Wei Hang KohSchool of Mechanical and

Aerospace Engineering,

Nanyang Technological University,

639798, Singapore

e-mail: KOHW0041@ntu.edu.sg

Khoi Seng LokNational Institute of Education,

Nanyang Technological University,

639798, Singapore

e-mail: khoiseng@gmail.com

Nam-Trung Nguyen1

Professor

Fellow ASME

Queensland Micro- and

Nanotechnology Centre,

Griffith University,

Brisbane, 4111, Australia

e-mail: nam-trung.nguyen@griffith.edu.au

A Digital Micro MagnetofluidicPlatform For Lab-on-a-ChipApplicationsThis paper reports the design and investigation of a digital micro magnetofluidic platformfor lab-on-a-chip applications. The platform allows a ferrofluid droplet to be drivenalong a preprogrammed path. The platform consists of a programmable x-y-positioningstage, a permanent magnet and a glass plate coated with a thin layer of Teflon. First, theactuation of a stand-alone water-based ferrofluid droplet was investigated. Circular, rec-tangular, triangular and number-eight-shape trajectories were tested and analyzed. Thespeed of the droplet is evaluated from the position data of the black ferrofluid using a cus-tomized MATLAB program. The results show that better positioning accuracy and steadymovement can be achieved with smooth trajectories. Next, the ferrofluid droplet as thedriving engine for a cargo of other diamagnetic liquid droplets is demonstrated. Thecharacteristics of different cargo volumes are investigated. Due to the liquid/liquid cohe-sion, a large cargo of five times the volume of a 3-lL ferrofluid droplet can be trans-ported. If the cargo is larger than the driving ferrofluid droplet, the liquid system forms along trail that faithfully follows the preprogrammed path. Various mixing experimentswere carried out. The effectiveness of mixing in this system is demonstrated with a titra-tion test as well as a chemiluminescence assay. The platform shows a robust, simple andflexible concept for implementing a complex analysis protocol with multiple reactionsteps. [DOI: 10.1115/1.4023443]

1 Introduction

Digital microfluidics is a branch of the research field of micro-fluidics, where discrete liquid droplets are manipulated on a sur-face [1]. Continuous-flow microfluidics requires external pumpsor micropumps [2] to deliver the liquids. Continuous-flow droplet-based microfluidics confines samples and reagents in a singledroplet [3]. However, manipulation and delivery still requires thesame pumping system as in continuous-flow microfluidics. Con-ventional digital microfluidics relies on electrowetting for actua-tion and manipulation of the discrete droplets. Applicationsranging from proteomics to immunoassay [4] to clinical diagnos-tics [5] have been demonstrated. With electrowetting, the trans-port path of the actuated droplets and the available manipulationschemes depend on the number and the arrangement of the elec-trodes. Thus, a digital microfluidic lab-on-a-chip system based onelectrowetting can only serve a given application with little flexi-bility in protocol. A thermocapillary driven platform can also beused for digital microfluidics [6]. However, the operation on sucha platform is limited by the induced heat and the fixed integratedmicro heaters [7].

The problems associated with integrated electrodes and heaterscan be solved using magnetism, which represents a wirelessscheme for manipulating liquids in a microfluidic device.Recently, Nguyen [8] reviewed the field of micro magnetofluidicsutilizing the interactions between magnetism and fluid flow in themicroscale. Actuation and manipulation schemes are categorizedaccording to the type of the working fluids: electrically conduct-ing or magnetic fluids. A magnetic droplet is the best candidatefor digital micro magnetofluidics, because of the simplicity ofusing an external magnetic field for wireless control of the droplet.Ferrofluid can serve well this purpose. Ferrofluid is a colloidalsuspension of super paramagnetic nanoparticles. In the absence ofa magnetic field, the particles are not magnetic. Under an appliedmagnetic field, the particle is magnetized and the bulk fluid

behaves as a liquid magnet. Ferrofluid conventionally serves assealant in computer hard disk drives and also acts as a damper andcoolant in loudspeakers.

Egatz-Gomez et al. [9] used an external permanent magnet tomanipulate discrete liquid droplets on a superhydrophobic surface.Relatively large polydisperse paramagnetic particles with sizesranging from 0.2 to 4.0 lm were used. Pipper et al. [10] appliedthis driving concept to implement polymerize chain reaction(PCR) of deoxyribonucleic acid (DNA) in a single droplet. Longet al. [11] investigated this concept in details using relatively largeparamagnetic particles of varying particle concentrations, drivingspeeds and droplet sizes. The results show that the large magneticparticles can be extracted from the droplet at high speed andstrong magnetic field. This problem can be avoided if paramag-netic nanoparticles are used because the strong Brownian forcecan overcome the magnetic force to retain the particles in thedroplet.

Previously, our group has used ferrofluid for actuation on a pla-nar surface [12]. One-dimensional [13] and two-dimensional [14]manipulation of a discrete ferrofluid droplet was demonstratedusing an integrated microcoil array, which was fabricated on adouble sided printed circuit board. A pair of permanent magnetwas used to induce the magnetic moment in the ferrofluid. Only asmall magnetic field contributed by the coil was able to move theferrofluid droplet. Recently, we also investigated the behavior of asessile ferrofluid droplet on a hydrophilic surface in the presenceof a moving permanent magnet [15]. An operation map was estab-lished for the three key parameters: droplet size, the speed of themagnet, and the strength of the magnet. The ability to manipulatethe ferrofluid droplet on a surface with a contact angle less than90 deg gives us the confidence of using ferrofluid as the drivingengine for other diamagnetic liquid droplets.

In our previous preliminary work, the motion of the permanentmagnet was realized in an one-dimensional and linear mannerusing the translation stage of a commercial syringe pump. In thispaper, we report the development and test of a programmabletwo-dimensional actuation platform for digital micro magnetoflui-dics using a ferrofluid droplet as the driving engine. The platformnot only allows the manipulation of magnetic droplets but also

1Corresponding author.Manuscript received April 7, 2012; final manuscript received October 8, 2012;

published online March 19, 2013. Assoc. Editor: Kendra Sharp.

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diagmagnetic droplets; thus suitable for practical lab-on-a-chip(LOC) applications. First, the two-dimensional actuation of a sin-gle ferrofluid droplet was investigated. Next, the ability of the fer-rofluid droplet to work as an engine for different cargo sizes wasinvestigated. Subsequently, mixing of two diamagnetic dropletsusing a driving ferrofluid droplet was demonstrated. Finally, sim-ple chemical assays such titration using pH indicator phenol redand chemiluminescence reaction were demonstrated on theplatform.

2 Materials and Methods

The platform consists of a programmable Z-Y stage (T-LS28M,Zaber Technologies), a permanent magnet and a holder with aTeflon-coated glass plate. The programmable X-Y stage was pur-chased from Zaber Technologies consisting of two linear actua-tors. The actuators have each a maximum 28-mm travel range, abacklash of less than 4 lm, a maximum speed of 4 mm/s, a mini-mum speed of 0.93 lm=s. The stage can carry up to 10 kg, whichis not relevant in our application due to the small weight of thepermanent magnet. The X-Y stage can be programmed with C#and MICROSOFT.NET 3.5 on the ZABER CONSOLE software (ZaberTechnologies). The stage communicates with the computer overthe serial interface RS232. The path of the moving stage is deter-mined by a preprogrammed table of position values. Thus, anytrajectory and protocol can be implemented by providing the cor-responding position table. A permanent magnet (N703-RB,Eclipse Magnetics, United Kingdom) was mounted on the X-Ystage. A holder made of polymethyl methacrylate (PMMA) wasbuilt to hold the glass plate on top of the permanent magnet. TheX-Y stage is further mounted on a scissor lift to adjust the gapbetween the magnet and the ferrofluid droplet on the glass surface.The magnetic field strength at the ferrofluid droplet can thereforebe adjusted by varying this gap. Figure 1 shows the schematic ofthe experiment setup.

The planar surface of the platform was realized on a Pyrex glasswafer as reported previously [15]. The wafer was first cleanedwith a Piranha solution to remove all organic conterminants. Sub-

sequently, the glass wafer was treated with a solution of 1 wt%1H,1H,2H,2H-perfluorodecyltriethoxysilane (Sigma Aldrich) anda solution of isopropanol, 5 wt % water and a drop of 0.1 M HCl.The glass wafer was immersed in this solution for 30 seconds anddried at 110 �C for 15 mins. Teflon solution (DuPont AF1600,1 wt% in Fluorinert) was spin-coated on the treated glass wafer toform a thin layer of approximately 200 nm Teflon. The coatedglass wafer was then baked at 110 �C for 10 mins, 165 �C for5 min, and 330 �C for 15 mins. The 3 cm� 3 cm square glass slideof the platform was diced from the treated glass wafer. The glassslide fits well to the 2.8 cm� 2:8 cm working range of the X-Ystage.

Water-based ferrofluid (EMG508, Ferrotech, USA) was used inour experiments. The ferrofluid has a saturation flux density of6 mT, a dynamic viscosity at 27 �C of 5 mPa s, a density at 25 �Cof 1.07 g/cm3. The initial susceptibility of the ferrofluid is 0.24.The surface tension was measured at 25 deg as 31.7 mN/m. Withthese properties, the critical radius of the ferrofluid droplet is1.74 mm, below which the droplet can assume a spherical shape[15].

3 Results and Discussion

3.1 Stand-Alone Ferrofluid Droplet. The behavior of astand-alone sessile ferrofluid was previously investigated in detailpreviously [15], where the contact angle hysteresis and and theside-view shape of the droplet was observed and discussed. Onthe treated glass surface, a sessile ferrofluid droplet has an appa-rent static contact angle between 50 and 70 degrees depending onthe strength and type of the permanent magnet holding it. A mov-ing sessile droplet has advancing and receding contact angles ofapproximately 65 and 45 degree, respectively. The present workfocuses on the investigation of the two-dimensional droplet trajec-tories. The speed of the droplet was evaluated based on the top-view image captured by a CCD camera (Pulnix, progressive scancamera, JAI Inc., Japan). The camera software (Video Savant 3.0,IO Industries, Ontario, Canada) allows image recording at a pre-scribed frame rate. Using a customized MATLAB program, gray-scale images of the droplet were converted into a binary image.The position of the ferrofluid was subsequently evaluated as thecentroid of the droplet shape and through calibration convertedfrom pixel values to the actual value. Four different trajectorieswere preprogrammed for the test: circular, rectangular, triangularand number-8 shape.

Figure 2 compares the preprogrammed path with the actual tra-jectories of a 3-lL ferrofluid droplet. The results indicate that forcurved trajectories, x-component of the position shows discrep-ancy between actual trajectories and programmed paths. The rea-son could be the deformation of the droplet which affectscorresponding centroid used as droplet position in the image proc-essing program. Another feature of the droplet trajectories is thebehavior at the sharp corners. During the turn, the magnet sloweddown so the ferrofluid droplet was practically pinched on the sur-face of the glass plate. As the magnet maneuvered around the cor-ner, the droplet only deformed. This behavior is more apparentfrom the speed data depicted in Fig. 3.

Figure 3 depicts the two components of the droplet position asfunction of time. The speed of the droplet is derived from theposition data as

v ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDx2 þ Dy2

p=Dt (1)

where Dx and Dy are the differences of the position componentsof the droplet between two subsequent image frames and Dt is thetime between them. The spikes in the time history of the speedindicate the stick-and-slide behavior at some places on the path.This behavior is caused by the inhomogeneity of the surface. Fig-ures 3(a) and 3(b) show that the droplet was able to maintain a rel-atively constant velocity. The reduction of the speed to almost

Fig. 1 The experimental setup of the digital magnetofluidicplatform

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zero at the sharp corners can be seen clearly in Figs. 3(b) and 3(c).At the corners, the deformation of the pinched droplet was stilldetected as a motion of the droplet centroid. The test results of astand-alone ferrofluid droplet indicate that droplet should bedriven on a smooth trajectory to maintain a steady movement. Inthe subsequent experiments, the ferrofluid droplet was driven on acircular path of a diameter of 10 mm as depicted in Fig. 2(a).

3.2 Ferrofluid Droplet as Driving Engine. The previoussection demonstrates that the stand-alone ferrofluid droplet can bedriven by the permanent magnet and the X-Y stage along an

arbitrary path. In the next experiment, the ferrofluid droplet wasused as the driving engine for a diamagnetic droplet working asthe cargo. Since the ferrofluid is water-based, it can be used forany aqueous cargo. The following investigation with de-ionized(DI) water droplets was carried out to determine the maximumcargo volume that the ferrofluid engine can drive. While the vol-ume of the ferrofluid was fixed at 3 lL, the volume of the waterdroplet was varied from 3 lL to 18 lL. That means, the volume ofthe cargo was varied from the same to six fold of the volume ofthe driving ferrofluid droplet.

Figure 4(a) shows the tracked speed of the ferrofluid before andafter merging with cargo droplet of the same volume. The mergeddroplet appears black because the ferrofluid cover almost theentire bottom area. Since the black ferrofluid can be clearlydetected by the image processing software, the same algorithmused for the experiment of the previous section applied. Besidesthe few small speed peaks caused by the stick-and-slide behavior,there is a large velocity peak of the merging process. When theferrofluid droplet merged with the water droplet, the additionalcapillary force accelerated the ferrofluid droplet toward the waterdroplet causing the large speed peak. After merging, the ferrofluiddroplet literally moved through the stationary water droplet. Thehigher viscosity causes a decrease in the detected speed. Thesteady programmed speed was achieved after the merged dropletwas dragged along on the surface.

Figure 4(b) shows the time history of the merging process andtransport of a cargo droplet twice the volume of the ferrofluiddroplet. The larger volume leads to a higher pulling speed at themoment of coalescence. This pulling speed remained almost atthe same value as the cargo volume increases, Figs. 4(c)–4(f). Asthe volume of the merged droplet became larger, the inertial forcebecame more significant relative to the surface tension force, thefriction force and the magnetic driving force. Because of the iner-tia and the friction, the merged droplet took longer to reach thespeed of the magnet and the droplet deforms significantly duringthis process. The inserts in Figs. 4(b) to 4(e) show the typicalbehavior of the merged droplet before and after coalescence. Asthe ferrofluid followed the magnet and traveled inside the mergeddroplet, the droplet was still stationary but deformed. As the

Fig. 2 Preprogrammed paths and actual trajectories of a ses-sile ferrofluid droplet of 3-lL volume: (a) circular; (b) rectangu-lar; (c) triangular; (d) number-8 shape

Fig. 3 Corresponding position components and speed of the droplet as functions of time: (a)circular; (b) rectangular; (c) triangular; (d) number-8 shape

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ferrofluid reached the front end of the droplet and pulled it for-ward, the rear end was still pinched on the glass surface. The com-petition between pulling magnetic force and the pinchingcapillary force at the rear stretched the droplet, and caused it toelongate along the wetting path, e.g., the circular path. As the rearend final gave up and moved forward, the surface tension restoredthe droplet back to its steady-state form, which still had the curvedshape.

If the cargo was too large (six times volume of the ferrofluid) asshown Fig. 4(f), the pinching force became larger than the driving

magnetic force. The ferrofluid traveled through the large cargoand moved out of it. The merged droplet underwent deformationand stretching, but was not able to move. A small amount of mag-netic particles remained in the cargo as the ferrofluid droplet con-tinued to follow the magnet. The two speed peaks in Fig. 4(f)indicate the entrance and exit moments of the ferrofluid. As a ruleof thumb, the maximum cargo volume was taken as five times theferrofluid volume. Since the magnetic force is a volume-basedforce, this rule of thumb should be valid for ferrofluid dropletslarger than the volume of 3 lL tested here.

3.3 Ferrofluid Droplet Driven Mixing. Because the ferro-fluid droplet can work as a driving engine, mixing of two diamag-netic droplets can be realized inside the cargo. Mixing is achievedinside the droplet by shear-driven vortices, similar to the case ofcontinuous-flow droplet-based microfluidics [3]. The cargos in thenext experiment were a 9-lL DI-water droplet and a 3-lL dyedroplet. The droplet system was driven by a 3-lL ferrofluid. Fig-ure 5(c) shows the snapshots of the merging and mixing processes.The coalescence moments of the two cargo droplets are character-ized by the two speed peaks shown in Fig. 5(b). Evaluating thequality of mixing inside of the droplet was difficult because of thelow quality of the image and the changing, nonrectangular shapeof the droplet, and the nonlinear correlation between gray scale ofthe ink and its concentration. We selected a small interrogationwindow at the rear of the droplet, which is free of shadows andbright spots reflected from the light source, for mixing evaluation.The homogeneity of the greyscale was used as measure for themixing efficiency. First, the mean value of the gray scale �I of thewindow was determined. Next the standard deviation of the grayscale values in the interrogation window was evaluated

Fig. 4 Time history of the speed of a 3-lL ferrofluid working asthe engine for different cargo volumes (circular path with 10-mm diameter): (a) 3 lL; (b) 6 lL; (c) 9 lL; (d) 12 lL; (e) 15 lL; (f)18 lL

Fig. 5 Mixing of a 9-lL water droplet with 3-lL ink dropletdriven by a 3-lL ferrofluid droplet (circular path with 10-mm di-ameter): (a) snapshots of the mixing process; (b) time history ofthe tracked speed of the ferrofluid; (c) mixing index of the reararea of the merged droplet

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r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XN

i¼1

ðIi � �IÞ

vuut (2)

If the window is homogeneous, the value of the standard deviationwill be r ¼ 0. Thus the mixing efficiency is subsequently deter-mined as g ¼ 1� r. The mixing efficiency was evaluated for ev-ery recorded image. Before the final coalescence with the dyedroplet, the value of g was evaluated with the gray scale of thedye droplet only. The result is shown in Fig. 5(c). The mixing pro-cess triggered by the second coalescence (the second speed peakin Fig. 5(b)) can be observed as a drop in the value of mixing effi-ciency. This value increased as the liquids in the cargo mixedwhile the merged droplet moved along the programmed path.

To demonstrate mixing and reaction, a pH indicator phenolsul-fonphthalein (Sigma Aldrich) or phenol red (PR) was used. Thecolor of the indicator changes according to the pH level of an acidsolution or a base solution. In this experiment, a 10 lL ferrofluiddroplet was used as the driving engine. The ferrofluid droplet firstmerges with a 10 lL phenol red solution (0.05 wt% in water). Thecomposite droplet was then moved along a circular path to mixwith a 10 lL acid droplet (0.1 M HCl) or a 10 lL base droplet(0.1 M NaOH). The mixing and reaction process was recordedwith a color CCD camera (EO0413C, Edmund Optics).

The ferrofluid droplet, the PR droplet and the base droplet wereplaced on the perimeter of the preprogrammed circular path with10-mm diameter. The base droplet appears colorless, while thephenol red droplet is light yellow; after merging, the mixed solu-tion turned dark red (Fig. 6(a)). A similar experiment was carriedout with the acid (HCl) droplet and the PR droplet. Since the acidreacts with the indictor to give a light yellow color, it was almostimpossible to distinguish the contrast between the initial color ofPR with the final product (Fig. 6(b)). To test the effectiveness ofthe acid reaction, the final test was carried out by merging the PRdroplet with the base droplet, and subsequently to an acid to returnthe solution in the droplet to the neutral condition. As expected,the pH indicator first gave a dark red color after merging with thebase droplet. The resulting droplet was further driven to mergewith the acid droplet. The dark red color turned back to the bright

yellow color of the original pH indicator, Fig. 6(c). The titrationexperiment proves that the acid and base had reacted to form aneutral salt which has no effect on the pH indicator.

3.4 Scaling Analysis. The following scaling analysisassumes a compound droplet consisting of ferrofluid of volumeVff and cargo fluid of volume Vcargo. The analysis follows the sim-plified approach reported previously [15]. The driving magneticforce of the system is determined as

Fmag ¼Vffvl0

BrB ¼ aVff (3)

where v is the magnetic susceptibility of the ferrofluid, l0 is thepermittivity of free space and B is the magnetic field of the perma-nent magnet applied on the ferrofluid. If all other parameters areconstant and grouped in the factor a, the relationship between themagnetic force and the volume of the ferrofluid droplet is F / Vff .

The friction force against the sliding motion at a constant veloc-ity v of the permanent magnet is proportional the contact surfaceA. Assuming that the compound droplet is large enough so that ithas a shape of a puddle with a fixed height h [16]. The frictionforce can then be estimated as

Ffric ¼ KfAlv ¼ Kf

Vff þ Vcargo

hlv ¼ bðVff þ VcargoÞv (4)

where Kf is the friction factor, l is the apparent viscosity of thedroplet liquids. Factor b groups all constant parameters of theabove equation.

The diameter of the compound droplet is generally proportionalto the cube root of its volume ðVff þ VcargoÞ1=3

. However, from theexperimental data, a large droplet elongates so that the width w ofthe moving droplet remains almost constant. The capillary forceagainst the motion can be estimated as [16]

Fcap ¼ wrðcos hr � cos haÞ (5)

where r is the surface tension of the compound droplet, ha and hr

are the advancing and receding contact angles, respectively. To

Fig. 6 Titration experiment on the digital magnetofluidic platform driven by a 10-lL ferrofluid droplet (circular path with 10-mm diameter): (a) 10 lL 0.1 M NaOHdroplet and 10 lL PR droplet; (b) 10 lL 0.1 M HCl droplet and 10 lL PR droplet; (c)10 lL 0.1 M NaOH droplet, 10 lL 0.1 M HCl droplet and 10 lL PR droplet

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simplify the scaling analysis, a constant width w ¼ const: and aconstant capillary force Fcap ¼ const: are assumed.

The inertial force acting on the compound droplet is

Finer ¼ ðqffVff þ qcargoVcargoÞdv

dt(6)

where qff and qcargo are the density of the ferrofluid and the cargofluid, respectively.

The force balance for a moving compound droplet is

Fmag ¼ Ffric þ Fcap þ Finer (7)

From our previous investigations on a single sessile ferrofluiddroplet [15], the force components are of the same order of magni-tudes. For a ferrofluid droplet with a diameter of 1 mm and asteady speed of 1 mm/s, the estimated values for a and b are3 lN/mm3 and 2 lNs/mm2, respectively [15]. With the assump-tion of a constant capillary force Fcap and a steady motion of thecompound droplet (dv=dt ¼ 0), the force balance simplifies to

aVff ¼ bðVff þ VcargoÞvþ Fcap (8)

Rearranging the above equation for the velocity of the permanentmagnet leads to the critical magnet speed above which the dropletcannot move

vcr ¼1

bðr þ 1Þ a� Fcap

Vff

� �(9)

where r ¼ Vcargo=Vff is the volume ratio between the cargo andthe ferrofluid. The above relationship shows that for a large cargoto ferrofluid ratio r, the magnet speed v should be reduced. At afixed ratio r, a large ferrofluid volume allows a higher magnetspeed. However, to keep the term a� Fcap=Vff

� �� �positive, the

ferrofluid volume should be larger than a critical valueVff;cr ¼ Fcap=a. That means, the ferrofluid volume and the corre-sponding driving magnetic force should be large enough to over-come the capillary force.

Rearranging Eq. (8) for the critical volume ratio between cargoand engine leads to

rcr ¼1

bva� Fcap

Vff

� �� 1 (10)

This relationship indicates that a high magnet speed would limitthe volume of cargo, while a large ferrofluid volume allows alarger cargo to be transported. In the experiment depicted inFig. 4, the critical volume ratio for the fixed ferrofluid volume ofVff ¼ 3 lL is rcr � 5

4 Conclusions

In this paper, we demonstrated that a ferrofluid droplet can beflexibly manipulated on a planar surface by a permanent magnet.The driven droplet is able to maintain a steady speed if the path isdesigned as smooth curves. The ferrofluid worked as an engine topick up diamagnetic droplets and transported them as cargo alonga preprogrammed path. The internal flow caused by the movingbottom wall, the flow of the ferrofluid and the shear-driven vorti-ces in the droplet allowed rapid mixing. The work reported in thispaper started with the development of a programmable two-dimensional system for an arbitrary path. To test mixing ability onthe platform, liquid droplets were driven and merged by the ferro-fluid droplet. The suitability of the platform for chemical reactionswas then investigated using acid/base titration with a pH indicator.The results reported in this paper show that the simplicity androbustness of this digital micro magnetofluidic platform wouldallow the implementation of complex chemical and biochemical

protocols for point-of-care applications. The dynamics of the in-ternal flow, the distribution of the ferrofluid and the chaotic advec-tion inside the composite droplet are interesting topics for futureinvestigations. The simplified scaling analysis presented in thispaper allows identifying key operation parameters of the platform.More detailed parametric investigation would need a complexthree-dimensional model that considers all the forces involved.

Nomenclature

A ¼ contact surfaceB ¼ magnetic flux density

Fmag ¼ magnetic forceFfric ¼ friction forceFcap ¼ capillary forceFiner ¼ inertial force

h ¼ height of the dropletr ¼ volume ratio between cargo and ferrofluid engine

rcr ¼ critical volume ratiot ¼ time

Vff ¼ volume of the ferrofluid dropletVcargo ¼ volume of the diamagnetic cargo

v ¼ velocity of the permanent magnetvcr ¼ critical velocity of the permanent magnetw ¼ width of the droplet perpendicular to the motion

directionx; y ¼ position of the dropletKf ¼ friction factora ¼ proportional factor for magnetic forceb ¼ proportional factor for friction forcel ¼ apparent viscosity of the compound dropletha ¼ advancing contact anglehr ¼ receding contact angler ¼ surface tension of the compound droplet

References[1] Fair, R. B., 2007, “Digital Microfluidics: Is a True Lab-on-a-Chip Possible?,”

Microfluid. Nanofluid., 3(3), pp. 245–281.[2] Truong, T. Q., and Nguyen, N. T., 2004, “A Polymeric Piezoelectric Micro-

pump Based on Lamination Technology,” J. Micromech. Microeng., 14(4), pp.632–638.

[3] Song, H., Chen, D. L., and Ismagilov, R. F., 2006, “Reactions in Droplets inMicrofluidic Channels,” Angew. Chem., Int. Ed., 45(44), pp. 7336–7356.

[4] Jebrail, M. J., and Wheeler, A. R., 2010, “Let’s Get Digital: Digitizing Chemi-cal Biology With Microfluidics,” Curr. Opin. Chem. Biol., 14(5), pp. 574–581.

[5] Pollack, M. G., Pamula, V. K., Srinivasan, V., and Eckhardt, A. E., 2011,“Applications of Electrowetting Based Digital Microfluidics in Clinical Diag-nostics,” Expert Review of Molecular Diagnostics, 11(4), pp. 393–407.

[6] Nguyen, N., and Huang, X., 2005, “Thermocapillary Effect of a Liquid Plug inTransient Temperature Fields,” Jpn. J. Appl. Phys., 44(2), pp. 1139–1142.

[7] Jiao, Z., Huang, X., Nguyen, N. T., and Abgrall, P., 2008, “ThermocapillaryActuation of Droplet in a Planar Microchannel,” Microfluid. Nanofluid., 5(2),pp. 205–214.

[8] Nguyen, N. T., 2012, “Micro-Magnetofluidics: Interactions Between Magne-tism and Fluid Flow on the Microscale,” Microfluid. Nanofluid., 12(1–4), pp.1–16.

[9] Egatz-Gomez, A., Melle, S., Garcıa, A. A., Lindsay, S. A., Marquez, M., Domı-nguez-Garcıa, P., Rubio, M. A., Picraux, S. T., Taraci, J. L., Clement, T., Yang,D., Hayes, M. A., and Gust, D., 2006, “Discrete Magnetic Microfluidics,” Appl.Phys. Lett., 89(3), p. 034106.

[10] Pipper, J., Inoue, M., Ng, L. F., Neuzil, P., Zhang, Y., and Novak, L., 2007,“Catching Bird Flu in a Droplet,” Nat. Med., 13(10), pp. 1259–1263.

[11] Long, Z., Shetty, A. M., Solomon, M. J., and Larson, R. G., 2009,“Fundamentals of Magnet-Actuated Droplet Manipulation on an Open Hydro-phobic Surface,” Lab. Chip, 9(11), pp. 1567–1575.

[12] Nguyen, N. T., Beyzavi, A., Ng, K. M., and Huang, X., 2007, “Kinematics andDeformation of Ferrofluid Droplets Under Magnetic Actuation,” Microfluid.Nanofluid., 3(5), pp. 571–579.

[13] Beyzavi, A., and Nguyen, N. T., 2009, “One-Dimensional Actuation of a Ferro-fluid Droplet by Planar Microcoils,” J. Phys. D, 42(1), p. 015004.

[14] Beyzavi, A., and Nguyen, N. T., 2010, “Programmable Two-DimensionalActuation of Ferrofluid Droplet Using Planar Microcoils,” Micromech. Micro-eng., 20(1), p. 015018.

[15] Nguyen, N. T., Zhu, G., Chua, Y., Phan, V., and Tan, S., 2010,“Magnetowetting and Sliding Motion of a Sessile Ferrofluid Droplet in thePresence of a Permanent Magnet,” Langmuir, 26(15), pp. 12553–12559.

[16] Berthier, J., 2008, Microdrops and Digital Microfluidics, William AndrewPub., Norwich, NY.

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