Letter pubs.acs.org/NanoLett
Selective Trapping and Manipulation of Microscale Objects Using Mobile Microvortices Tristan Petit,† Li Zhang,* Kathrin E. Peyer, Bradley E. Kratochvil, and Bradley J. Nelson Institute of Robotics and Intelligent Systems, ETH Zurich, CH-8092 Zurich, Switzerland S Supporting Information *
ABSTRACT: Controlled manipulation of individual microand nanoscale objects requires the use of trapping forces that can be focused and translated with high spatial and time resolution. We report a new strategy that uses the flow of mobile microvortices to trap and manipulate single objects in fluid with essentially no restrictions on their material properties. Fluidic trapping forces are generated toward the center of microvortices formed by magnetic microactuators, that is, rotating nanowire or self-assembled microbeads, actuated by a weak rotating magnetic field (|B|< 5 mT). We demonstrate precise manipulation of single microspheres and microorganisms near a solid surface in water. KEYWORDS: Fluidic trapping, nanowire, microvortex, low Reynolds number flow, noncontact manipulation
O
ptical tweezers,1−3 magnetic tweezers,4−6 and dielectrophoresis7,8 are commonly used for the manipulation of individual microscale objects such as microspheres,9 cells, or bacteria.10,11 A limitation of these techniques is that high intensity lasers, physical attachment to magnetic objects, or strong electrical fields cannot be used with many biological samples.11,12 Several alternative methods based on near field photonics,13,14 electrostatic,15 electokinetic,16,17 or acoustic traps18 have been proposed to circumvent these limitations but only offer static trapping possibilities. Single-cell manipulation with a high throughput can be achieved using microfluidics,19 however the fluid flow is generally controlled by geometrical means, such as channels or pillars in “lab-on-achip” systems,20−22 which limits its versatility for manipulation tasks. While static trapping of micro-objects has been demonstrated in recirculating flows generated by different device geometries,23−25 dynamically manipulating a single micro-object with high spatial resolution is not possible with these techniques. We have created a new approach for precisely manipulating micro-objects using mobile microvortices at low-Reynolds numbers (10−1 to 10−4) generated by the rotation of magnetic microactuators such as nickel nanowires or self-assembled magnetic bead doublets in fluid. A trapping force is locally induced by the flow velocity gradient toward the center of the microvortex. The amplitude and position of the microvortex can be precisely controlled to selectively trap and transport individual micro-objects near a solid surface. Only a very weak rotating uniform magnetic field is required as an energy source (|B|< 5 mT). This makes the technique well adapted for manipulating biological samples over a large working volume and can be incorporated into most existing microfluidic systems. © 2011 American Chemical Society
When a microactuator rotates around its geometrical center, a localized shear flow is formed between its two distal ends,26 as shown in the simulation of the tangential velocity in Figure 1a. The model uses the low Reynolds number assumption and is based on the method of fundamental solutions27 (see Supporting Information). The model shows the tangential flow near a 13 μm long nanowire rotating at 95 Hz, which corresponds to a rotational speed of 5700 rpm in an unbounded fluid. The flow velocity and the shear rate decrease rapidly with distance from the nanowire. Averaged over one complete rotation of the nanowire, the amplitude of the tangential flow profiles in planes normal to the rotational axis exhibits a radial symmetry. The simulation indicates that a local minimal flow velocity exists at the center of the nanowire, whereas maximal flow velocities occur above its ends. Therefore, the averaged tangential flow resembles a microvortex centered on the rotational axis of the nanowire, as shown in Figure 1b. The shear rate in planes normal to the rotational axis is directly tuned by the rotational speed of the nanowire, which in turn is controlled by the frequency and strength of the rotating magnetic field. Such a microvortex is experimentally demonstrated by rotating a 13 μm long nickel nanowire with a diameter of ca. 200 nm horizontally above a flat silicon surface in sync with a rotating magnetic field of 3 mT. The uniform magnetic field was generated by a three-axis Helmholtz coil setup. Further experimental details are available in the Supporting Information. To observe the hydrodynamic interaction between the microvortex and a microobject, a 6 μm polystyrene microReceived: September 17, 2011 Revised: November 18, 2011 Published: November 23, 2011 156
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Figure 1. Simulation of the tangential flow field induced by a rotating nanowire. The simulation uses the low Reynolds number assumption and is based on the method of fundamental solutions (see Supporting Information). (a) Two-dimensional flow velocity profile induced by the rotation of a 13 μm long nanowire with a frequency of 95 Hz in the plane formed by the nanowire and its rotational axis. The flow velocity is plotted from Z = 1 μm. The nanowire rotational axis, rotational direction, and velocity direction are represented as a dashed line, red arrow, and black arrows, respectively. (b) Two-dimensional tangential flow velocity averaged over a full rotation of the nanowire in the plane normal to the rotational axis at Z = 2 μm.
sphere is positioned above the rotating nanowire. Initially, the rotational frequency is set to 25 Hz and the microsphere translates along a circular streamline in the microvortex. Surprisingly, when the rotational frequency is increased to 95 Hz, the microsphere translates to the center of the microvortex
(see Supporting Information movie S1). This result suggests that a trapping force is applied inside the microvortex for high shear rates. The trapping force is applied perpendicular to the flow velocity and toward the center of the microvortex, where the flow velocity is minimal. The center of the microvortex, 157
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Figure 2. Manipulation of individual polystyrene microspheres with a microvortex generated by a rotating nickel nanowire (see also Supporting Information movie S1). (a) A 13 μm long nickel nanowire tumbles in the direction of a 6 μm diameter polystyrene microsphere with an input field frequency f = 23 Hz. The dashed line represents the trapping trajectory. (b) The microsphere is trapped in the microvortex and translated with the rotating nanowire with f = 25 Hz. Images obtained during 10 s are superimposed. (c) The nanowire rotates in a plane parallel to the horizontal wall and the microsphere is immobilized during 16 s. The input field frequency is progressively increased up to f = 95 Hz to induce fluidic trapping and then decreased to f = 59 Hz before the release of the microsphere. (d) Release of the microsphere after changing the rotational plane from horizontal to vertical orientation. Images obtained during 1 s are superimposed. (e) The microsphere is driven over a 100 μm step with f = 28 Hz. Surfaces “A” and “B” are the bottom and upper surfaces of the step, respectively. A lateral drift was observed during the vertical translation, attributed to surface roughness of the wall. (f) Sequential pick-and-place manipulation of five microspheres to form a crosslike pattern. Insets illustrate the different configurations with black and red arrows corresponding to the velocities of the nanowire and the microsphere, respectively. The magnetic field strength is 3 mT in all manipulation tests. Scale bars are 20 μm.
near a surface, the asymmetric boundary condition creates a velocity difference between the two ends of the nanowire and results in a combination of translational and rotational motion, a kind of tumbling. The translational velocity of the tumbling nanowire is tuned by the input frequency and its orientation depends on the rotational plane of the magnetic field. The tumbling motion of a nickel nanowire is used to approach and perform pick-and-place of a 6 μm microsphere with a mobile microvortex. If the nanowire is driven toward the center of the microsphere, the success rate of trapping is low because the repulsive shear flow surrounding the microvortex pushes the microsphere (see Supporting Information Figure S2). However, if the nanowire is driven tangentially to the side of the microsphere, as shown in Figure 2a, with a relatively low rotational frequency in the range of 15−30 Hz, the repulsive shear flow has a significantly reduced impact on the static microsphere. The nanowire translates at higher velocity than the microsphere, which reduces the distance between the microvortex and the microsphere until fluidic trapping occurs. Once the microsphere is trapped, it is transported with the same translational velocity as the microvortex, that is, the translation velocity of the nanowire. This enables precise dynamic control of the microsphere as shown in Figure 2b (see also Supporting Information movie S1). Furthermore, static control is achieved by rotating the nanowire horizontally (Figure 2c).
which we call a fluidic trap, corresponds to a stable position for a microobject in the microvortex. Outside the microvortex, the opposing flow velocity gradient induces a repulsive force. Consequently, only microobjects positioned in the microvortex are trapped, which makes fluidic trapping a highly localized trapping method. Previously, the behavior of spheres in shear flow and vortices has been studied in various conditions. For example, the trapping of spheres in microvortices was reported,24 but this phenomenon occurred at higher Reynolds numbers (Re > 10). Alternatively, the influence of inertia in low Reynolds number (Re < 1) shear flow has been studied by Saffman,28 but his findings, that is, the Saffman lift force, predict the migration of the sphere to the high velocity region, rather than low-velocity region of the shear flow. More recently, a similar trapping force generated by microeddies around a fixed cylinder has been reported.23 The Reynolds number of the oscillating flow and the microeddies, induced by the oscillating flow, are approximate 10 and 1, respectively. Our experimental results reveal that a trapping force, which points toward the vortex center, still exists at Reynolds numbers smaller than one. The physical origin of the trapping force in microvortices and microeddies requires further investigation. In order to precisely move the microvortex, the rotating nanowire must be propelled in a controllable fashion. At low Reynolds number, propulsion is induced when the time reversibility of the swimming motion is broken, for example, near a solid surface.29,30 When the nanowire rotates vertically 158
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The controlled release of the trapped microsphere is achieved by abruptly tilting the microvortex 90° from the horizontal to vertical plane or reducing the amplitude of the microvortex. The change of orientation of the microvortex removes the microsphere from the fluidic trap. When the rotational frequency is high, the microsphere ends up outside the microvortex but is dragged by the surrounding flow induced by the rotating nanowire for several micrometers resulting in an imprecise release position, as shown in Figure 2d (see also Supporting Information movie S1). Alternatively, when the change of the rotational plane of the magnetic field is performed at a lower rotational frequency, the microsphere remains in the microvortex and translates along a circular streamline. Then, by decreasing the rotational frequency to less than 5 Hz, the microvortex amplitude shrinks and no longer interacts with the microsphere. In this manner, the nanowire can be driven away from the microsphere without significantly affecting the microsphere position (see Supporting Information movie S2). Transport of a microsphere over a 100 μm deep step is also performed. The nanowire is rotated toward the step and is automatically propelled upward when near the vertical wall (Figure 2e). This result suggests that manipulation over 3D structures is feasible. To illustrate the manipulation possibilities of the fluidic trapping method, five randomly distributed microspheres on a flat surface were picked and placed to form a cross-like pattern shown in Figure 2f. During manipulation experiments, translational velocities of up to 87 ± 2 μm/s (14.5 body-lengths per second) were obtained. Microsphere trapping reduces the nanowire’s translational velocity by approximately 10−15%, depending on the input magnetic field frequency, which is small compared to the velocity decrease reported by other transport methods such as cargo pushing with a catalytically propelled nanowire31 or a tumbling nanowire29 (Figure 3). An estimation of the trapping force can be given by means of the Stokes’ law, which describes the drag force (Fdrag = 6πηRV) on a sphere, where η is the dynamic viscosity of the fluid, and R and V are the radius and translational velocity of the sphere, respectively. Thus, the 3 μm radius bead transported at a velocity of 87 μm/s encounters a drag force of 4.9 pN, which serves as a lower bound estimation of the trapping force. Furthermore, automated motion control of a trapped microobject can be achieved (see Supporting Information movie S2). The rotating magnetic field is automatically updated to drive the microvortex along a predefined circular path with micrometer precision using a visual servoing approach.32 The dimension and shape of the microvortex is crucial for trapping individual micro-objects. For example, trapping nonflagellated E. coli bacteria, which have a capsule-like body with a dimension of approximate 1 μm × 2 μm, is not possible with 10−15 μm long nickel nanowires, because the nanowireinduced fluidic trap is several micrometers larger than the bacteria body. However, by creating a self-assembled doublet composed of two 1 μm diameter superparamagnetic microspheres, a microvortex with a similar size to the bacterium can be generated and fluidic trapping and transportation achieved, as shown in Figure 4. The experimental results, therefore, reveal that fluidic trapping occurs robustly when the microactuator has a length between 1 and 2 times the size of the manipulated object. Though these superparamagnetic microspheres exhibit Brownian motion when the magnetic field is off, these forces are negligible when a weak-strength magnetic field is applied
Figure 3. Velocity change due to cargo loading by different methods. Cargo transport with microvortices generated by a 13 and a 15 μm long nickel nanowire is compared to pushing the cargo with a tumbling 7 μm long nanowire in water (see Supporting Information Figure S1) and catalytically propelled nanomotor in 5 wt % H2O2 solution.30 The velocity change between the translating microactuator (blue) and the cargo after loading (red) are expressed above the red bars. The magnetic field strength is 3 mT for the 7 and 13 μm long nanowires and 4 mT for the 15 μm long nanowire. The cargos are microspheres with diameter of 3, 1.3, and 6 μm for the pushing nanowire, the catalytic nanomotor, and the fluidic tweezers, respectively.
Figure 4. Manipulation of an individual E. coli bacterium with a microvortex generated by a self-assembled microsphere doublet. (See also Supporting Information movie S3) The input frequency was f = 21 Hz for the approach of the E. coli bacterium and was increased to f = 31 Hz for the fluidic trapping. Images obtained during 8 s are superimposed. Inset is a magnified view of the doublet and the E. coli bacterium. The magnetic field strength is 5 mT. Scale bars are 10 and 2 μm for the image and the inset, respectively.
during micromanipulation. The bacterium aligns the long axis of its body perpendicular to the rotating doublet, which minimizes total drag force during fluidic trapping (see Supporting Information movie S3). In addition, trapping and transport of individual microorganisms using a rotating nanowire are demonstrated (see Supporting Information movies S4 and S5). Individual micro-objects can be effectively manipulated with mobile microvortices. Quantitative estimation of the hydrodynamic forces in microvortices could be used to measure force and torque exerted on individual micro-objects.33,34 Parallel manipulation over large working volumes is also possible without increasing the complexity of the experimental setup. 159
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The control of fluid flow with high static and dynamic precision using externally actuated micro- or nanostructures will extend manipulation and analysis possibilities of future microfluidic systems.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information is available on materials and methods, experimental setup and simulation details. Another noncontact manipulation method with a nickel nanowire is also demonstrated (Figure S1). Five video clips are available that demonstrate trapping and manipulation with microvortices. Movie S1 shows trapping, transport, rotation, and release of a 6 μm polystyrene microsphere with a microvortex generated by a 13 μm long nickel nanowire. Movie S2 shows the automated transport of a 6 μm polystyrene microsphere along a circular pathway using a microvortex generated by a similar nanowire and the controlled release of the microsphere. Movie S3 shows the trapping and release of an E. coli bacterium with a microvortex generated by a self-assembled superparamagnetic microbead doublet. Movie S4 shows the rotation and trapping of a microorganism using a nanowire rotating in the horizontal plane. When the input frequency is increased from 40 to 50 Hz, the microorganism is moved toward the trapping center of the microvortex. The rotational speed of the trapped microorganism is in a range of ca. 225−300 rpm, which is approximately 1 order of magnitude lower than the rotating nanowire with a rotational speed of 3000 rpm at 50 Hz. Movie S5 shows trapping and transport of a capsule-like microorganism using a ca. 8.6 μm long nanowire. The short and long axes of the microorganism’s capsule-like body are ca. 4 and 9 μm, respectively. In all video clips, the blue and green lines (in the upper left) indicate the plane of rotation of the uniform magnetic field in which the green line represents the direction of the input field. In the user interface, yaw is the angle of the red line (in the upper left) observed in the horizontal imaging plane, and pitch is the orientation of the nanowire (or selfassembled microsphere doublet) with respect to the horizontal plane (pitch = 0° or ±180° means the nanowire rotates horizontally and pitch = ±90° means the nanowire rotates vertically). All video clips were recorded in real time. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected]. Present Address † Diamond Sensors Laboratory, CEA-LIST, 91191 Gif-SurYvette, France.
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ACKNOWLEDGMENTS We thank Professor Jun Lou from Rice University for furnishing the nickel nanowires and Dr. Peter Lindner from the University of Zurich for furnishing E. coli bacteria. The microorganisms shown in the supplementary movies S4 and S5 were collected from Lake Zurich and directly used for the trapping tests. We thank the FIRST lab of ETH Zurich for technical support. Funding for this research was partially provided by the European Research Council Advanced Grant “Microrobotics and Nanomedicine (BOTMED).” 160
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