wang, Lidong Yang, Ben Wang, Edwin Yu, Jiangfan Yu, and Li Zhang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 18 Dec 2018 Downloaded from http://pubs.acs.org on December 18, 2018

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ACS Applied Materials & Interfaces

Collective Behavior of Reconfigurable Magnetic Droplets via Dynamic Self-assembly Qianqian Wang,† Lidong Yang,† Ben Wang,†,§ Edwin Yu,† Jiangfan Yu,† and Li Zhang∗,†,‡,¶ †Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, China ‡Chow Yuk Ho Technology Centre for Innovative Medicine, The Chinese University of Hong Kong, Shatin, Hong Kong, China ¶T Stone Robotics Institute, The Chinese University of Hong Kong, Shatin, Hong Kong, China §Department of Biomedical Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, China E-mail: [email protected]

Abstract Dynamic self-assembly represents an effective approach to form energy-dissipative structures by introducing interactions among multiple building blocks with a continuous energy supply. Time-dependent magnetic fields are treated as a convenient energy input to construct such a dynamic self-assembled system. The induced interactions can be further tuned by modulating the input field, resulting in a diversity of assembled patterns. However, the formation of a functional dynamic pattern with controllability remains a challenge. Herein we report the formation and pattern control of dynamically self-assembled magnetic droplets at an air-liquid interface, energized by a precessing

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magnetic field. The formation process involves the assembly of magnetic microparticles into particle chains inside droplets, and then highly ordered patterns are generated by balancing the induced interactions among droplets. By modulating the input field, the interactions and collective behaviors are adjusted and the pattern can be reversibly tuned, i.e., expand and shrink, in a controlled manner Furthermore, the assembled droplets are able to be steered in 2-D as an entity by applying a magnetic field gradient. Utilizing dynamic pattern control and steerability of the assembled structure, cargoes are successfully trapped, transported and released in a noncontact fashion, indicating that the dynamically assembled droplets can act as a reconfigurable untethered robotic end-effector for manipulation. Keywords: Magnetic assembly, magnetic actuation, collective behavior, reconfigurable pattern control, magnetic droplet

Introduction Collective behavior is a common phenomenon in the biological world, and various forms of cooperation are displayed by a group of individuals, such as bird flocks 1 and insect swarms. 2 The gathered swarm can migrate as an entity and dramatically change its shape in response to environmental stimuli. Such swarming intelligence has inspired the design of artificial systems that can regulate their collective behaviors on demand, and these systems have been exploited to perform coordinated tasks that would be impossible using a single agent. 3–6 The interactions among the building blocks in these systems give us opportunities to bring aspects of these natural behaviors to practical applications. Dynamic self-assembly, as a promising approach, enables the use of complex interactions to form diversified patterns and structures that cannot be accessed from traditional assembly processes. Out-of-equilibrium swarming patterns can be assembled and sustained under various external energies, such as magnetic fields, 7–11 electric fields 12,13 and light. 14,15 Compared to static self-assembly, dynamic selfassembly enables a pattern to rapidly adjust its shape and function by changing the energy

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supply. 16–21 However, dynamic patterns are sensitive to changes in local interactions between building blocks, making the assembled pattern difficult to control for further application. Magnetic self-assembly is considered an effective tool for organizing matter into complex structures. 22,23 Magnetic fields have advantages in inducing large and long-range forces between magnetic matters and low interaction with nonmagnetic media. In addition, magnetic field can penetrate deep tissues and is considered harmless to tissues of living organisms, making magnetic assembly has the potential for biomedical applications, such as targeted energy delivery. 24 Time-dependent magnetic fields are widely applied to polarize magnetic elementary units for further assembly processes 25–28 and propel the assembled structures (e.g., magnetic asters, 16 rings, 29 carpets 30 and rollers 31 ). These assembly processes are mostly based on direct interactions between colloidal-scale units in one medium, mainly due to the controllability, fast response and diversity of interactions of active colloidal suspensions. However, the use of colloidal suspensions as subunits to form self-assembled functional structures or to exhibit multilevel self-assembly behaviors has yet to be investigated. In this study, we report the formation and pattern control of dynamic self-assembled magnetic droplets at an air-liquid interface. Unlike ferrofluid droplets, which have homogeneous properties, 32 the microparticles inside our droplets are dynamically assembled into rotating particle chains under a precessing magnetic field, resulting in rotating droplets. Highly ordered patterns of droplets are generated by balancing the induced magnetic, hydrodynamic and capillary interactions among the droplets. The ordered pattern requires a continuous external energy supply and can be treated as a dissipative structure. By modulating the input magnetic field, interactions between droplets are able to be adjusted, and the structure of the pattern can be tuned, i.e., expand and shrink. Simulations are built to further investigate the hydrodynamic interactions and induced fluid flow by the ordered pattern, indicating that induced circular flows at the central region of the pattern provide a mechanism for the noncontact trapping of cargo. Moreover, the assembled dynamic droplets can be steered as an entity in a controlled manner using a magnetic field gradient, and hence,

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automated steering of the droplets can be realized. Taking advantage of the reconfigurable magnetic droplets, noncontact cargo trapping and release is demonstrated at the air-liquid interface.

Results and discussion Dynamic self-assembly of droplets. We first study one droplet under a precessing magnetic field (Figure 1). One drop (5 µL) of carbonyl iron microparticle (BASF, China) water suspension (30 mg/mL) is added into benzyl ether (Aladdin industrial Co., China) using a pipette, and a droplet with a diameter of approximately 2 mm lies beneath the air-liquid interface. Carbonyl iron microparticles are microspheres with an average diameter of 3 µm based on images from scanning electron microscopes (JEOL Model JSM-7800F), and they are ferromagnetic based on the magnetic hysteresis loop (Quantum Design 6000 Physical Property Measurement System). Before turning on the external field, all iron microparticles sink to the bottom of the droplet due to gravitational force. Particle chains will be assembled and gathered rapidly after turning on the precessing field, and these microparticles will be sink again due to the lack of an external field, showing a reversible particle assembly/disassembly process (Figure 1b, 1c). Figure 1d schematically shows that a particle chain rotates synchronously with the precessing magnetic field. These microparticles form particle chains inside the droplet due to the induced magnetic interaction between particles. All chains are aligned with the external field and are parallel to each other, and each chain is repelled magnetically by neighboring chains due to the induced magnetic dipoledipole interaction. Due to the limitation of the boundary (the inner wall of a droplet), these chains are distributed separately in the droplets and show a ring-shaped distribution (top view). The dissipative self-assembly process of the magnetic droplets is demonstrated in Figure 2a, where an ordered pattern consisting of five droplets is successfully formed under a

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precessing magnetic field. The time of successful formation of an ordered pattern depends on the initial distribution of droplets, and an ordered pattern consisting of five droplets can usually be formed within 120 s if the distance between droplets is smaller than 6 mm (three body lengths). Various patterns consisting of a different number of droplets can also be formed (Figure 2b). Interestingly, there is no central space in a pattern formed by more than five droplets. In this paper, we take the pattern consisting of five droplets as the study object. After successfully forming an ordered pattern, the droplets will stop rotating if we turn off the magnetic field. Due to capillary attraction between the droplets, these droplets will come into contact with their neighbors gradually (Figure 2c). The capillary attraction between two millimeter-scale spheres separated by a distance r at an air-liquid interface can be expressed as 33,34 Fc (r) ∝ ( where Lc =

p

r r −1 ) 2 exp(− ) Lc Lc

(1)

γ/ρs g is the capillary length, γ and ρs are the surface tension and density

of the surrounding fluid. By turning on the precessing magnetic field again, an ordered pattern can be reformed again, indicating a reconfigurable assembly process. The precessing magnetic field is generated by a three-axis Helmholtz coil system, comprising an in-plane rotating field and a static field applied orthogonally to the air-liquid interface, as B(t) = B · {sin θ[sin(2πf )ˆ x + cos(2πf )ˆ y ] + cos θzˆ}, where θ is the precession angle to the Z-axis and f is the applied frequency. Unlike the previous work reported by Grzybowski et al, 7 no net force is exerted to the droplet directly from the external field due to the uniformity of the field strength (B). Therefore, the magnetic interaction between droplets is essentially a magnetic dipole-dipole interaction induced by the external field. Here we consider the force of interaction averaged over a field cycle (2π/ω), and the interaction force between two droplets with a separation distance r (centered distance) is expressed as 35 3µo m2d 3 cos2 θ − 1 ( ) Fm (θ, r) = − 4πr4 2

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(2)


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where µo is the magnetic permeability of free space and md is the induced magnetic dipole moment of a droplet, which is always aligned with the external field. The averaged force equals the force of the aligned dipoles times a factor (3 cos2 θ − 1)/2, which can change continuously from -1/2 to 1 depending on the precession angle θ (Supporting Information). Based on this analysis, the interaction between droplets can be changed from repulsive to attractive, i.e., repulsive if 0◦ < θ < 54.7◦ and attractive if 54.7◦ < θ < 90◦ . Since the assembled process occurs in a fluid environment, the hydrodynamic interaction between droplets plays an important role. The force acting between rotating spheres is essentially an effect of fluid inertia in a nonzero Reynolds number regime. 36 In terms of system energetics, the energy supplied by the external field is dissipated through the hydrodynamic interactions of the droplets with the surrounding fluid. 8 In our experiments, the Reynolds number is calculated as Re = ρa2d ωd /η, where ad is the radius of a droplet, ωd is the angular velocity of droplets and η is the dynamic viscosity of the surrounding fluid (in experiments, Re is approximately 0.1-1 during self-assembly process). The force acting on the ith droplets by the generated fluid of the jth droplets is estimated as 37

Fr = −cf ρωd2

a7d (ri − rj ) |ri − rj |4

(3)

where cf is a constant of proportionality, ρ is the density of the surrounding fluid, and ri − rj is the center vector between the centers of the two droplets, which has a length of |ri − rj | (separation distance). Hence, a larger repulsion can be induced between droplets by increasing the angular velocity (ωd ). Rotation of a droplet is induced by the friction force between the particle chains and the inner boundary of the droplet. As mentioned above, particle chains are formed inside the droplet due to magnetic interactions among the microparticles. During our experiments, all the particle chains exhibit rotation synchronous with the external field. The friction torque acting on a droplet is counterbalanced by the drag torque, and the angular velocity can be estimated. Figure 3a shows the angular velocity

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of droplets under different precession angles (θ) and input frequencies. The droplet exhibits increased velocity by increasing the precession angle, and higher velocities are obtained under higher frequency. However, with a precession angle larger than 60◦ , the velocity shows a decrease. The reason is that particle chains cannot maintain stability due to the increased drag, and fragmentation will occur. 38 This will cause a decrease in the friction force and will yield a lower angular velocity of droplets (Supporting Information). Tuning of an ordered pattern. The formation of an ordered pattern is based on the balance of interactions among droplets, i.e., magnetic, hydrodynamic and capillary interactions. The balance can be disrupted and reestablished by modulating the external field, resulting in tunable patterns. As shown in Figure 3b, the pattern exhibits expansion gradually by increasing the precession angle (θ), meanwhile the magnetic strength and frequency remain the same. Furthermore, the expanded pattern can be reserved by decreasing the precession angle from 50◦ to 10◦ . Here we use the mean separation distance r (centered distance between droplets) as the evaluation criterion. The relationship between the mean separation distance and the precession angle under different input frequencies is experimentally studied and shown in Figure 3c. Assume that the separation distance between droplets remains the same at the moment we change the precession angle. For example, if we change the precession angle from 30◦ to 40◦ with an input frequency of 3 Hz, the hydrodynamic repulsion 2 2 between droplets will increase by over two times (Fr ∝ ωd2 , ωd,θ=40 ◦ /ωd,θ=30◦ ≈ 2.4) based

on the experimental data in Figure 3a. Meanwhile, the magnetic repulsion will decrease (Fm,θ=40◦ /Fm,θ=30◦ ≈ 0.6). Thus, the repulsion between droplets increases and the pattern will gradually expands. We also found that the pattern is able to be tuned by adjusting the magnetic interaction between droplets. Figure 3d shows that the assembled droplets exhibit expansion with increasing field strength due to the increased magnetic repulsion between droplets. If the precession angle is increased over 60◦ , the magnetic interaction becomes attraction instead of repulsion. At the same time, the angular velocity of droplets decreases, resulting in weaker hydrodynamic repulsion. Taking all the interactions into account, the

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repulsion between droplets decreases, and the pattern consequently begins to shrink. Induced fluid flow by rotating droplets. Each rotating droplet is affected by the velocity field generated by the rest of the droplets. During actuation, the pattern also exhibits rotation around the center as an entity. To better understand the induced flow and fluidic interaction among droplets, finite element method (FEM) models are established. A droplet is modeled as a sphere with a diameter of 2 mm that lies beneath the air-liquid interface. First, we study the fluid flow induced by one rotating droplet (Figure 4a). Based on Stokes equation, the velocity field generated by a rotating sphere is u(x) = ωd × rx (ad /rx )3 , and rx is the position vector defined from the center of the sphere. The simulated fluid flow and the theoretical model are compared in Figure 4b, where the difference between the model and simulated data is due to the existence of the Reynolds number. 36 Figure 4c shows the fluid flow induced by the pattern, and circular flow is generated at the central region of the pattern. The repulsive forces acting on the sphere are studied with different separation distances and angular velocities (Figure 4d). The repulsion force is related to the angular velocity and separation distance, i.e., Fr ∝ ωd2 /r3 based on our analysis in equation (3). In addition, the rotation of the whole pattern (precession) is also studied experimentally. The precession angular velocity is defined as Ω = u/R, where R is the center distance between a droplet and the pattern, and u is the induced fluid flow. For the five-droplet pattern (pentagon structure), we can obtain a relationship geometrically as R = r · sin(0.3π)/ sin(0.4π). Combined with the analysis of induced flow, the relationship of angular velocity between the pattern and the droplets is derived as Ω ∝ ωd /r3 . The relationship between the angular velocity of droplets and the precession of the pattern is experimentally investigated (Figure 4e) and shows good agreement with our analysis. Steering of assembled droplets and manipulation. The assembled droplets are steered as an entity using magnetic field gradients while the precessing field is also applied as the energy supply. The relationship between the field gradient and the translational velocity of the assembled droplets is experimentally investigated as shown in Figure 5a. The

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maneuverability of the assembled droplets is essential for further robotic applications. Figure 5b shows the automated guidance of the whole assembled pattern in real time. All the droplets are visually tracked, and the center of the pattern can be calculated. 39 Actuated by a field gradient, the assembled droplets successfully follow the preset route (rectangular) using the tracking position as a real-time feedback (Supporting Information). Combining the features of the assembled structure, a demonstration of cargo transpiration using the assembled five droplets is shown in Figure 5c. First, the droplets are assembled using a precessing field and then steered closer to the cargo by using a field gradient. The polypropylene cargo has a size of 1.7 mm × 1.5 mm × 1.5 mm and lies beneath the interface. By increasing the precession angle of the external field, the pattern exhibits expansion and the cargo is encaged in the central region of the structure. We shrink the pattern before transporting the cargo for two reasons: to avoid the release of the cargo through the gaps between droplets and to obtain more capillary attraction among the droplets. The fluidic drag during motion may affect the stability of the assembled structure (t = 25 s in Figure 5c), and capillary attraction is applied to reorder the droplets towards an ordered structure. By adjusting the direction of the field gradient, transportation of the cargo can be realized. Once reaching the desired location, the cargo is released through the gap between two droplets by expanding the pattern again. During the manipulation process, we found that the cargo is transported in a noncontact manner. Based on the simulated results in Figure 4c, the cargo is trapped by induced circular flow at the central region of the pattern. For further applications to biological samples, the level of shear stress is critical. Any excessive shear stress induced by flows during the noncontact manipulation process may cause damage to biological samples, such as the shear-induced detachment of membranes due to excessive pressure. The local shear stress of the central space of the assembled droplets can be calculated as the product of the shear rate and fluid viscosity. The simulated results in Figure 4f indicate that the largest shear rate near a droplet is approximately 3.67 s−1 , and the shear stress can be calculated at approximately 0.02 Pa (viscosity of benzyl ether η = 5.44 × 10−3 P a · s−1 ). As a reference,

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normal physiologic levels of shear stress within arteries and veins range from 1-7 Pa and 1-6 Pa, 40 respectively, indicating that the objects trapped by our assembled droplets should be biologically safe. In addition, a batch of cargoes can also be transported in a noncontact manner (Figure 5d). Compared to previously reported noncontact manipulation methods based on the pure fluidic effect, 41,42 the encaging ability of our assembled droplets provides a more reliable solution. Our method provides a new approach for cargo manipulation via self-assembled dissipative structure. The assembled droplets have a great potential to be further applied in handling cargoes at small-scales, e.g., micrometer-scale, using scale-down droplets. The induced circular flow by the assembled pattern also offers possibility for sorting cargoes with different sizes.

Conclusions In conclusion, we report the dynamic self-assembly of magnetic droplets at the air-liquid interface energized by a precessing magnetic field. Active magnetic colloids inside droplets are dynamically assembled into rotating chains, providing magnetic and hydrodynamic interactions between rotating droplets. These interactions can be tuned by modulating the precessing field, and the ordered pattern of droplets can consequently exhibit expansion and shrinkage. Moreover, the assembled droplets can be steered in a controlled manner using a magnetic field gradient, and automated navigation is demonstrated, showing good controllability of the dynamic assembled structure. Simulation indicates that the induced circular flow at the central region of the pattern provides a mechanism for noncontact cargo manipulation. Considering all the advantages, we demonstrate that these assembled droplets are capable of performing noncontact manipulation of cargoes at the interface. Our work provides a new approach towards controlling dissipative structure as a dynamic functional entity to perform coordinated tasks.

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Supporting Information Available Analysis of interactions between droplets; model of mean separation distance between droplets; dynamics of the assembled droplets; control scheme and experimental setup; characterization of materials (PDF) Process of dynamic self-assembly droplets from Figure 2a and demonstration of ordered patterns from Figure 2b. (Video S1) Reversible pattern from Figure 2c. (Video S2) Dynamic assembled pattern exhibits expansion and shrinkage from Figure 3b. (Video S3) Automated steering of the assembled droplets along a preset path from Figure 5b. (Video S4) Cargo trapping and release using the reconfigurable assembled droplets from Figure 5c. (Video S5) Noncontact transportation of a batch of cargoes from Figure 5d. (Video S6) This material is available free of charge via the Internet at http://pubs.acs.org/. AUTHOR INFOMATION Corresponding Author E-mail: [email protected]. ORCID Qianqian Wang: 0000-0001-8011-171X Lidong Yang: 0000-0002-5757-7885 Ben Wang: 0000-0001-7037-3660 Jiangfan Yu: 0000-0002-7981-6744 Li Zhang: 0000-0003-1152-8962 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes 11



The authors declare no competing financial interest.

Acknowledgement The research work is financially supported by the General Research Fund (GRF) with Project Nos. 14203715, and 14218516 from the Research Grants Council (RGC) of Hong Kong, the ITF projects with Project No. ITS/440/17FP funded by the HKSAR Innovation and Technology Commission (ITC). We thank Chi-Ian Vong for technical assistance and Dongdong Jin for helpful discussion.

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Figure 1: Magnetic droplets under a precessing magnetic field. (a) Schematic drawing of droplets in a Petri dish. They are gradually assembled into an ordered pattern under a precessing field. (b) Top view and corresponding side view of a droplet with or without a magnetic field. These microparticles form chains under the magnetic field and will sink to the bottom of the droplets after the field is turned off. The scale bar is 1 mm. (c) A side view schematically illustrates the reversible assembly of separated rotating particle chains inside the droplet with or without a precessing magnetic field. ωd is the angular velocity of the rotating droplet. (d) Microparticle chains are formed under a precessing magnetic field with frequency ω, precession angle θ and field strength B. α is the phase lag and is defined as the angle between the external field and long axis of the chain.

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Figure 2: Self-assembly of magnetic droplets. (a) Formation of the self-assembled pattern consisting of five droplets. The precessing field has a frequency of 4 Hz with a precession angle of 30◦ (inset). At t = 0 s, the microparticles (dark region) still sink at the bottom of the droplets. After approximately 120 s, an ordered pattern is formed at the air-liquid interface (see Supporting Information video S1). Blue and red arrows illustrate the rotation of droplets and precession of the whole pattern, respectively. (b) Ordered patterns formed by different numbers of droplets. The frequency and precession angle of the external field are 3 Hz and 30◦ (inset). All patterns are formed using the same external field. The number of droplets is marked at the right corner (see Supporting Information video S1). (c) After successfully forming an ordered pattern, droplets move gradually closer to their neighbors without the external field (t = 0 s). The pattern can be formed again after turning on the field (t = 90 s, see Supporting Information video S2). All the scale bars are 4 mm.

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Figure 3: Tunable pattern under the precessing magnetic field. (a) Angular velocity of a droplet under different precession angles of the precessing field at frequencies of 2 Hz, 3 Hz and 4 Hz. (b) The pattern can expand and shrink by adjusting the precession angle (θ). The magnetic field remains at a strength of 8 mT with a frequency of 3 Hz (see Supporting Information video S3). (c) The relationship between the mean distance (r) between droplets and the precession angle (θ) of the precessing field at frequencies of 2 Hz, 3 Hz, and 4 Hz. The strength of the magnetic field is 8 mT. The mean distance is defined as the mean value of the five droplet-droplet distances (inset). (d) The pattern exhibits expansion with increasing field strength (θ = 30◦ ). Arrows indicate the precession of the assembled droplets. The scale bars are 4 mm in b and d.

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b

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Simulated flow Theoretical model

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Tangential flow velocity u (mm/s)

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Shear rate (S )

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Tangential flow (mm/s)

Hydrodynamic repulsion (×10-8 N)

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Figure 4: (a) Fluid flow induced by a rotating droplet at the equatorial plane of the droplet. The droplet is modeled as a sphere with a radius of 1 mm and lies beneath the air-liquid interface. Angular velocity of the droplet is 4π rad/s (two full rotation per second). White arrows refer to the direction of the flow, and the color contour shows the magnitude of the flow velocity (mm/s). (b) Profile of the tangential velocity (uy ) along the X-axis (dash line in a). The blue points refer to the data extracted from simulation results, and the missing data at rx from -1 to 1 are due to the existence of the sphere. Two red curves are the plot based on the theoretical model. (c) Fluid flow induced by the five rotating droplets. Angular velocity of droplets is 4π rad/s. (d) Hydrodynamic repulsion force (Fr ) among rotating droplets. The pattern has a separation distance between 2.5-5 mm (1.25-2.5 body lengths) with angular velocity varied from 2π-6π rad/s. The inset illustrates the repulsive force exerted on a droplet. (e) The relationship of angular velocity between the pattern (precession angular velocity Ω) and droplets (ωd ). The red dots denote data from experimental measurements and the blue line is the best linear fit. The inset illustrates the rotation direction of the whole structure during experiments. (f) The induced tangential flow (black line) and shear rates (blue line) from the central cut line of the droplets. Blue dot and curve are calculated data based on tangential flow and the corresponding fitting curve, respectively. The cut line is parallel to the X-axis and passes the center of the pattern as shown in the inset. Curves are produced using MATLAB based on the data points extracted from the simulation results of Figure 4c.

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Figure 5: Manipulation of cargoes using the reconfigurable magnetic droplets. (a) The relationship between the velocity of the assembled droplets and the applied magnetic field gradient (a precessing field is applied as well). Points are data measured from experiments, and the line is the linear fitting of these data. Insets illustrate the reconfigurable droplets during actuation. The pattern cannot maintain stability under higher actuation velocities due to increased fluidic drag (data inside the ellipse). (b) Automated guidance of the assembled droplets. The motion trajectory is marked with a blue line, and the red rectangle represents the preset path. In addition to the field gradient, a precessing field with a frequency of 3 Hz and a precession angle of 30◦ is also applied (see Supporting Information video S4). (c) The assembled droplets are steered to the cargo using a field gradient before t = 6 s. Then, it is expanded, and the cargo is encaged in the central region of the pattern (t = 41 s). The cargo can be noncontact transported to the desired location. Release of the cargo is realized by expanding the pattern (see Supporting Information video S5). (d) Noncontact transportation of a batch of cargoes. Yellow arrows refer to the motion directions (see Supporting Information video S6). All scale bars are 4 mm.

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Collective Behavior of Reconfigurable Magnetic Droplets via Dynamic

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