We present a novel system for localized magnetic manipulation of magnetotactic bacteria in microfluidic systems. Where other methods require small conductive tracks directly below the sample, the new system consists of an array of permanent magnets switchable by a drive current to either trap or guide bacteria. This allows for much higher magnetic fields at reduced power consumption. Both a theoretical analysis and experimental analysis are presented. The system is scalable and is suited for integration in microfluidics

Abelmann, Leon

Altmeyer, Matthias

Hageman, Tijmen Antoon Geert

Manz, A

Pichel, M.P.

Pichel, Marc Philippe

English

University of Twente Research Information

AN INTEGRATED MAGNET ARRAY FOR TRAPPING AND MANIPULATION OFMAGNETOTACTIC BACTERIA IN MICROFLUIDICST.A.G. Hageman1, M.P. Pichel1, M.O. Altmeyer2, A. Manz1 and L. Abelmann1,21KIST Europe, Saarbrücken, Germany2University of Twente, Enschede, The NetherlandsAbstract — We present a novel system for localizedmagnetic manipulation of magnetotactic bacteria inmicrofluidic systems. Where other methods requiresmall conductive tracks directly below the sample,the new system consists of an array of permanentmagnets switchable by a drive current to eithertrap or guide bacteria. This allows for much highermagnetic fields at reduced power consumption. Botha theoretical analysis and experimental analysis arepresented. The system is scalable and is suited forintegration in microfluidics.Keywords: Permanent magnets, magnetic array,microfluidics, magnetotactic bacteriaI – IntroductionSince the discovery of magnetotactic bacteria (MTB)in 1975 [1] much research has been put into explo-ration of their properties. More recently people havestarted experimenting with utilizing these creatures asmicrobots by using external magnetic fields as steeringsignals [2, 3]. Most manipulation systems use globalfields generated by single or multiple coils or permanentmagnets. Only few works have described the generationof local magnetic fields on small scale, which allowlocal navigation and manipulation of MTB [4]. Thesemethods are based on fields generated by current car-rying wires in close proximity to the sample, requiringcooling to prevent thermal breakdown. [4]An alternative would be to use arrays of permanentmagnets which could be inserted directly next to aMTB-carrying channel in a microfluidic chip (seefigure 1). This array is able to switch between a ‘pass’state - allowing the bacteria to swim along the channel- and a ‘trap’ state - trapping the bacteria in clusters.Without external influence, the magnets will tend toalign along each others magnetization axis. Switchingto the other state can be achieved by generating amagnetic field by currents directly below the magnets.Jacobs and Bean [5] proved theoretically that rotatingall magnets in parallel requires more magnetic energythan rotating each subsequent pair in anti-paralleldirection, referred to as ‘fanning’. In this contibutionwe describe theoretical and experimental data about theproperties of such arrays.II – Theoretical analysisThe behavior of permanent magnet arrays can bestudied by calculating its magnetic energy, as the systemFigure 1: An integrated permanent magnet array in the ‘pass’state (top) and ‘trap’ state (bottom). The latter state will beused to form bacteria clusters.θφmBearthBI1 2 n-1 nFigure 2: Model of a chain of n permanent magnets withmagnetic dipole moment m fanning out with angle θ withrespect to the chain axis. The earth magnetic field Bearth andcurrent-generated field BI influence the stability of θ .will always fall back to a state with local minimumenergy. Figure 2 shows a model of an array with nmagnets with angle θ with respect to the array axis.They are modeled as magnetic dipoles with momentm. Background magnetic fields, such as the earth mag-netic field, are not insignificant in this system. Thesebackground fields are modelled by Bearth at an angleφ with respect to the array axis. Red arrows indicatethe direction of fields generated by currents via wirestructures underneath the magnets.The energy function as derived by Jacobs andBean [5] has been rewritten to SI units and has been ex-tended by including the magnetic energy of the switch-ing current. In total we consider the energy of the non-parallel (Ln) and parallel (Mn) magnets, the energy ofthe earth magnetic field (Bearth), and the energy cre-ated by the drive current (BI). The following function0 50 100 150 200 250 300 350−0.7−0.6−0.5−0.4−0.3−0.2−0.100.1θ [deg]Magnetic energy [µJ]  φ = 0oφ = 45oφ = 90oφ = 135oφ = 180oFigure 3: Effect of the angle φ of the earth magnetic field Bearthon the magnetic energy contained by the array as a functionof the magnet orientation θ .remains after omitting constant terms:Wn =−µ0m2n8πa3(Ln +3Mn)cos(2θ)−mBearth [n1 cos(φ −θ)+n2 cos(φ +θ)]−mnBI sin(θ)withLn =12 (n−1)< j≤12 (n+1)∑j=1n− (2 j−1)n(2 j−1)3Mn =12 (n−2)< j≤12 n∑j=1n−2 jn(2 j)3BI =µ04π2IrHere, µ0 is the permeability of vacuum, a is thespacing of the magnets and BI is the magnetic fieldstrength as a result of the switching current I at distancer from the wire.Using realistic values for the parameters and settingBI = 0, the influence of the earth magnetic field hasbeen studied. Figure 3 shows the magnetic energy ofthe array as a function of the orientation of the magnetsθ for several values of the angle of the earth magneticfield φ . A direct observation is the existence of onlytwo local minima, which are along the array axis, ofwhich the height but not the position is influenced bythe earth magnetic field. The trap state of the array is ameta-stable state only.Figure 4 shows the influence of drive current I on thesystem. The general trend, both for φ = 0◦ and φ = 90◦is the shift of the global minimum towards θ = 90◦ atincreasing current, the latter case migrating faster.III – Fabrication0 50 100 150 200 250 300 350−3−2−10123θ [deg]Magnetic energy [µJ]  I = 0AI = 0.5AI = 1AI = 1.5AFigure 4: Effect of drive current I on the magnetic energycontained by the array. Solid and dotted lines indicate respec-tively parallel and orthogonal alignment of the array axis withrespect to Bearth.Although intended for use in microfluidic chips, thebehavior of a magnet array has been studied in largerdimensions. For this purpose, four grade N45 NdFeBmagnets were spaced 10 mm apart by means of insertingthem in holes with diameter 1.7 mm drilled in 1.5 mmthick PCB material (see figure 5). They automaticallyalign along the array axis. Their magnetic force ofattracting nature increases the friction of the magnetswith their holder. The roughness of the hole will thus bean important factor in system behavior. The holder wasplaced on top of a second PCB containing copper leadsdirectly underneath the magnets. A current induces amagnetic field on the magnets in such a way that the po-larity of the current of subsequent magnets is reversed.For use in microfluidics, the distance between magnetsshould decrease. As a result, weaker magnets shouldbe use in order to keep the required drive current fromincreasing.Hole fabrication in microfluidic glass chips is lessstraightforward than in the current system. Severalof the options include powder-blasting and millingusing diamond tips. Figure 6 shows SEM images ofcross-sections of all mentioned methods. PCB drillingdelivers straight, vertical edges. Milling shows near-vertical edges, with V-shaped profiles at both ends,which is usable for the application. Powder-blastingshows a parabolic profile, which is problematic; if thebottom hole would be fit to the size of the magnets, itwould become relative easy for them to rotate acrosshorizontal axes.IV – Experimental DetailsDynamics of the array were analyzed by applyinga triangular-shaped current through the leads with anamplitude of 4 App at 0.1 Hz. A digital camera wasrecording the array from the top at 25 fps, while it wasmanually synchronized to the waveform by a LEDFigure 5: Top: trapping layer for magnet array. Bottom: Ac-tuation current tracks. Magnets are placed on the dot-shapedwire widenings.Figure 6: SEM images of magnet insertion holes by vari-ous fabrication methods. Top: general drilling through PCBmaterial. Middle: diamond-milling through glass. Bottom:Powderblasing through glass.signal in the video. The angle θ as a function of thecurrent of a single magnet in the array was analyzedoffline. Three waveforms were analyzed under bothparallel and orthogonal orientation of the array withrespect to the earth magnetic field in order to testreproducibility of the measured profile.V – Results and DiscussionA. Parallel to earth magnetic field−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−100−80−60−40−20020406080100I [A]θ [deg]  Loop 1Loop 2Loop 3TheoryFigure 7: Magnet orientation as a function of the drive currentduring parallel orientation of Bearth to the array axis. Differentgraphs represent multiple repetitions of the experiment.Figure 7 shows the array angle as a function ofthe applied current for the case where the array is inparallel alignment with the earth magnetic field. TheS-shaped curve approaches the assymptotes at 90◦ and−90◦ but needs currents in excess of 2 A to get close.This can be explained by the fact that at high angles themagnetic field generated by the current will be (almost)orthogonal to the magnets’ magnetic moment, losingmost of the potential torque. The measured curvesare near-saturated at 1.5 A and −1.5 A and matchthe theoretical curve. Hysteresis can be observed athigher currents (between −1.5 and −0.4 A and 0.5 and1 A). At lower currents it is below measurement noiselevels. This effect might be explained by non-linearCoulomb friction behavior. The results also prove thata continuous current is needed in order to maintain thedesired magnet orientation. Finally, it can be observedthat - although not completely overlapping - the curvesof multiple hysteresis iterations show a high similarityand can be considered reproducible.B. Orthogonal to earth magnetic fieldFigure 8 shows the array angle as a function ofthe applied current for the case where the array is inorthogonal alignment with the earth magnetic field. Theshape is completely different from the parallel situation,as assymptotic behavior is replaced by clipping of themagnet angle to −80◦ and 90◦, occuring at drivecurrents of −1.2 A and 0.8 A respectively. There isa horizontal offset of −50 mA as well. This non-symmetric behavior is likely caused by the influenceof the earth magnetic field, which has an orientationof 90◦. This does not fit with the theory, which can beexplained by the fact that the mathematical model onlysupports synchronous fanning, forcing the same angleon all magnets. In reality this constraint does not exist.The graph shows a much greater hysteresis effect than−2 −1 0 1 2−100−80−60−40−20020406080100I [A]θ [deg]  Loop 1Loop 2Loop 3TheoryOffset = −50 mAFigure 8: Magnet orientation as a function of the drive currentduring orthogonal orientation of Bearth to the array axis. Dif-ferent graphs represent multiple repetitions of the experiment.the parallel case. This effect at high angles might beexplained by the fact that the magnetic energy slope forthese currents is lower than in the parallel case, whichamplifies the effect of non-linear Coulomb friction(see figure 4). At low currents the slope is higher andshows a less strong hysteresis effect. In comparisonto the parallel situation, the currents to maintain themagnet orientation can be kept much lower as a resultof the hysteresis. Finally, repeated experiments showreproducible results.C. Evaluation of methodAlthough the theory and experiments show thatthe system can be utilized for the intended function,it has some significant drawbacks. First of all thereis a need for a continuous current in order to keepthe magnets aligned as desired. The use of elongatedmagnets could provide a more stable configuration forwhich less or no current is needed. By lowering theenergy level of the orthogonal state, for instance bymounting rigid magnets in proximity to the array, thisproblem can be circumvented. The system shows aclear sensitivity to the direction of the earth magneticfield. Orthogonal orientation is most suitable for theapplication due to guaranteed 90◦ switching and lowercontinuous currents. Magnetically shielding the systemcould decrease the influence of external fields. Finally,the system is scalable to smaller dimensions.VI – ConclusionsWe investigated the possibility to apply magneticfields to microfluidic chips using miniature cubic per-manent magnets of 1 mm3 on top a printed circuit boardwith current leads that can be used to rotate the magnets.A continuous current is needed to prevent the magnetsfrom falling back to aligned state, as mutual magneticforces drive the array to an aligned state. The currentneeded to switch the magnets from parallel alignmentalong the array axis towards orthogonal alignment isdependent on the direction of the background magneticfield.If the background magnetic field is aligned with thearray axis, asymptotic behavior can be observed, inwhich 1.5 A is needed for near-saturation of the angle at80◦. In case of orthogonal alignment of the backgroundmagnetic field with respect to the array axis, the switch-ing behavior becomes asymmetric, requiring −800 mAin one direction versus 1200 mA in the other direction(the latter never reaching 90◦ rotation). Furthermore,a drive current offset of −50 mA has been observed.These asymmetries are caused by the background mag-netic field.In both alignments a reproducible hysteresis effectcan be observed, which is more significant in the or-thogonal situation. We believe that this is caused bynon-linear Coulomb friction.Our theoretical model describes the angular orienta-tion of the magnet within measurements errors, but doesnot capture the hysteresis effect. The agreement in theorhogonal case is correct for low currents, but fails topredict the angle at higher current. For a more accu-rate prediction, non-linear friction and non-symmetricangles of the magnets with respect to the magnet arrayshould be included.These preliminary results show that miniature perma-nent magnets can succesfully be positioned by a simpleprinted circuit board using only single current leads. Inthis way one can easily generate strong local magneticfields in microfluidics chips to manipulate magneticobjects such as magnetic particles or microrobots.SEM images prove that powderblasting is anunsuitable method for creating holes in glass chipsdue to tapered edges. Glass milling provides a suitablealternative.VII – AcknowledgementsThe authors would like to thank Carsten Brill forSEM imaging and Kees Ma and Jukyung Park forproviding glass samples.References[1] R. Blakemore. Science, 190(4212):377–379, 1975.[2] S. Martel, C.C. Tremblay, S. Ngakeng, and G. Lan-glois. Applied Physics Letters, 89(23):–, 2006.[3] I. Khalil, M. Pichel, L. Abelmann, and S. Misra. In2013 IEEE International Conference on Roboticsand Automation, pages 5488–5493, 2013.[4] H. Lee, A. Purdon, V. Chu, and R. Westervelt. NanoLetters, 4(5):995–998, 2004.[5] I. Jacobs and C. Bean. Physical Review,100(4):1060–1067, 1955.

An integrated magnet array for trapping and manipulation of magnetotactic bacteria in microfluidics

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An integrated magnet array for trapping and manipulation of magnetotactic bacteria in microfluidics

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