Manipulation of Self-Assembled Structures of Magnetic Beads for

We present an original concept of manipulation of mag- netic microbeads in a microchannel. It is based on the dynamic motion of a self-assembled struc...
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Anal. Chem. 2004, 76, 6239-6246

Manipulation of Self-Assembled Structures of Magnetic Beads for Microfluidic Mixing and Assaying A. Rida and M. A. M. Gijs*

Institute of Microelectronics and Microsystems, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne EPFL, Switzerland

We present an original concept of manipulation of magnetic microbeads in a microchannel. It is based on the dynamic motion of a self-assembled structure of ferrimagnetic beads that are retained within a microfluidic flow using a local alternating magnetic field. The latter induces a rotational motion of the magnetic particles, thereby strongly enhancing the fluid perfusion through the magnetic structure that behaves as a dynamic random porous medium. The result is a very strong particle-liquid interaction that can be controlled by adjusting the magnetic field frequency and amplitude, as well as the liquid flow rate, and is at the basis of very efficient liquid mixing. The principle is demonstrated using a microfluidic chip made of poly(methyl methacrylate) with integrated soft ferromagnetic plate structures. The latter are part of an electromagnetic circuit and serve to locally apply a magnetic field over the section of the microchannel. Starting from a laminar flow pattern of parallel fluorescein dye and nonfluorescent liquid streams, we demonstrate a 95% mixing efficiency using a mixing length of only 400 µm and at liquid flows of the order of 0.5 cm/s. We anticipate that the intense interaction between the fluid and magnetic particles with functionalized surfaces holds large potential for the development of future bead-based assays. After demonstration of the first concept of miniaturized total analysis systems or microTAS in 1990,1,2 fluidic microchip technologies overcame multiple experimental hurdles, opening the field for numerous pharmaceutical and biological applications. A comprehensive overview of all the important developments in technology, theoretical understanding, and applications is given in refs 3-5. Miniaturized devices take benefit from a large surfaceto-volume ratio at small length scales, which leads to considerable time saving due to reduced diffusion times and to cost reduction * To whom correspondence should be addressed. Tel: +41 21 693 67 34. Fax: +41 21 693 59 50. E-mail: [email protected]. (1) Manz, A.; Graber, N.; Widmer, H. M. Sens. Actuators, B 1990, 1, 244-248. (2) Manz, A.; Fettinger, J. C.; Verpoorte, E.; Lu ¨ di, H. M.; Harrison, D. J. Trends Anal. Chem. 1991, 10, 144-149. (3) Reyes, D. R.; Iossifidis, D.; Auroux, P. A.; Manz A. Anal. Chem. 2002, 74, 2623-2636. (4) Auroux, P. A.; Iossifidis, D.; Reyes, D. R.; Manz, A. Anal. Chem. 2002, 74, 2637-2652. (5) Vilkner, T.; Janasek, D.; Manz, A. Anal. Chem. 2004, 76, 3373-3385. 10.1021/ac049415j CCC: $27.50 Published on Web 09/30/2004

© 2004 American Chemical Society

due to the decreasing consumption of reagents. Moreover, the use of beads in microchannels may further increase the chemical binding area per unit volume in surface-based biochemical assays.6 In particular, the use of magnetic beads has facilitated the downscaling of conventional analysis techniques to the micrometer scale:7,8 magnetic microbeads with specific surface-immobilized biomolecules have been shown very suitable for fast immunoassaying,9 DNA hybridization,10 or high-yield mRNA capture.11 Still, diffusion-limited reaction rates and slow mixing of components often are issues in laminar flow microsystems where viscosity effects dominate fluid transport. In a laminar flow, two merging fluid streams will flow smoothly next to each other and will be mixed only slowly by diffusion processes. Therefore, numerous mixing concepts for fluidic microchannels have been introduced. In a first type of active mixing devices, mechanical actuation is used to actively mix fluid components.12-14 Some microfluidic applications require that mixing be inexpensive and simple to operate, which partly explains the interest for passive mixing devices that do not need dedicated external actuation forces. The most common passive mixing device at low Reynolds numbers (Re < 1) is based on the splitting of the liquid flow into smaller laminar flow patterns, decreasing the diffusive mixing length.15,16 At higher Re, several mixing concepts based on chaotic flows in microfluidic channels have been demonstrated.17,18 Chaotic advection typically is obtained in microchannels with distorted (6) Verpoorte, E. Lab Chip 2003, 3, 60N-68N. (7) Pe´rez, F. G.; Mascini, M.; Tothill, I. E.; Turner, A. P. F. Anal. Chem. 1998, 70, 2380-2386. (8) Krogh T. N.; Berg T.; Højrup P. Anal. Biochem. 1999, 274, 153-162. (9) Hayes, M. A.; Polson, N. A.; Phayre, A. N.; Garcia, A. A. Anal. Chem. 2001, 73, 5896-5902. (10) Fan, Z. H.; Mangru, S.; Granzow, R.; Heaney, P.; Ho, W.; Dong, Q.; Kumar, R. Anal. Chem. 1999, 71, 4851-4859. (11) Jiang, G. F.; Harrison, D. J. Analyst 2000, 125, 2176-2179. (12) Hosokawa, K.; Fujii, T.; Endo, I. In Proceedings of Micro Total Analysis Systems 2000; A. van den Berg, et al., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000; pp 481-484. (13) Liu, R. H.; Ryu, K. S.; Liu, C. J. Microelectromech. Syst. 2002, 11, 462-469. (14) Yang, Z.; Matsumoto, S.; Goto, H.; Matsumoto, M.; Maeda, R. Sens. Actuators. A 2001, 93, 266-272. (15) Bessoth, F. G.; de Mello, A. J.; Manz, A. Anal. Commun. 1999, 36, 213215. (16) Hinsmann, P.; Frank, J.; Svasek, P.; Harasek, M.; Lendl, B. Lab Chip 2001, 1, 16-21. (17) Mengeaud, V.; Josserand, J.; Girault, H. Anal. Chem. 2002, 74, 4279-4286. (18) Liu, R. H.; Stremler, M. A.; Sharp, K. V.; Olsen, M. G.; Santiago, R. J. A.; Aref, H.; Beebe, D. J. J. Microelectromech. Syst. 2000, 9, 190-197.

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side walls. These structures generate transverse components of flow that stretch and fold volumes of liquid over the cross section of the channel and thereby strongly reduce the mixing length.19-21 A particular kind of passive mixing is based on the disruption of flow paths by obstacles placed in well-defined zones of a microfluidic circuit.22 For example, polystyrene beads packed within microbarrier-limited zones of a microchannel can be used as obstacles for chaotic advection-like mixing; in addition, such obstacles provide at the same time a large chemically active surface, which opens new perspectives for miniaturized analysis systems.23 Instead of ordered mixing structuresslike packed beadsswhere the longitudinal mixing is enhanced, additional lateral mixing can be obtained by use of a heterogeneous mixing matrix containing large irregular pores.24 In this paper, we demonstrate a new concept of active fluid mixing in microchannels, which is based on the manipulation by a local alternating magnetic field of self-assembled porous structures of magnetic microbeads that are placed over the section of the channel. These objects, known as magnetorheological structures (MRS), are composed of a complex network of magnetic chains, the shape of which is controlled by several competing magnetic forces.25,26 More specifically, by using an alternating magnetic field, we show the possibility to induce a rotational motion of the magnetic particles, thereby strongly enhancing the fluid perfusion through the MRS that behaves as a dynamic random porous medium. We generate the localized time-dependent magnetic field using a current-fed coil and a soft magnetic yoke structure, which is partly integrated within a plastic microfluidic chip. By varying the flow rate and the magnitude and frequency of the field, we determine the conditions at which the MRS is stable and magnetically retained within the microchannel. The magnetic field-induced rotational dynamics of the MRS, causes a vortex-like motion of the fluid in the microchannel, as visualized by video microscopy of the trajectories of fluorescent microparticles at the interface of the MRS. The mixing is the result of the chaotic splitting of fluid streams through the dynamic and randomly porous structure of the MRS and the relative motion of magnetic entities with respect to the fluid flow. We quantify the mixing by monitoring the fluorescent intensity of initially parallel fluorescent and nonfluorescent laminar streams. When using fluorescein dye, we obtain a 95% mixing efficiency over a channel length of 400 µm and at flow rates of 0.5 cm/s; this mixing length is considerably smaller than the several millimeters reported for a static packed bead27 or porous polymer monolith mixers24 at flow rates of the same order. Our results demonstrate the large lateral mass transfer induced by the MRS as a consequence of the highly heterogeneous, open, and dynamic nature of the MRS. (19) Johnson, T. J.; Ross, D.; Locascio, L. E. Anal. Chem 2002, 74, 45-51. (20) Stroock, A. D.; Dertinger, K. W.; Ajdari, A.; Mezı´c, I.; Stone, H. A.; Whitesides, G. M. Science 2002, 295, 647-651. (21) Stroock, A. D.; Whitesides, G. M. Acc. Chem. Res. 2003, 36, 597-604. (22) Wang, H.; Iovenetti, P.; Harvey, E.; Masood, S. Smart Mater. Struct. 2002, 11, 662-667. (23) Ahmadian A.; Russom A.; Andersson H.; Uhlen M.; Stemme G.; Nilsson P. Biotechniques 2002, 32, 748. (24) Rohr, T.; Yu, C.; Davey, M. H.; Svec, F.; Fre´chet, J. M. J. Electrophoresis 2001, 22, 3959-3967. (25) Mohebi, M.; Jamasbi, N.; Liu, J. Phys. Rev. E 1996, 54, 5407-5413. (26) George, A. F.; Jing, L. Phys. Rev. E 1999, 59, 751-762. (27) Seong, G. H.; Crooks, R. M. J. Am. Chem. Soc. 2002, 124, 13360-13361.

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EXPERIMENTAL SECTION Reagents and Materials. Tris(hydroxymethyl)aminomethane (TRIS; pH ) 8.3) buffer is prepared using 135 mg of TRIS (pH ) 8.3) (product no. 93389, Fluka, Buchs SG, Switzerland) in 10 mL of water. For visualization of the flow patterns, solutions of fluorescent beads are prepared by dissolving 1 µL of a suspension of 2.1- or 1.0-µm-diameter polystyrene fluorescent microbeads, F-8888 kit (Molecular Probes, Leiden, The Netherlands) in 2 mL of water. For the mixing experiments, a fluorescent solution is obtained by dissolving fluorescein, 76 µM (product no. 46960, Fluka), directly in the buffer. A suspension of magnetic particles in 2-propanol is obtained from the MagNA Pure LC DNA isolation Kit from Roche Diagnostics (Rotkreuz, Switzerland). These particles are characterized by a small remnant magnetic moment after exposure to a magnetic field (see further), due to the high magnetic content of the particle core; such ferrimagnetic particles have a much stronger interaction with the magnetic field than superparamagnetic particles. Poly(methyl methacrylate) (PMMA) sheets of different thickness (Plexiglas films), ranging between 0.2 and 1.0 mm, were obtained from Degussa AG (Marl, Germany) and are the basis material for the realization of the microfluidic chip. Triethylene glycol diamethacrylate solution (product no. 90412, Fluka) is used for bonding these PMMA layers into a monolithic chip. The chip-integrated soft magnetic parts are of pure iron and obtained from Advent Research Material Ltd. (Oxford, England). Microchip Fabrication. The microfluidic chip is composed of PMMA layers, which are micropatterned using mechanical erosion by micropowder blasting. In our process, we use an HP-2 Texas Airsonics abrasive jet machine, which is connected to a 6-bar pressurized air source. The eroding powder consists of 30µm-size alumina particles (Al2O3) (EFK 320, Strahltechnik Bachmann AG, Remetschwil, Switzerland) and is dosed to an exit nozzle by a vibration feeder in an air jet. Until now used only for the structuring of brittle materials such as glass,28,29 we demonstrate here the potential of this technique for rapid and low-cost micropatterning of PMMA. The powder blasting process is highly anisotropic, as it is based on the physical impact of eroding particles that generate cracks in the brittle substrate material. Channels with aspect ratios of 2-3 and a smallest size of 70-80 µm are possible, the latter dimension being of the order of the size of the used powder. The intrinsic “beam spot size” of the alumina jet is of the order of 1 cm2, which mostly is too large for “direct-write” applications. Instead, the lateral resolution of the process is purely a consequence of the mask features and the powder particle size. We use in-house laser-patterned 0.5-mm-thick metallic sheets as contact masks in the powder blasting process. As schematically shown in Figure 1a, the realized chip (22 mm × 32 mm) is composed of four PMMA layers, which all have hole structures at two opposite corners for pin alignment during the bonding process. The mean layer (second) contains a Y-shaped microchannel with cross section of 200 µm × 200 µm and two adjacent holes (5 mm × 7 mm) to integrate the ferromagnetic iron parts (labeled as (1) and (2)). Such holes are also present in the third PMMA layer in order to fully accommodate the 0.5-mmthick iron parts inside the chip. The fourth PMMA layer has, (28) Belloy, E.; Sayah, A.; Gijs, M. A. M. Sens. Actuators, A 2001, 92, 358-363. (29) Schlautmann, S.; Wensink, H.; Schasfoort, R.; Elwenspoek, M.; van den Berg, A. J. Micromech. Microeng. 2001, 11, 386-389.

Figure 1. (a) Schematic diagram of the microfluidic mixer structure. Two soft iron plates (1 and 2) of 0.5-mm thickness are integrated at both sides of a 200-µm Y-shaped microchannel realized in a PMMA microfluidic chip; (b) schematic side view of the chip (3), which is connected to an external electromagnet assembly, formed by a soft magnetic core (4) and a coil (5).

besides the fluidic entrance holes (2-mm diameter), two holes (5 mm × 5 mm) through which the soft iron parts will be magnetically contacted with the external electromagnet. For the microchip bonding, we use a triethylene glycol diamethacrylate cross-linker solution, containing methacrylate groups that bind to the activated acrylate groups of the PMMA sheets. Small amounts of this cross-linker are applied on the PMMA layers. Heating at a temperature of 60 °C for 10 min is necessary to activate the reaction between the cross-linker and the PMMA layers. After this process, we obtain a threedimensional and monolithic microfluidic PMMA chip with embedded soft iron parts. In the inlet fluidic entrance holes of the obtained chip, hollow stainless steel tubes are glued to serve as connectors to external syringe pumps via Teflon tubes. On the outlet hole, a glass cylindrical reservoir (5 mm high and 3-mm inner diameter) is glued to serve as waste collector. Magnetic Circuit. Figure 1b is a schematic side view of the microfluidic chip (3) in which the soft iron parts (1) and (2) are in direct contact with an external electromagnet, formed by a soft magnetic core (4) and a coil (5). The electromagnet, placed on top of the microchip, consists of an in-house-realized U-shaped pure iron core of 14.5-mm width, 9-mm height, and 4 mm × 4 mm cross section, wired with 150 Cu windings (wire diameter 0.12 mm). The magnetic flux generated by this external electromagnet is focused by the integrated iron parts in the microfluidic channel. These parts are structured in-house using laser cutting and end in a tip; the inner distance between the two tips (magnetic gap), sandwiching the microchannel, is 0.5 mm. The shape of the soft iron parts is important, since it determines the magnetic focusing and magnetic field gradient in the microchannel. In principle, the narrower the tip width, the stronger the focusing effect and field gradient. However, focusing is also limited by the distance between the pole tips: as the emerging magnetic flux from the tip spreads out in the magnetic gap region, the area in the microchannel where there is an appreciable magnetic field will be an increasing function of the magnetic gap size. Typically, in our microchip, we chose the tip width to be 200 µm, i.e., the channel width, resulting in an “active” magnetic field region of

about 200 µm × 400 µm in the microchannel. Note that the effective mixing area may be somewhat larger in the y-direction (a few hundred micrometers) due to the influence of lateral chaotic advection flows and vorticity effects generated in the microchannel (see further). Experimental Setup. For the visualization, image acquisition. and fluorescence detection, a CCD camera (ORCA-C4742-95ER, Hamamatsu) is mounted on a microscope platform (Zeiss) equipped with various objectives (Achroplan 4×, 10×, and 20×), a mercury arc lamp, and a filter set (Zeiss filter set no 9). The excitation, dichroic mirror, and emission wavelengths for this filter set are 450-490, 510, and 520 nm, respectively. The image and data analysis software AquaCosmos, also obtained from Hamamatsu, have been used for quantitative analysis of the fluorescence and video data. Typically, fluorescent profiles over the channel width are recorded and analyzed 1 mm upstream in the y-direction with respect to the position of the magnetic pole tips for the unperturbed flow, or 1 mm downstream for the mixed flow, respectively. The PMMA chip is placed on a support equipped with two manual (X-Y) micrometric translation stages (Zeiss). For liquid driving, the chip is connected to two syringe pumps (48000 steps module) from Kloehn Ltd. (Las Vegas, NV) controlled using in-house-developed C++ software. The coil of. the electromagnet is powered by a bipolar operational power supply BP50-2M (Kepco Inc, Flushing, NY) that is connected to a 33250A arbitrary waveform generator from Agilent (Palo Alto, CA). Methods. The two pumps, equipped with 50-µL volume syringes, are filled with water and fluorescent solution, respectively, and connected to the microchip, which is mounted on the microscope platform. The magnetic particles are introduced by aspirating 2 µL of magnetic particle suspension from the outlet reservoir in the channel at a flow rate of 0.1 µL/s. At the same time, we apply a static magnetic field generated by a dc current of 0.1 A in the coil. During the bead suction process, the magnetic particles are trapped in the microchannel region in the air gap of the magnetic circuit. When the magnetic particles are completely loaded in the microchip, a time-varying (alternating) magnetic field is applied by adjusting the current in the coil using the arbitrary Analytical Chemistry, Vol. 76, No. 21, November 1, 2004

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waveform generator. The resulting MRS is observed by video microscopy (30 frames/s) as a function of both field frequency and amplitude and liquid flow rate. The magnetic field amplitude for a given coil current is calculated using a finite element simulation of the magnetic field in the magnetic gap of our magnetic circuit geometry, using the 3-D magnetostatic module of Femlab30 software; calculated values outside the gap region are checked experimentally using a F. W. Bell 6010 Hall probe (Sypris, Orlando, FL). In the mixing experiments, the fluorescent and water streams are applied at the same flow rate through the microchannel (in a flow range of 0.1-3 cm/s) and the resulting fluorescence distribution profile over the channel width is monitored before and after the active magnetic mixing area, using the pixel profile analysis of the AquaCosmos software. The maximum fluorescence intensity in the channel before mixing is normalized to 1. The mixing efficiency E is calculated by the equation22

E)

(

∫ |I 1∫ |I l

)

0 l

am

- I∞| dx

0

bm

- I∞| dx

× 100%

(1)

where Iam(x) is the fluorescent intensity distribution over the channel width l after the mixing area, taken at a y-coordinate that is 1 mm downstream with respect to the symmetry line defined by the pole tips, I∞ is the fluorescent intensity at perfect mixing. and Ibm(x) is the fluorescent intensity distribution over the channel width l before the mixing area, taken at a y-coordinate 1 mm upstream with respect to the symmetry line defined by the pole tips. Using this definition, a perfect mixing is characterized by a mixing efficiency of 100%. RESULTS AND DISCUSSION Magnetic Field in the Microchannel. Retaining magnetic particles in the microchannel under a fluid flow requires a large magnetic field, so that the particles withstand the viscous drag force due to the flow. Moreover, manipulating these particles in a small region (less than 1 mm2) of the microchip requires a localized magnetic field gradient. These conditions are hard to achieve by use of a simple external permanent magnet or electromagnet. The integration of magnetic components with the fluidic channels is necessary to achieve an accurate manipulation of magnetic beads.31-33 Figure 2 is a finite element calculation of the magnetic induction in the plane of the soft iron parts. We clearly observe flux focusing: a magnetic induction of 0.1 T is calculated in the magnetic gap between the two tips, by just applying a current of 100 mA in the coil. Limited by magnetic gap losses34 and the magnetic saturation of the soft iron parts (2.2 T), a maximum magnetic induction of 0.6 T can be obtained in (30) COMSOL, Inc. www.comsol.com. (31) Choi, J.-W.; Liakopoulos, T. M.; Ahn, C. H. Biosens., Bioelectron. 2001, 16, 409-416. (32) Lee, C. S.; Lee H.; Westervelt, R. M. Appl. Phys. Lett. 2001, 79, 33083310. (33) Rida, A.; Fernandez, V.; Gijs, M. A. M. Appl. Phys. Lett. 2003, 83, 23962399. (34) When a magnetic gap g is present in an otherwise closed circuit of length L of a magnetic material with permeability µ, the presence of the gap reduces the effective permeability of the circuit, µeff ≈ µ/(1 + gµ/L), and thereby the maximum obtainable magnetic induction in the gap region.

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Figure 2. Finite element simulation of the magnetic induction generated by the system of Figure 1. The magnetic circuit is characterized by an air gap of 0.5 mm to accommodate the microchannel; a current of 0.1 A is used in the coil with winding number N ) 150. A maximum magnetic field of 0.1 T is generated in the middle of the air gap.

the microchannel. The maximum of the magnetic force is substantially “localized” in the y-direction over a distance of the order of the pole tip width (400 µm). Magnetorheological Structure. The used magnetic glass particles have an inner core composed of nanometer-size magnetite crystals and an outer glass surface; they have a variable diameter in the range of 1-10 µm, with a mean diameter of 3 µm, as determined by scanning electron microscopy. The relatively high magnetic content of the particles is at the basis of a saturation magnetization µ0Msat ) 0.2 T, a magnetic susceptibility χ ) 1.5, and a small remanence µ0Mrem ) 0.04 T, as determined using a SQUID magnetometer (Quantum Design, Inc.). Typically, a spherical particle with radius r )1.5 µm, placed in a magnetic induction field µ0H ) 10 mT will have a magnetic moment m ) (4/3)πr3(µ0χH/3) ) 7.1 × 10-20 Tm3, while two of such particles will have a maximum magnetic attraction energy |Umax| ) (m2/ 2πµ0)(1/(2r)3) ) 2.4 × 10-17 J, much larger than the thermal energy kBT ) 4.0 × 10-21 J at T ) 293 K, resulting in strong dipolar forces between the particles. When exposed to an external magnetic field, the magnetic microparticles acquire a magnetic dipole moment and coalesce, under influence of the magnetic dipole interaction into a MRS consisting of chainlike “columnar” structures along the field direction. The exact shape of this MRS depends on parameters such as the particle concentration and the applied magnetic field. It is known that a constant and homogeneous magnetic field enables the generation of equally spaced arrays of columns of chains in a microchannel.35,36 Such quasi-regular MRS has been recently demonstrated to form a new type of electrophoresis separation column for DNA separation in microchips.37 When we use a static field in our chip, magnetic columns are attracted to (35) Sandre, O.; Browaeys, J.; Perzynski, R.; Bacri, J.-C.; Cabuil, V.; Rosensweig, R. E. Phys. Rev. E 1999, 59, 1736-1746. (36) Hayes, M. A.; Polson, N. A.; Garcia, A. A. Langmuir 2001, 17, 2866-2871. (37) Doyle P. S.; Bibette J.; Bancaud A.; Viovy J.-L. Science 2002, 295, 2237.

Figure 3. Schematic diagram of the MRS under a fluid flow and in an applied magnetic field: (a) static magnetic field; (b) oscillatory magnetic field at a phase where the field is close to maximum (indicated by the arrow and black dot on the right); (c) oscillatory magnetic field at a phase where the field is close to zero (indicated by the arrow and black dot on the right). While a compact and aggregated MRS is obtained in a static field, a more open MRS is obtained when using an alternating magnetic field.

the center of the air gap by the magnetic field gradient, forming a strongly agglomerated and compact MRS across the cross section of the microchannel, as schematically shown in Figure 3a; this compact structure causes a high flow resistance and reduced perfusion of the fluid flow through the MRS.9 A more open MRS can be obtained by use of an alternating magnetic field B ) B0 sin(2πft): the field-oriented and aggregated magnetic dipoles will tend to follow the changing magnetic field polarity. During this process, a viscous torque, arising from rotational friction of the structures in the suspending fluid, will act on the aggregates. To minimize the total viscous energy, the magnetic chains will break up in more open and smaller size structures, a process being more important at higher frequencies of the field. This process is consistent with the observed dynamics of magnetic chains in a rotating magnetic field, reported in refs 38 and 39. Figure 3b is a schematic diagram of the MRS under a flow and subjected to such alternating field at a phase where the field is close to maximum (as indicated by the arrow). (38) Melle, S.; Caldero´n, O. G.; Fuller, G. G.; Rubio, M. A. J. Colloid Interface Sci. 2002, 247, 200-209. (39) Vuppu, A. K.; Garcia, A. A.; Hayes, M. A. Langmuir 2003, 19, 8646-8653.

When the magnetic field strength decreases, the magnetic retention force weakens and the MRS eventually will be released from the air gap region by the viscous drag flow (see Figure 3c). We define Bv as the magnetic induction where the release starts and τ as the characteristic period in time during which the magnetic field strength |B| < |Bv| is insufficient to retain the MRS against the flow (see Figure 3c). For low frequencies, the MRS will be totally released by the flow and definitively lost from the air gap. However, when the frequency f or the amplitude B0 are high enough, the period τ will be sufficiently short that the MRS will move back and be retained in the air gap region. The result of this process will be an open MRS showing an oscillatory motion along the microchannel direction (y+-direction). Figure 4a is a photograph of the MRS retained within the magnetic gap in the absence of a flow, using a magnetic induction with amplitude B0 ) 50 mT and frequency f ) 20 Hz. Timerecorded video microscopy sequences of the MRS show clearly the dynamic character of the magnetic bead motion. To illustrate the effect of the rotation dynamics of the MRS on the fluid in the microchannel, a 2.1-µm-diameter fluorescent particle solution is injected. Figure 4b is a fluorescent photograph showing the Analytical Chemistry, Vol. 76, No. 21, November 1, 2004

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Figure 4. (a) Photograph of the MRS manipulated using a magnetic field of amplitude B0 ) 50 mT and a frequency f ) 20 Hz; (b) fluorescent microscopy photograph of a 2.1-µm fluorescent particle solution at the MRS-liquid interface, zooming in on the region indicated in (a); (c) zoom of the region of (b), showing the superposition of 30 video frames taken at 0.06-s time intervals. The trajectories of the fluorescent beads form a vortex rotating along the sense indicated by the arrows.

Figure 5. “Phase diagram” showing, for three frequencies of the sinusoidal magnetic field, the zones where the MRS is stable and retained at a given flow and amplitude of the magnetic field. The area underneath each of the curves represents the zone of a stable MRS retained within the gap.

fluorescent particles near the interface with the MRS. Video microscopy sequences show clearly the dynamic fluorescent particle motion. To trace the rotational motion of the fluorescent particles, we (numerically) zoom in on Figure 4b and superimpose in Figure 4c 30 video frames taken at 0.06-s time intervals. The trajectories of the fluorescent particles clearly form a kind a “vortex” rotating along the sense indicated by the arrows. Evidently, such motion will be highly beneficial for mixing and bead-based assay applications. The “liquid flow rate-magnetic field amplitude” phase diagram of stable MRS is shown in Figure 5 for three different frequencies. The linear curves are guides to the eye; the area below each curve is a parameter region where the MRS is stable and can be used for mixing or assaying applications. The data points fix the stability 6244

Analytical Chemistry, Vol. 76, No. 21, November 1, 2004

limits of the MRS and are obtained as follows: a liquid flow rate and large magnetic field amplitude are imposed to retain the MRS within the gap. While maintaining the flow, the field amplitude is slowly decreased until the MRS becomes unstable and is released from the gap region, which results in the data point for the given critical flow vc. The linear dependence of the critical flow on the magnetic field amplitude can be easily explained using the diagram on the right of Figure 3c. The MRS is released from the gap region, when the flow velocity exceeds vc ≈ ∆y/τ, with ∆y the distance along the channel where the field is localized. Developing the sinusoidal magnetic induction B ) B0 sin(2πft) in the time domain of small induction, one finds using the diagram of Figure 3c that B0πfτ ≈ Bv, giving vc ∝ B0f, in agreement with the data of Figure 5. It is important to point out that the MRS retention conditions derived from Figure 5 are valid for a MRS “plug length” in the y-direction of 200 µm. If the initial MRS length considerably exceeds the magnetic pole tip region (>200 µm), less magnetic force is available to completely retain such MRS. Mixing Experiments. A schematic diagram of the Y-shaped channel and the integrated magnetic parts is shown in Figure 6a. When fluorescein-containing and nonfluorescent water streams are introduced through the respective inlets of the Y-shaped microchannel, they form a typical laminar flow pattern before the mixing region, as shown in Figure 6b. This behavior is due to the low Reynolds number (Re ∼ 1):40 mixing between the two streams is possible by diffusion only. This process is slow and requires a long channel length to obtain fully developed mixing for the applied flow v ) 0.5 cm/s. The required mixing distance xm ≡ vl2/D, where D is the molecular diffusion constant and l ) 200 µm the microchannel width, can vary from 20 cm for fluorescein dye (D ≈ 10-5 cm2/s) to 2000 m for 1-µm-diameter particles (D ≈ 10-9 cm2/s).41 At the location of the MRS in the microchannel, the initial laminar flow pattern of the fluorescein dye will be strongly disturbed due to the high random porosity of the MRS and due to the angular momentum transfer of the magnetic beads to the liquid solution, as shown in Figure 6c. Panels d and e of Figure 6 show the fluorescent intensity of the flow after passing through the MRS, when using a sinusoidal and a square-shaped magnetic induction (f ) 5 Hz and B0 ) 30 mT), respectively. A clear difference in mixing performance is obtained between the two cases. Figure 7 shows the quantitative distribution of the fluorescent intensity over the channel width at a flow rate of 0.5 cm/s. Using eq 1, the mixing efficiency of the fluorescent distribution is zero before entering the MRS mixing area.42 When a sinusoidal magnetic field with amplitude of 30 mT and a frequency of 20 Hz is applied, a mixing efficiency of ∼80% is obtained; by reducing the frequency to 5 Hz, the mixing efficiency increases to 95%. However, when one uses a square-shaped magnetic field, we note (40) Re ) (vF l)/η, where we use as typical parameters v ) 0.5 cm/s for the flow velocity, F ) 1000 kg/m3 for the density, µ ) 10-3 kg/ms for the viscosity of water, and l ) 200 µm for the microchannel width. (41) For Brownian motion of particles of diameter dp in a liquid, D can be written as D ) kT/(6πηdp), where k is Boltzman constant and T is the absolute temperature of the fluid. See, for example, in: Incropera, F. P.; DeWitt, D. P. Fundamentals of heat and mass transfer, 4th ed.; John Wiley & Sons: New York, 1996. (42) For the integration limits of eq 1, we take 30 and 170 µm, respectively, to avoid the influence of optical diffraction effects at the channel edges.

Figure 6. (a) Schematic diagram of the microfluidic structure and the iron parts. The photographs (b-e) are taken at different locations and represent the fluorescent intensity over the channel; (b) is taken before the mixing region and shows the laminar flow pattern of parallel fluorescent and nonfluorescent streams; (c) is taken directly in the mixing region; (d) is after the mixing using a sinusoidal external field with f ) 20 Hz; (e) is after mixing using a square-shaped external field at f ) 5 Hz.

Figure 7. Profile of the fluorescent intensity of a fluorescein dye solution across the channel at a liquid flow rate of 0.5 cm/s and a magnetic field amplitude B0 ) 30 mT.

a reduction of the mixing efficiency to 70%. To understand the influence of the applied magnetic field on the mixing performance, one refers to the phase diagram of Figure 5. At a flow rate of 0.5 cm/s and a sinusoidal magnetic field with amplitude of 30 mT and frequency of 20 Hz, one is relatively far away from the MRS instability region and the MRS is relatively compact. At a frequency of 5 Hz, one approaches the instability line and the MRS evolves to a less rigid and more porous structure with an increase of the lateral relative motion of the magnetic entities with respect to the liquid flow. On the other hand, the MRS becomes more compact (reduction of the porosity) when a square-shaped magnetic field is applied, since the MRS remains tightly fixed within the gap region. Overall, the large obtained mixing efficiencies over a very short distance are indicative for the strong disturbance of the flow by the MRS, which can be understood from chaotic advectionlike effects. With a porous structure, one promotes the chaotic splitting of the fluid streams through the MRS network. An additional factor enhancing the mixing in a sinusoidal field is the rotation and lateral oscillation dynamics of the magnetic particles during the magnetic field alternation.43 Additional understanding of how the MRS behaves in an alternating magnetic field is obtained when mixing a solution of (43) Wilson, C. F.; Wallace, M. I.; Morishima, K. Simpson, G. J.; Zare, R. N. Anal. Chem. 2002, 74, 5099-5104.

fluorescent particles of 1.0-µm diameter. Such particles are much larger than the fluorescein dye, making transport through the porous MRS less evident. For this reason and in order to enhance the mixing efficiency, an initial plug length of the MRS of ∼400 µm is used. Retaining such relatively large MRS necessitates a larger magnetic field amplitude (100 mT) and frequency (20 Hz). Before entering the zone of the MRS network, a typical laminar flow pattern is observed (similar to the experiment of Figure 7). When a sinusoidal magnetic field is applied, a mixing efficiency of ∼96% is obtained. When switching to a square-shaped magnetic field, we note a reduction of the mixing efficiency to 40%, which indicates the difficulty for the 1-µm particles to pass through the agglomerated MRS and the increasing importance of flow channeling through the MRS. These fluorescent particle experiments clearly illustrate the importance of the porosity of the MRS and the possibility to control it in an advantageous way in our system. The efficient mixing of particles with large diameter demonstrates the large lateral mass transfer obtained by the heterogeneous and dynamic nature of the MRS. CONCLUSION We demonstrated the retention and manipulation of magnetorheological structures in a liquid flow microchannel by an alternating magnetic field. By varying the flow rate and the magnitude and frequency of the field, we determine the conditions at which the MRS is stable and magnetically retained within the microchannel and the fluid shows maximum perfusion through the MRS. The dynamic vortex-like motion of the MRS, induced by the alternating field, causes a rotational fluid flow by angular momentum transfer. The mixing is the result of the chaotic splitting of fluid streams through the dynamic and randomly porous structure of the MRS and the relative motion of magnetic particles with respect to the fluid. We demonstrate this concept using a plastic microchip with integrated soft ferromagnetic plate structures, which are part of an external electromagnetic circuit and which focus the magnetic field over the section of the microchannel. The efficient mixing (>90%) of particles having a diameter as large as 1 µm over very short distances (