Journal of Magnetism and Magnetic Materials

1 Magnetic particle mixing with Magnetic micro-convectionfor microfluidicsGuntars Kitenbergsa,b,c,n, Kaspars E rglisa, R gine Perzynskib,c, Andrejs C bersaaMMML Lab, Department of Theoretical Physics, University of Latvia, Ze u 8, LV-1002 R ga, LatviabSorbonne Universites, UPMC Univ Paris 06, UMR 8234, PHENIX, 4 place Jussieu, F-75005 Paris, FrancecCNRS, UMR 8234, PHENIX, 4 place Jussieu, F-75005 Paris, Francearticle infoArticle history:Received 30 June 2014 Received in revised form29 September 2014 Accepted 4 October 2014 Available online 18 October 2014 Keywords:MicrofluidicsMixingMagneticflui dFerrofluidMagnetic micro-convectionDiffusionabstractIn this paper we discuss the Magnetic micro-convection phenomenon as a tool for mixing enhancementin microfluidics systems in cases when one of the misciblefluids is a Magnetic particle colloid. A systemof a water-based magneticfluid and water is investigated experimentally under homogeneous magneticfield in a Hele Shaw cell.

2 Subsequent image analysis both qualitatively and quantitatively reveals thehigh enhancement of mixing efficiency provided by this method. The mixing efficiency dependence onthe magneticfield and the physical limits is discussed. A suitable model for a continuous-flow micro-fluidics setup for mixing with Magnetic micro-convection is also proposed and justified with an ex-periment. In addition, possible applications in improving the speed of ferrohydrodynamic sorting andmagnetic label or selected tracer mixing in lab on a chip systems are Elsevier All rights IntroductionOver the last 15 years thefield of microfluidics has con-tinuously advanced, providing an interesting framework for var-ious applications and scientific studies. As these systems typicallyhave a small Reynolds number, a lot of effort has been devoted toenhance mixing, which is otherwise limited by diffusion speed[1],causing long channel lengths. Mixers in microfluidics can be di-vided into passive and active, where the latter need an externalenergy supply[2].

3 A convenient energy source for active mixingsystems is an external magneticfield, as the energy can betransmitted to the microfluidics chip or cell without direct con-nectors. It is particularly interesting for systems with magneticparticles. Magneticfluid, being a colloidal dispersion of magneticparticles, can be used as a model system for future examples of Magnetic and non-magneticfluid mixing havealready been demonstrated[3,4]. Here we evaluate the possibleuse of the Magnetic micro-convection phenomenon for mixingapplications, applying the knowledge obtained in previous theo-retical and experimental studies[5,6].2. Theory, Materials and methodsMagnetic micro-convection,first described in 1980s[7],iscaused by a ponderomotive force of the non-homogeneous self-magneticfield of the magneticfluid. Above a certain magneticfield threshold, an instability forms on the Magnetic /non-magneticfluid interface. A characteristicfingering pattern results from themagnetic particleflow induced by the acting force, pushingmagnetic particles into the non- Magnetic liquid.

4 This force de-pends on particle concentration gradient, which decreases withmixing time as a result of the ongoing particle diffusion. Here wewill focus on the practical application of the Magnetic micro-convection, whereas more information on the fundamental as-pects can be found in our previous studies[5,6].Experimentally Magnetic micro-convection is tested in a Hele Shaw cell as a microfluidics model system. It is placed on a stagewith a coil system in an inverted microscope (Leica DMI3000B)with a 10 magnification (seeFig. 1). The coil system ( (1))consists of two identical coils that are 19 mm high and have innerand outer diameters of=d45 mminand=d57 mmout, respec-tively. Each coil has 200 turns of copper wire with a diameterd mm. Coils arefixed on both sides of a microscope stage(1 mm thick,Fig. 1(2)) so that their axes and the optical axis of themicroscope coincide. A current (up to 3 A)flowing through thecoils that are connected in series =R( )totcreates a 25 mm2large area with a homogeneous magneticfield inzdirection (up toContents lists available atScienceDirectjournal of Magnetism and Magnetic Elsevier All rights author at: MMML Lab, Department of Theoretical Physics, Uni-versity of Latvia, Ze u 8, LV-1002 R ga, E C bers).

5 Journal of Magnetism and Magnetic Materials 380 (2015) 227 230B 20 mT) where the center of the cell is placed. The cell ( (3))is made of two ParafilmMsspacers, cut in U shapes, that are putopposite to each other between two glass slides to form a rec-tangular cell leaving two outlets for air on the sides. Two metaltubes, glued in drilled holes in the upper glass slide, providetubing connections ( (4)) to a syringe pump. After assembly,glass slides with spacers are welded together on a hot plate (75 C,5 min), creating a cell with a 5 20 mm3size. The process isfilmed in the bright-field mode with a fast camera (MikrotronMC1363, maximum resolution 1280 1024 px). It is recording truecolor images atf 50 Hz and its white balance is calibrated for thetungsten halogen lamp used for illumination. Color images arelater converted to 8-bit grayscale images= +II( + )GBfor subsequent misciblefluids are water based magneticfluid ( (5))and distilled water ( (6)).

6 The magneticfluid is made byMassart's coprecipitation method[8]and results in maghemiteparticles that are stabilized with citrate ions and have a meandiameterd nm, saturation magnetization= kA/msatat=B1 Tsat, susceptibility = (SI units) in the range up toB 20 mT and volume fraction = (from magnetizationmeasurements).Bothfluids are slowly brought into contact inside the cellthrough the tubing connections by a syringe pump, while themagneticfield is already present. When droplets touch and aninterface is formed along they-axis, the pump is turned off,stopping theflow offluids. The Magnetic micro-convection is re-corded for further analysis in m2area ( (7)) with themicroscope camera, forming imagesIij(,)t, wheretis the time, andiandjdenote spatial indices with the total lengthN 360 px forbothxandyaxes (seeFig. 2(a)).To characterize a mixing system quantitatively, information onconcentration distribution is necessary.

7 As we use brightfieldmicroscopy and magneticfluid is absorbing light, wefind nor-malized concentration plotscij(,)tfrom imagesIij(,)tvia the Beer Lambert law (seeFig. 2(b))= cijIijIII(, )lg ( , ) lglg lg,(1)ttHOFFH O22whereIHO2andIFFare the intensities of initial water and magneticfluid concentrations, found in images att 0. A spatially averagedconcentration ci()tis then calculated from concentration data, tocharacterize concentration in the mixing direction along thex-axis(seeFig. 2(c)) ==ciNcij()1(, ).(2)tjNt1To quantify mixing dynamics, we define mixing efficiencyMt()effas follows:= = = Mtci c ici c i() 1(() ())(() ()),(3)NiNtNiNeff1121102wherec0and care theoretical concentration distributions beforemixing starts (t 0) and when mixing hasfinished ( t) (seeFig. 2(c)). Definition ofMeffis a slight variation of other measure-ments from the literature, mixing ratio[3]and percentagemixed[9], adjusted for better representation of the experiment involves an interface formation, which createsa slightly mixed state that differs from one time to another, due tothe experimental limitations instead of a theoretical step likeconcentration distributionc0.

8 We remove this influence by in-troducing a relative mixing efficiencyMt()rfor>tt0, which sub-tracts the mixing efficiency that has been made due to the inter-face formation. This valueMt()eff 0is taken at a manually chosentimet0, when it can be seen that the interface formation isfinished(typicallyt0 s)= Mt Mt Mt()()( ).(4)reffeff03. Results and discussionThe experiments are performed for various magneticfield va-lues. Snapshots of Magnetic micro-convection development atseveral time moments can be seen inFig. 3(a). Largerfield pro-vokes a faster evolution of the instability, enhancing mixing. Itbecomes more apparent, when one observes the spatially averagedconcentration ctdynamics, shown inFig. 3(b) contour plots. In thecase of diffusion (B 0), more than 2 s are needed for mixing tochange the initial concentrationsc0near the edges of mmfield of view, whereas for the largestfieldB mT ithappens in less than s.

9 Clearly, an increase in thefield strengthincreases the mixing development, although interface formationinfluence makes it less more quantitative result of the Magnetic micro-convectioninfluence can be seen inFig. 4(a), where relative mixing efficiencyMr(t) is shown for the magneticfield values. AchievedMrvaluesmight seem small, but it is important to remember its definition(Eqs.(3) and (4)) and the experimental cell, which is much largerthan the consideredfield of view ( mm2) and accordinglyhas two large basins of the original concentrations, making it verylong to reach completely mixed state. Overall, smallfields<B(7mT)seem to enhance mixing over diffusion only slightly,while further increase of magneticfield boosts mixing. This can beexplained byFig. 4(b), where relative mixing efficiency is plottedas a function of magneticfield squared for several time points in graph agree well with thefitted lines, implyingFig.

10 Setup consists of a coil system (1)fitted on a microscope stage(2). A Hele Shaw cell (3) with tubing connections forfluid introduction (4) isplaced in the center. A closer view of the cell displays how magneticfluid (5) andwater (6) droplets are brought to a contact in the center of the Hele Shaw is recording only the central part of the cell (7) where droplets of image analysis sequence forfinding concentration distribution.(a) Original imageI. (b) Concentration plotc, found via the Beer Lambert law (Eq.(1)). (c) Spatially averaged concentration ccalculated with Eq.(2)is marked withdots, while theoretical initial statec0andfinal mixed state care marked with solidand dashed Kitenbergs et al. / Journal of Magnetism and Magnetic Materials 380 (2015) 227 230228mixing efficiency to be square dependent on thefield. This result isconsistent with previousfindings of thefield dependence ofmagnetic micro-convection characteristics[6].