mass transport improvement in microscale using diluted ...€¦ · eld was analysed for different...

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PAPER

Mass transport im

aQueensland Micro- and Nanotechnology

Australia. E-mail: nam-trung.nguyen@griffitbSchool of Mechanical and Aerospace Engine

Singapore

Cite this: RSC Adv., 2016, 6, 62439

Received 5th May 2016Accepted 22nd June 2016

DOI: 10.1039/c6ra11703a

www.rsc.org/advances

This journal is © The Royal Society of C

provement in microscale usingdiluted ferrofluid and a non-uniform magnetic field

Majid Hejazian,a Dinh-Tuan Phanb and Nam-Trung Nguyen*a

This paper demonstrates that a non-uniform magnetic field and diluted ferrofluid can improve mass

transport of non-magnetic solutes in a microfluidic device. A hydrodynamic flow-focusing configuration

was employed to test this hypothesis. The system consists of a core stream and two sheath streams. The

core stream contains a diluted ferrofluid and a fluorescent dye. Without a magnetic field, both magnetic

nanoparticles of the ferrofluid and the fluorescent dye in the core stream rely on molecular diffusion to

spread transversally. The susceptibility mismatch between the core and focusing fluids results in

a magnetoconvective secondary flow and subsequently the mass transport of the non-magnetic

fluorescent dye. We observed a significant enhancement in mass transport of the fluorescent dye. The

platform presented here could be used as a microfluidics-based gradient generator or micromixer.

1. Introduction

Over the last two decades, microuidics has proven to bea technology that provides highly effective tools for biologicaland chemical research.1,2 This technology has been exploited fordesigning a diverse range of uid handling devices in themicroscale such as micropumps,3 microvalves,4 micromixers,5

and microseparators.6,7 Micro gradient generator and micro-mixer are the two typical microuidic devices that rely oneffective mass transport in the microscale, but are currentlylimited to molecular diffusion due to the predominant laminarow in this size scale.

Recently, microuidics-based concentration gradientgenerators8 have been used for cell migration studies. Aconcentration gradient generator is capable of creatinga gradient of biochemical signals such as growth factors,hormones and chemokines.9 Pressure-driven gradient gener-ator is one of the most common types in continuous-owmicrouidics, where mass transport is governed by molec-ular diffusion and convection through a network of micro-channels. Lung cancer chemotherapy resistance, for instance,has been studied using this device.10 An integrated micro-uidic device having an upstream gradient network anddownstream cell culture chambers was used for this purpose.Other type of gradient generators relies solely on moleculardiffusion. An example of this type is a device for bacterialchemotaxis analysis, the movement of cells in a channelinduced by the cells chemotactic response.11 The diffusion of

Center, Griffith University, QLD 4111,

h.edu.au

ering, Nanyang Technological University,

hemistry 2016

a chemical through a porous membrane adjacent to thechannel wall formed a static linear chemical gradient in themicrochannel.

Micromixers are other microuidic devices that play animportant role for biological and chemical research. Micro-mixers can be categorised in passive and active groups.5 Passivemicromixers solely rely on diffusion or chaotic advection formixing, while active micromixers take advantage of an externalenergy eld, such as temperature, magnetic eld, electric eldand acoustic eld. Parallel lamination micromixers are a type ofpassive micromixers that has been exploited to study diffusivemixing in microchannels. Wu et al. developed a analyticalmodel and used a diluted uorescent dye to evaluate theconcentration distribution across a microchannel width.12 Theauthors further examined analytically and experimentallydiffusive mixing in hydrodynamic ow-focusing congurationwith three uid streams.13 The concentration was measuredusing recorded images of a uorescent dye, while the velocitydistribution was determined with micro particle image veloc-imetry (micro-PIV).

Active mixing employs externally induced disturbance toimprove mass transport. For instance, magnetouidic micro-mixers utilize a magnetic eld and magnetic particles sus-pended in a uid to enhance mass transport throughmagnetophoresis, the migration of magnetic particles. Wanget al. investigated numerically a magnetouidic micromixerusing magnetic beads for uid agitation.14 Tsai et al. and Fuet al. used a permanent magnet and ferrouid, a liquid witha suspension of magnetic nanoparticles, to improve theperformance of a Y-mixer.15,16 The non-uniform magnetic eldre-distributes the magnetic nanoparticles in the microchanneland consequently induces magnetoconvective ow. Mixingefficiency between water and ferrouid can be higher than

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Fig. 1 (a) Schematic of the setup with a microchannel and a set ofpermanent magnets. (b) Characterisation of magnetic field. The insetshows the setup used for magnetic field measurement. The distancewas adjusted using the linear stage of a syringe pump (x* ¼ 2x/W, y* ¼

RSC Advances Paper

90%, which is signicant compared to the value of below 15%for pure molecular diffusion in the same microchannel. Azimiet al. utilised ferrouid and a stationary magnetic eld toenhance mixing in an Y-micromixer.17 The mixing efficiencycan reach up to 70% with an optimal concentration ofmagnetic nanoparticles. Mao et al. reported the design andsimulation micro-mixer utilizing paramagnetic ferrouid.18

Using a low-voltage excitation, the device could achievesignicant improvement in mass transport and consequentlycomplete mixing within seconds. Wen et al. reported an AC-driven electromagnet for mixing ferrouid and Rhodamine Bin a micro device.19 The magnetic eld causes the ferrouid toexpand into the non-magnetic ow. The mixing efficiency of95% was achieved within 2.0 s. Zhu et al. investigated themixing phenomena in a circular chamber using ferrouid andunder a uniform magnetic eld.20 Full mixing was achieved ata relatively low magnetic ux density up to 10 mT as a result ofsusceptibility mismatch between the paramagnetic ferrouidand non-magnetic sheath ow. Wen et al. reported mixing offerrouid and deionized (DI) water was using an electro-magnet driven by DC or AC power to induce transient inter-active ows.21 The magnetic force results in a body force thatcauses the ferrouid to move into the non-magnetic ow.Extremely ne nger structures along the direction of localmagnetic eld lines at the interface were observed and veriedboth numerically and experimentally. Our group previouslyexploited an uniform magnetic eld and the susceptibilitygradient between a diamagnetic uid and a ferrouid toinduce mixing in a circular chamber.22,23 The gradient ofmagnetic susceptibility led to instability at the liquid–liquidinterface and consequent mixing. In a recent work, wedemonstrated that even without the existence of a magneticsusceptibility gradient, mixing could be achieved with a non-uniform magnetic eld.24 The eld of a permanent magnetinduces a body force on the ferrouid inside the chamber,resulting in a secondary ow called magnetoconvection. Themagnetoconvective transport was traced by both uorescentdye and non-magnetic particles.

As discussed above, mixing of ferrouid and water has beenreported, but mass transfer enhancement for other non-magnetic species such as uorescent dye through magneticeld have not been studied and reported before. In the presentwork, we employed permanent magnets in a simple hydrody-namic focusing device to create a non-uniform magnetic eld.The transport process of the uorescent dye was evaluatedbased on the recorded uorescent images. The concentrationeld was analysed for different ow rates to compare therelative signicance of hydrodynamic transport and thesecondary magnetoconvective transport induced by themagnetic eld. A numerical study was also carried out tosimulate the concentration eld and velocity eld in theabsence of magnetic eld. Magnetically induced mass transferwas observed and discussed based on our experimentalresults. The enhancement in mass transfer is benchmarked bythe convective/diffusive ow-focusing system that relies onmolecular diffusion only.

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2. Materials and methods

Fig. 1(a) shows the schematic of the hydrodynamic focusingdevice. The microchannel has a depth of H ¼ 50 mm, a width ofW ¼ 500 mm, and a length of L ¼ 12 mm. The device wasfabricated in polydimethylsiloxane (PDMS) using the standardso lithography technique. Detailed information about thefabrication procedure can be summarized as follows.25,26 First,photoresist SU-8 with a thickness of 50 mm was coated evenlyand patterned on a Si wafer by a standard photolithographyprocess. A mixture of Sylgard 184 base and a curing agent (DowCorning Inc.) at 10 : 1 ratio by weight was poured onto the SU-8mould and subsequently degassed for one hour in a vacuumchamber. A 2 hour baking at 80 �C in the oven followed.Subsequently, the top PDMS layer was peeled off from the SU-8mould and the 1 mm access holes were punched. The PDMSmicrochannel was bonded to another at PDMS base with thehelp of oxygen plasma treatment and underwent another post-baking process at 80 �C for 10 minutes to enhance the bondingstrength.

Three precision syringe pumps (SPM100, SIMTech Micro-uidics Foundry) delivered the uids into the microuidicdevice. The whole setup was placed on an inverted microscope(Nikon Eclipse TS 100) equipped with a high-speed camera(Photron 120K-M2) for visualization. The commercial water-based ferrouid (EMG707, Ferrotec) containing 2% vol.magnetic nanoparticles, was used to make a diluted para-magnetic solution for the core stream. For this purpose, 0.05 gof uorescein sodium salt (acid yellow, Sigma-Aldrich Co.) wasdissolved in 20 mL of DI-water. Then the commercial ferrouidwas diluted with the uorescent dye and DI-water solution to

2y/W).

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Paper RSC Advances

20% vol. Three identical 3.2 mm3 neodymium–iron–boron(NdFeB) permanent magnets (B222, K&J Magnetics Inc.)provided the magnetic eld for this experiment. DI-water servedas the liquid in both sheath streams. The experiments werecarried out with a constant ow rate ratio, for three differentow rates (30 : 2.5 : 30, 60 : 5 : 60, 120 : 10 : 120 mL min�1). Themagnetic eld of the permanent magnets was measured andcalibrated using a gauss meter (Hirst Magnetic InstrumentsLtd). Fig. 1(b) shows the measured magnetic ux density asa function of the distance from the edge of the magnet. Thedistance between themagnets to channel wall was 1mm. Acrossthe microchannel width, the magnetic ux density drops fromapproximately 250 mT to 175 mT.

Fig. 2 Simulation results: (a) velocity field; (b) concentration distri-bution at the lower flow rate of 30 : 2.5 : 30 mL min�1, and D ¼ 1 �10�9 m2 s�1.

3. Numerical simulation

We used diffusive/convective transport as the reference for themagnetoconvective/convective transport that is characterizedlater experimentally. A numerical model with COMSOL (COM-SOL Inc., USA) simulated the diffusive/convective transport inthe ow-focusing conguration to predict the distribution ofuorescent dye in the microchannel, Fig. 1(a). The two-dimensional model consists of three inlets, a straight rectan-gular channel and one outlet. Because of the low aspect ratiobetween channel height and channel width, the velocity isaveraged in the z-axis. All streams were considered as incom-pressible. Steady-state conditions were applied. The modelsolves the continuity equation:

V(rfuf) ¼ 0 (1)

and the Navier–Stokes equation:

Vh� pfI þ mf

�Vuf þ

�Vuf�T�i� 12

muf

H2¼ 0 (2)

where uf is the uid velocity, pf the pressure (Pa), V()T thedivergence operator, V() the gradient operator, I the identitymatrix, mf the uid dynamic viscosity (Pa s), and H is the heightof the channel.

The normal inow velocities are set for the three inlets, noslip conditions were considered at the walls, and pressure hasno viscous stress at the outlet. Using single phase model, thedensity of the ferrouid is calculated by:27

rf ¼ (1 � 4)rwater + 4rnp (3)

where rnp and 4 are the density of nanoparticles and volumefraction, respectively. The effective dynamic viscosity of theferrouid is estimated as:28

mf ¼ mwater

1

ð1þ 4Þ0:25!

(4)

Diffusive/convective transport of a solute is obtained bysolving:

�V(�DVc + cu) ¼ 0 (5)

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where c (mol m�3) is the concentration, and D (m2 s�1) is thediffusion coefficient of the solute. The concentrations for themiddle inlet and the sheath inlets were set to 4 mol m�3 and0 mol m�3 respectively. For the numerical solution of the aboveequations, nite element discretization was based on secondorder functions for velocity, while the pressure and concentra-tion elds are described by linear basis functions. We used thene mesh consisting of 64 324 domain elements and 1976boundary elements. As mentioned above, the two-dimensional(2D) model considers the depth-averaged velocity. The numer-ical simulation was carried out for three ow rates at a xedratio as used in the later experiments. Fig. 2 shows the repre-sentative results for ow eld and concentration eld.

4. Results and discussion

The experiments were carried out for a constant ow rate ratiobetween the sheath and core streams but different total owrates, to vary the strength of convective transport. Diluted fer-rouid mixed with uorescent dye serves as the uid of the corestream. DI-water works as the sheath uids sandwiching thecore stream in the microchannel. Our aim is to investigate thetransport and spreading of the core ow in response to themagnetic eld. Without a magnetic eld, the width of the coreow (measured as the width between the maximum concen-tration gradients) is expected to remain constant, as the owrates and the viscosity determine this width only. We also aim toevaluate the effect of magnets on the mass transport of theuorescent dye. A relatively high concentration of diluted fer-rouid, 20% vol., was selected to observe the phenomenonthoroughly: the expansion of the ferrouid stream, movementtoward themagnet and then accumulation of the ferrouid nearthe magnet. Lower concentrations of the ferrouid could notcreate high enough magnetic susceptibility mismatch tomanifest this effect. Six images were taken at different locationsalong the channel: x ¼ 0, 4, 5.75, 7.5, 10, 12 mm. The magnetswere located between x ¼ 4 mm to x ¼ 7.5 mm. We normalisedthe length scale by half of the channel width W/2 (x* ¼ 2x/W, y*

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Fig. 3 Simulation results: concentration profiles along the channel forall flow rates: low flow rate (blue), medium flow rate (green), and highflow rate (red).

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¼ 2y/W). Half channel width W/2 was used as the characteristiclength because we later use the location y*¼ 0 as the centre lineof the microchannel. The negative space (y* < 0) is next to themagnet and exposed to the eld of the permanent magnets.

Fig. 3 shows the simulated concentration distribution atlocations along the channel length for different ow rates asused later in the experiments. Without a magnet, the concen-tration has its maximum value at the centre line of the channel(y* ¼ 0). The proles for different ow rates are almost over-lapping because the ow rate ratio was kept constant. A diffu-sion coefficient of D ¼ 1 � 10�9 m2 s�1 was used in oursimulation.29

We also carried out a calibration of uorescent intensity, tounderstand the light-blocking role of magnetic nanoparticleson the uorescent intensity. The intensity calibration correctsthe intensity value and converts it into the dimensionlessconcentration c* of the uorescent dye. Three streamscomprising DI-water mixed with uorescein dye, ferrouidmixed with uorescein dye, and ferrouid are fed into the

Fig. 4 The calibration results: normalized intensity versus y*. Theinserted image is the one used for the evaluation of intensity at x* ¼ 0.

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microchannel with identical ow rates. Fig. 4 depicts thenormalized intensity across the channel width. Fig. 4 shows thatthe ratio between the intensity of ferrouid/uorescent dye toDI-water/uorescent dye mixture is around 0.55.

Fig. 5 compares the experimental results at x* ¼ 40 and atthe lower ow rate of 2.5 mL min�1 and 30 mL min�1 for the coreand sheath ows, respectively. In the absence of a magneticeld, experimental and numerical data agree relatively well. Inthe presence of a magnetic eld, substantial transport of uo-rescent dye toward the magnets was observed. The masstransport of uorescent dye was obviously enhanced in thepresence of the permanent magnets. The magnetic nano-particles move towards the magnets as result of the suscepti-bility mismatch between the sheath ows and the core streammagnetic susceptibility gradient lead to a body force that causesthe so-called magnetoconvective secondary ow. This secondaryow transports along the dye molecules, which are too small tobe affected by negative magnetophoresis effect.

Next, we evaluated the uorescent intensity across thechannel width, to examine the extent of the transport of uo-rescent dye. Fig. 6 shows the normalised intensity distributionof all positions along the x* axis for the three different total owrates mentioned above. The results consistently show that thedye molecules moved toward the permanent magnet, and fol-lowed the same path of the magnetic nanoparticles. At low andmedium total ow rates, the dye reached and accumulated atthe top channel wall (y* ¼ �1). As the total ow rate increases,the pressure-driven hydrodynamic ow competes withmagnetically driven secondary ow, and the intensity gradientbecomes steeper. At the higher ow rate, the uorescent dyecould not reach the top channel wall.

Fig. 6 also indicates that the magnetic eld has no effect onthe concentration distribution of the dye at the inlet (x* ¼ 0).The distribution of the uorescent dye is similar to thatnumerically simulated and previously reported.12 The masstransport of the dye in the channel width direction relies onmolecular diffusion only. The saddle shape on top of theintensity proles at x*¼ 0, is the result of the different diffusioncoefficients of uorescent dye and magnetic nanoparticles.30

The smaller dye molecules, having a larger diffusion coefficient,migrate more into the sheath streams of DI-water, while

Fig. 5 A comparison between simulation and experimental results forthe lower flow rate of 30 : 2.5 : 30 mLmin�1,D¼ 1� 10�9 m2 s�1 and atx* ¼ 40.

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Fig. 6 Normalized intensity versus y* axis for six x* positions along thechannel (x* ¼ 0: blue, x* ¼ 16: green, x* ¼ 23: red, x* ¼ 30: cyan, x* ¼40: purple) and three flow different flow rates: (a) 30-2.5-30; (b) 60-5-60; (c) 120-10-120.

Fig. 7 Evaluation of the width of the core stream: (a) the width isevaluated as the distance between the gradient peak to the centreline(y* ¼ 0); (b) spreading width at y* > 0 along the channel; (c) spreadingwidth at y* < 0 along the channel. Low flow rate: red, medium flowrate: blue, high flow rate: green.

Paper RSC Advances

magnetic nanoparticles with a diffusion coefficient of D ¼ 4.29� 10�11 m2 s�1, three orders of magnitude smaller then that ofuorescent dye do not diffuse signicantly. As a result, thecentre of the core stream appears darker than its border.

A further interesting phenomenon could be observed fromthe intensity proles in Fig. 6. As the maximum intensity isexpected at the channel inlet, where species in the core streamhave not diffused into the sheath steams. However, at x* ¼ 16(medium ow rate) and x*¼ 16, 23 (high ow rate), the intensitypeak exceeds the maximum intensity of the inlet, and movesaway from the magnets. This phenomenon could be explainedby the migration of the dark iron oxide nanoparticles toward themagnets due to positive magnetophoresis. The migrationdilutes the ferrouid at the positions in the proximity of theinterface between the core and the sheath streams. Conse-quently, the remaining uorescent dye appears to be brighterwithout the light-blocking magnetic nanoparticles.

At positions near the outlet, two intensity peaks can beobserved. The lower one at y* > 0 represents a more

This journal is © The Royal Society of Chemistry 2016

concentrated uorescein line at the interface. The differencebetween diffusion coefficients of uorescent dye and magneticnanoparticles at the inlet and the absence of blocking magneticnanoparticles created this bright line. As more magneticnanoparticles moved toward the permanent magnet in down-stream locations (x* ¼ 16, 23, 30), this peak appears to move tothe le and approaches y* ¼ 0.

The second peak on the le side (y* < 0) is higher comparedto the right peaks. This peak appears next to the wall on the sideof the magnets. As mentioned above, uorescent dye is trans-ported toward the magnet by magnetoconvective secondary owand accumulates on the channel wall. The spread of uorescentdye on the le side (y* < 0) conrms that magnetoconvectivetransport induced by the magnetic eld is the dominant masstransfer mechanism in this ow conguration. Fluorescent dyedoes not spread to the right side (y* > 0), due to the insignicantmolecular diffusion relative to the pressure-driven convectivetransport.

We further evaluated the spreading width of the core stream.Fig. 7(a) describes how the spreading width is determined from

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RSC Advances Paper

the maximum intensity gradients at the interface between coreand sheath streams. Fig. 7(b) plots the width a at y* > 0 alongthe channel length x*. Fig. 7(c) shows the width b at y* < 0 alongthe channel length x*. Fig. 7(c) indicates that at the lower owrate the spreading width for the le part (y* < 0) quickly reachesthe value of the half width W/2. As the ow rate increases, thespreading width b decreases, as the pressure-driven hydrody-namic ow dominates over the magnetoconvective ow.

5. Conclusions

We used a ow focusing system with three streams to investi-gate the mass transport of uorescein dye in a microchannelusing diluted ferrouid and an external non-uniform magneticeld. The sheath streams were non-magnetic DI water, while thecore stream was diluted ferrouid. Fluorescein dye was dis-solved in the core stream to trace the mass transport of thesecondary magnetoconvective ow. Various phenomena wereinvolved in the transport process of the uorescent dye: mag-netoconvective secondary ow due to the magnetic suscepti-bility difference, molecular diffusion, and pressure-drivenhydrodynamic ow. The susceptibility gradient of the uidtogether with the magnetic eld of the permanent magnetcauses a bulk force acing on the uid and consequently themagnetoconvective ow. As shown in our experiments, thetransport process of uorescent dye caused by magneto-convective secondary ow is comparable to that of the pressure-driven hydrodynamic ow and signicantly higher thanmolecular diffusion. The signicance of the observedphenomenon is that transport of a non-magnetic sampletransversal to the main pressure-driven ow could be improvedby orders of magnitude using permanent magnets and dilutedferrouid. The observed phenomenon has potential applica-tions in designing more efficient micro-mixers or gradientgenerators.

Acknowledgements

The authors acknowledge the Australian Research CouncilLinkage grant LP150100153 to NTN and the international PhDscholarship to MH. This work was performed in part at theQueensland Node of the Australian National FabricationFacility, a company established under the National Collabora-tive Research Infrastructure Strategy to provide nano andmicro-fabrication facilities for Australia's researchers.

Notes and references

1 N. T. Nguyen and S. T. Wereley, Fundamentals andApplications of Microuidics, Artech House, Boston, 2002.

2 M. Hejazian, W. Li and N.-T. Nguyen, Lab Chip, 2015, 15, 959.3 D. J. Laser and J. G. Santiago, J. Micromech. Microeng., 2004,14, R35–R64.

4 K. A. Au, H. Lai, B. R. Utela and A. Folch, Micromachines,2011, 2, 179–220.

62444 | RSC Adv., 2016, 6, 62439–62444

5 N.-T. Nguyen and Z. Wu, J. Micromech. Microeng., 2005, R1–R16.

6 N. Pamme, Lab Chip, 2007, 7, 644–1659.7 Y. Chen, P. Li, P.-H. Huang, Y. Xie, J. D. Mai, L. Wang,N.-T. Nguyen and T. J. Huang, Lab Chip, 2014, 14, 626–645.

8 A. G. G. Toh, Z. P. Wang, C. Yang and N. T. Nguyen,Microuid. Nanouid., 2014, 16, 1–18.

9 S. Kim, H. J. Kimz and N. L. Jeon, Integr. Biol., 2010, 2, 584–603.

10 W. Siyana, Y. Feng, Z. Lichuan, W. Jiarui, W. Yingyan, J. Li,L. Bingcheng and W. Qi, J. Pharm. Biomed. Anal., 2009, 49,806–810.

11 J. Diao, L. Young, S. Kim, E. A. Fogarty, S. M. Heilman,P. Zhou, M. L. Shuler, M. Wu and M. P. DeLisa, Lab Chip,2006, 6, 381–388.

12 Z. Wu, N.-T. Nguyen and X. Huang, J. Micromech. Microeng.,2004, 14, 604–611.

13 Z. Wu and N.-T. Nguyen, Sens. Actuators, B, 2005, 107, 965–974.

14 Y. Wang, J. Zhe, B. T. F. Chung and P. Dutta, Microuid.Nanouid., 2008, 4, 375–389.

15 T.-H. Tsai, D.-S. Liou, L.-S. Kuo and P.-H. Chen, Sens.Actuators, A, 2009, 153, 267–273.

16 L. M. Fu, C. H. Tsai, K. P. Leong and C. Y. Wen, 12thInternational Conference on Magnetic Fluids, PhysicsProcedia, 2010, vol. 9, pp. 270–273.

17 N. Azimi, M. Rahimi and N. Abdollahi, Chem. Eng. Process.,2015, 97, 12–22.

18 L. Mao and H. Koser, Int. Conf. Solid-State Sensor. Actuat.Microsyst., 2007, pp. 10–14.

19 C. Y. Wen, C. P. Yeh, C. H. Tsai and L. M. Fu, Electrophoresis,2009, 30, 4179–4186.

20 G. P. Zhu and N. T. Nguyen, Lab Chip, 2012, 12, 4772–4780.21 C. Y. Wen, K. P. Liang, H. Chen and L. M. Fu, Electrophoresis,

2011, 32, 3268–3276.22 G.-P. Zhu, M. Hejiazan, X. Huang and N.-T. Nguyen, Lab

Chip, 2014, 14, 4609–4615.23 G.-P. Zhu and N.-T. Nguyen, Microuid. Nanouid., 2012, 13,

655–663.24 M. Hejazian and N.-T. Nguyen, Lab Chip, 2015, 15, 2998–

3005.25 C. Song, N. T. Nguyen, S. H. Tan and A. K. Asundi, Lab Chip,

2009, 9, 1178–1184.26 D.-T. Phan, C. Yang and N.-T. Nguyen, RSC Adv., 2015, 5,

44336–44341.27 M. K. Moraveji and M. Hejazian, Numer. Heat Transfer, Part

A, 2014, 66, 315–329.28 M. K. Moraveji and M. Hejazian, Int. Commun. Heat Mass

Transfer, 2013, 44, 135–146.29 C. T. Culbertson, S. C. Jacobson and J. M. Ramsey, Talanta,

2002, 56, 365–373.30 F. R. Ismagilov, A. D. Stroock, P. J. A. Kenis, G. Whitesides

and H. A. Stone, Appl. Phys. Lett., 2000, 76, 2376–2378.

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