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Chemical Engineering and Processing 71 (2013) 77– 82

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

jo ur nal homepage: www.elsev ier .com/ locate /cep

iant effective liquid-self diffusion in stagnant liquids by magneticanomixing

ouya Hajiani, Faïc al Larachi ∗

hemical Engineering Department, Laval University, Québec G1V 0A6, Canada

r t i c l e i n f o

rticle history:vailable online 8 February 2013

eywords:agnetic nanoparticleniform rotating magnetic fieldixing

a b s t r a c t

Many chemical engineering applications require tools to intensify processes in regions where Fickianmolecular diffusion is the dominant mechanism, such as in boundary layers, microporous catalysts ormicrofluidics. We demonstrate in this study that spinning magnetic nanoparticles (MNPs) by means ofrotating magnetic fields (RMFs) gives rise to an intriguing nanomotion mechanism capable of triggeringgiant diffusion in stagnant liquids and thus able to stimulate transport beyond the molecular diffusionbarrier especially in stagnant liquids. To evidence this mechanism, we report original water self-diffusion

elf-diffusion coefficientcoefficients measured in aqueous media containing very low concentrations of ferrite MNPs that can berotated in uniform RMF. The self-diffusion coefficient of distilled water (i.e., D0 ≈ 3.5 × 10−9 m2/s) wasenhanced up to 200 times by application of a rotating magnetic field in stagnant-liquid conditions. It wasconcluded that in absence of macroscopic convective flows, MNPs may prove to be efficient nanostirrersto enhance liquid transport properties at nanoscale. By delivering giant diffusion around them, rotatingMNPs can constitute an appealing nanomixing process intensification tool.

. Introduction

Molecular transport and diffusion in liquids play a key role inany different contexts of physics, chemistry, biology and chemical

ngineering [1,2]. Quite recently, an emerging trend in science andngineering attempts to enhance liquid phase transport operationssing seeded nanoparticles, beyond what can be accomplished inhe classical diffusion paradigm [2]. For example, it has been statedhat the presence of nanoparticles in liquids (so-called nanoflu-ds) may modify heat [3–5] and mass transport [6–14] propertiesf the medium. Most prominently, magnetic nanoparticles (MNPs)ave been applied in a few studies to direct mass transfer, both

n absence [8,15] and in presence [7,16] of an external magneticeld. Although, the general effect of nanoparticles on liquid trans-ort properties is still anomalous [17], the method of excitingNPs seeding liquids with a time-varying external magnetic field

eems to be a promising approach to achieve process intensifica-ion. A related magnetic field assisted nanomixing is the basis ofhe present work as a stable suspension of single-domain MNPsre externally modulated by means of a uniform rotating magnetic

eld (uRMF).

Briefly, external magnetic fields exert magnetic torque on theagnetic moment of MNPs suspended in liquids thus forcing MNP

∗ Corresponding author.E-mail address: faical.larachi@gch.ulaval.ca (F. Larachi).

255-2701/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.cep.2013.01.014

© 2013 Elsevier B.V. All rights reserved.

to orient to be aligned with magnetic field direction [18]. Forthose MNPs whose magnetic moment is locked in the solid crys-tal structure (so-called rigid-dipole MNPs), magnetic torque is feltbodily and associated momentum is transferable to the adjacentliquid phase [18]. In purely hydrostatic conditions, this magneticbody torque is opposed only by Brownian collisions from the sol-vent molecules as suspensions are at rest [18]. Interestingly, thenature of mechanical interactions between magnetically excitedMNPs and the bulk of liquid depends on the characteristics ofapplied magnetic field. For instance, a time-varying magnetic fieldsuch as uRMF exerts an angular torque on MNPs forcing themto gyrate versus the contiguous liquid. Note that, while chang-ing direction continuously at any point of the domain, uRMF hasconstant field intensity over time. In their quest to catch-up withuRMF direction, the suspended rdMNPs spin in a direction primar-ily imposed by RMF [18]. The goal of this work is to investigatethe effect of these spinning MNPs on liquid self-diffusion coeffi-cient. As the main result, we observed that this technique triggersa giant enhancement of liquid self-diffusion, exceeding its fieldfield-free diffusivity by more than two orders of magnitude. More-over, magnetic field intensity (H0), field frequency (f) and MNPconcentration (�) were found to influence the extent of diffusionenhancement.

The current approach stands out from other magnetic mixingprocesses (which rely on applying magnetic Kelvin force and arerestricted to the boundary of magnetic and nonmagnetic fluids[19]) as it is versatile and can be used in magnetically homogenous

7 ineering and Processing 71 (2013) 77– 82

omf

2

2

(aema(cfrd

Table 1Magnetic properties of EMG 705 from magnetometry measurement.

Saturation magnetization, Ms (kA/m) 18.7

Ft

8 P. Hajiani, F. Larachi / Chemical Eng

r inhomogeneous liquid media. Also, those systems that induceagnetic mixing in electrolytic media [20–23] are very different

rom ours.

. Experimental

.1. Colloidal suspension

Dilute concentrations of ferrite (Fe3O4) MNPs (� = 0.001–0.01v/v) magnetic content) dispersed in water were prepared from

commercial ferrofluid, EMG705 (FerroTec). The magnetic prop-rties of EMG 705 were measured by an alternating gradientagnetometer, MicroMag model 2900 (Princeton Instrument Co.)

t 298 K in low-field (for initial susceptibility, �0) and high-fieldfor saturation magnetization, Ms) asymptote of magnetization

urve. Using these values, particle core diameter was estimatedollowing a method proposed by Chantrell [24]. Table 1 summa-izes the magnetic properties of EMG-705 ferrofluid. Particle sizeistribution of dilute ferrofluid with different concentrations was

ig. 1. (a) Top and side view of the magnet with diffusion cell embedded inside with cell cohree-phase magnet energized by a three-phase power supply. (c) Diffusion cell with two

Initial susceptibility, �0 2.9MNP volume fraction, � (v/v) 0.042Estimated median magnetic core diameter, dp (nm) 16.0

measured via magnetometry. The results assured us of no clusteror chain formation during the course of experiments.

2.2. Magnet

To generate uRMF, a tubular two-pole and three-phase (5.5-cmhigh and 4.5-cm i.d. cylindrical bore) magnet has been designedand built in collaboration with MotionTech LLC and Winding Inc.

(Fig. 1a). The magnet has the capacity to provide both uniform andnon-uniform magnetic fields at moderate strength (<50 mT) at thebore center with up to 3 A three-phase currents. Since RMF emergesfrom superposition of three oscillating magnetic fields that are 120◦

ntaining MNP suspension. (b) Diffusion cell subject to uRMF generated by two-pole sets of electrical conductivity sensors.

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P. Hajiani, F. Larachi / Chemical Eng

ut of phase, the coils are fed by three balanced AC currents from aariable frequency drive (ABB, ACS150, 2.2 kW Variable Frequencyerive) as illustrated in Fig. 1a and b. Both magnetic field strengthnd frequency can be controlled directly by means of this powerupply. The temperature of the magnet solid part is controlled by aater cooling jacket that encompasses the outer shell of the stator

nd filled with a coolant circulated in and out from a constant-emperature thermostated bath (Lauda, Model RKT20).

.3. Diffusion measurement

A simplified conductimetric method originally proposed byeaist [25–28] was employed in this study to estimate self-diffusionoefficients of liquids loaded with MNPs with and without uRMF.

he conductimetric cell consists of a short capillary tube sealedt both ends and fitted with two pairs of miniature electrodes ashown in Fig. 1c. The glass capillary had 1 mm inner diameter and0 mm length (L). Platinum wire electrodes, 0.7 mm in diameter

5

5.5

6

6.5

0 20 0 40 0 60 0 t (m

Titre du graph NO MAGN

Nor

mal

ized

conc

entra

tion

Electr(up str

Electrode(do wnstrea

D0,calc = 3.5×10-9 m2

f = 0 HzH0 = 0 kA/mφ = 0.00 4

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0 1 2 3 4 t

Nor

mal

ized

con

cent

ratio

n (C

1, C

2)

Dcalc = 6.

f = 100 HzH0 = 31 .4 kA/mπ = 0.01

a

b

ig. 2. Electrode responses of a conductivity cell, with and without uRMF nanomixing

d = 1 mm) and tracked at two positions, 5 and 35 mm down the injection point by two sepresent the time evolution of tracer conductivity as detected by upstream and downstrender uRMF, � = 0.01, H0 = 31.4 kA/m, f = 100 Hz.

g and Processing 71 (2013) 77– 82 79

were sealed with epoxy glue into horizontal holes drilled at L/6 and5L/6 accurately from one end [29]. The electrodes were connectedto the conductivity meter (Omega CDTX-90) which generates asignal in mV, reflecting the electrical conductivity of the fluidin between each electrode pair. We employed (NaCl solution)electrolyte at low concentration (i.e., 0.05 M) mixed with diluteferrofluids as a tracer. By virtue of Kohlrausch’s law when electricconductances are relatively small, the transient behavior of thesignal intensities is a linear function of electrolyte concentration inthe liquid (Fig. 2a and b). The conductivity cell has been calibratedfor several tracer concentrations. The calibration curve showsthat the electrical conductivity has linear dependency versus NaClcontent in the low tracer concentration range. Great care wasexercised in the preparation of the tracer solutions so that after

dilution the MNP concentration in the tracer must be identical tothat of the ferrofluids provided in the cell. This manner preventedmagnetic Kelvin force [18] interference resulting from magneticsusceptibility discontinuities at the moment of injecting the tracer

800 100 0 120 0 140 0in)

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y = -0.001 x + 0.308 7R² = 0.992 7

-1

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0600 80 0 100 0 120 0 140 0

Ln (C

-C)

Time (min)

ETIC FIELD

ode Iea m)

II m)

/s

5 6 7 8 9(min)

65×10-7 m2/s

y = -0.6867 x + 3.255 9R² = 0.996 7

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0

0.5

1

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3 4 5 6 7

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stimulation. Minute volume of tracer is injected upstream into the capillary tubeets of electrodes measuring cross-sectional average electrical conductivity. Trendsam electrodes (a) magnetic field disabled, � = 0.004 and (b) magnetic field enabled

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nto the capillary. The applied voltage on the electrodes is tunedo be less than 1 V to avoid heating the suspension.

Before each run, the diffusion chamber was rinsed carefully,oaked and then overfilled with the MNP suspension. A thin filmf high-vacuum nonmagnetic grease (silicone grease, Dow Corning12) was applied around the outer edges of the capillary. The dif-

usion chamber was then sealed by two microscope slides pressednto the capillary edges. After filling and sealing the cell, it was sett the middle height of the magnet and the desired magnetic fieldas applied. Only after reaching thermal equilibrium, which was

ecognized after detecting a constant conductivity signal, the celleceived a tracer injection. A small volume of tracer (i.e., 0.5 �L)as injected into the cell gradually to minimize convection. D can

e evaluated by least squares analysis of the slope of the conduc-ance difference between upstream and downstream probe pairslotted against time according to the expression [30]:

= −(

L

�

)2 ddt

ln[C1 − C2] (1)

here C1 and C2 stand for the first and second conductance mea-ured at time t and corrected by the ratio of cell constant (Fig. 2and b). This conductimetric cell was used to determine distilledater self-diffusion coefficient in ambient conditions (atmosphericressure and 298 K). We measured D = 2.1 × 10−9 m2/s which com-ared within 5% with the reference self-diffusion coefficient valuef water (2.2 × 10−9 m2/s) reported in the literature [31]. Also, thepparent self-diffusivity variations in presence of excited MNPsnder different magnetic field intensities and frequencies werexamined to assess their influence on liquid molecular transport.

. Result and discussion

Fig. 2 presents conductimetric responses to the tracer injec-

ion with and without rotating magnetic field. It is clearly evidenthat magnetically-excited spinning of MNPs generate nano-mixingn capillaries as demonstrated by the dramatic attenuation ofesponse time relative to that in magnetic-field-free test.

ig. 3. Schematic diagram of MNPs spin in hydrostatic conditions with and without uRMrownian thermal agitation; MNP time-average spin vector (ω) is equal to zero since MRMF (H0), MNP spin vector (ω) turns normal to H0 and hence lateral mixing occurs in al

g and Processing 71 (2013) 77– 82

Since the average MNP particle–particle distance is severaltimes longer than the MNP diameter (e.g., dp–p ∼ 95 nm for� = 0.0025) [18], particle mutual interactions may be neglected[32,33] and the mixing phenomenon can be interpreted as result-ing from the individual particle behavior under magnetic field.Fig. 3a shows schematically the motion of MNPs in the absence ofexternal magnetic field while their diffusional translation and dif-fusional rotation is due to random collisions of solvent molecules(i.e., Brownian motion). Accordingly, the particle spin vector (ω,the ensemble-average of single particle spin) is equal to zero andMNP magnetic moments (m) are randomized in all directions due tothermal agitation. Enabling uRMF yields strong enough a magnetictorque, (�0m × H, H is magnetic field and �0 is vacuum perme-ability) on individual MNPs to overcome Brownian agitation. Thus,MNPs undergo rotational reorientation which forces them to spinperpendicular to H0 (Fig. 3b). Consequently, spinning MNPs dissi-pate kinetic energy in the cell prompting effective mixing in theliquid spheroids enclosing each MNP. It is the stimulated motion ofliquid molecule in these spheroids that is thought to generate giantself-diffusion in the liquid.

To gain more insights into this nanomixing mechanism, we havefurther investigated the relationship of D to H0 (0–35 kA/m), �(0–0.01) and f (0–200 Hz). D/D0 is plotted as a function of H0, fand � in Fig. 4 where D0 refers to suspension self-diffusion coeffi-cient at H0 = 0 (Fig. 4a and b) or � = 0 in Fig. 4c. In logarithmic scale,D/D0 increases almost linearly with H0 (Fig. 4a) echoing sensitivityof effective mixing on magnetic torque. Moreover, D/D0 increasesversus frequency, and then plateaus (Fig. 4b) after nearly all magne-tized nanoparticles synchronize with the rotation of a sufficientlystrong H0. One interpretation for the plateauing effect would bethat there must be a threshold in rotational speed of MNPs (ca.ω = 50 Hz in Fig. 4b) in which MNP solid-body faster rotation maynot proportionally transfer more hydrodynamic torque to the adja-

cent solvent. Such rupture may occur because at this threshold, theboundary condition on MNP surface may change from no-slip to slipcondition [34]. Fig. 4c illustrates the pronounced effect of concen-tration of nanostirrers on the enhancement factor. This observation

F (a) in absence of magnetic field, MNPs gyration and translation is solely due toNP magnetic moments (m) are randomized in all directions and (b) in presence ofl directions along capillary.

P. Hajiani, F. Larachi / Chemical Engineerin

1

10

100

1000

0 5 10 15 20 25 30 35

Enh

ancm

ent F

acto

r ( D

/D0)

H 0(kA/m)

φ = 0.0025f = 100 Hz

95% Co nfid ence interval

1

10

100

1000

1 10 100 1000

Enh

ancm

ent F

acto

r ( D

/D0)

f (Hz)

φ = 0.002 5H0 = 31.4 kA /m

95% Co nfid ence interval

a

b

c

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1

Enh

ancm

ent F

acto

r (D

/D0)

φ×10-2

f = 100 HzH0 = 31.4 kA /m

95% Confid enc e interval

Fig. 4. Diffusion enhancement factor under uRMF versus (a) magnetic field strength,(c

itdcd

[8] S. Komati, A.K. Suresh, Anomalous enhancement of interphase transport rates

b) magnetic field frequency and (c) MNP concentration. D0 is liquid self-diffusionoefficient without magnetic field.

ndicates that at low MNP concentration, at least a part of massransport over some distance between the spinning MNPs is still

ominated by molecular diffusion only. Increasing the MNP con-entration shrinks the length scale of the domains where moleculariffusion is the only dominant transport mechanism.

g and Processing 71 (2013) 77– 82 81

It is worthy to mention that the mixing mechanism investi-gated in this study occurs within a single-phase homogeneous diluteferrofluid. As such, it is different from mixing of ferrofluids withnonmagnetic liquids under the effect of a time-varying magneticfield [19]. A distinguishable feature of this latter system is thatit is the Kelvin magnetic force that drives mixing due to MNPconcentration gradients. Accordingly, the mixing phenomenonper se vanishes once uniform MNP concentration throughout thesuspension is achieved. In contrast, the nanomixing mechanismhighlighted in our study is not tied to magnetic-force mixing effectsand occurs regardless of whether MNP concentration gradientsexist or not.

4. Conclusion

Although there have been several studies on the effect ofnanoparticles on liquid transport properties of nanofluids, the pos-sibility of using magnetically-excited MNPs to stimulated mixingand diffusion in a still-liquid medium that serve as nanomixingdevices has so far not received enough attention. Thus, we per-formed self-diffusion coefficient measurements in a capillary staticcell to identify in which manner interactions between excited MNPsunder uRMF and solvent molecules may affect apparent transportproperties of the mixture. We note that even at low MNP concentra-tion (e.g., � = 0.0025), moderate uRMF strength (e.g., �0H < 50 mT)and ultra-low frequency (e.g., f < 200 Hz), the liquid self-diffusioncoefficient can be intensified up to two-orders of magnitude. MNPexcitation at distance combined with intrinsic magnetic field pen-etrability into nonmagnetic materials has the potential to openup a range of process intensification strategies where controlledmixing is required in sub-micron thin regions. The fact that sus-pended functionalized MNPs are finding extensive applications ina variety of disciplines will broaden the scope of this nanomix-ing tool beyond that inherent to molecular transport limitation.Hence, uRMF-excited MNPs can easily be converted into catalyst orenzyme supports endowed with magnetic property where nano-stirring enhances the rates of diffusion-limited reactions or of heattransfer from reaction sites toward bulk flows. Finally, the MNPscan then be magnetically separated downstream and used anew.

Acknowledgements

Support from the Natural Sciences and Engineering ResearchCouncil of Canada and the Canada Research Chair “Green processesfor cleaner and sustainable energy” is gratefully acknowledged.

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