optical transport in bidispersed magnetic colloids with varying refractive index

$: Optical Transport in Bidispersed Magnetic Colloids with Varying Refractive Index$
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Journal of NanofluidsVol. 2, pp. 188–193, 2013(www.aspbs.com/jon)

Optical Transport in Bidispersed Magnetic Colloidswith Varying Refractive IndexHem Bhatt1 and Rajesh Patel2,∗

1Shantilal Shah Engineering College, Sidsar, Bhavnagar 364060, Gujarat, India2Department of Physics, Bhavnagar University, Bhavnagar 364002, Gujarat, India

A modified approach is established to analyze magnetic tuning of refractive index and subsequent variation inoptical transport in bidispersed magnetic colloids. Conceptual equivalence of wavelength variation with refrac-tive index tuning is utilized using effective medium approach. Magnetic tuning of refractive index of magneticnanofluids controls the optical scattering by large magnetic spheres in bidispersed magnetic colloids. The inten-sity correlation with varying refractive index is used to compare the experimental optical transport. Reductionin optical transport is explained on the bases of standing waves generated due to Mie resonance within thescatterers that delays the magnetically induced optical transport. Here, we examine the role played by refractiveindex tuning in optical transport in bidispersed magnetic colloids. This new approach can be useful for tunableoptical and photonic devices.

KEYWORDS: Varying Refractive Index, Light Scattering, Magnetic Colloids, Correlations.

1. INTRODUCTION

Magnetically tunable light scattering by magnetic col-loids has recently shown some fascinating photonicproperties.1–4 Electromagnetic scattering by magnetic par-ticles has many potential applications in magneticallytunable optical scattering,5�6 field dependent refractiveindex7–9 and optical transmission,10–11 tunable magneticphotonic crystals,12–15 etc. Several potential MF-basedoptical devices have been proposed and demonstrated,for instance, MF tunable optical gratings,16�17 MF opti-cal switch,18�19 MF optical modulator,20–23 MF opticalcapacitor,24 MF optical limiters,25�26 and MF sensors.27–31

Recently magnetic field sensing using V–shaped groovefilled with magnetic fluid is studied.32 In our earlierwork33–37 zero forward scattering, coherent backscatteringof light, magnetically induced photonic band gap, Levydistribution of time delay, energy transport velocity is stud-ied. Magnetically induced reduction in optical transportin magnetic nanofluid due to Mie scattering is studiedby Laskar et al.38�39 Recently, Brojabasi et al.40 has stud-ied the effect of applied magnetic field on the backscat-tering from a magnetic nanofluid. Patel41 has studiedmagnetically induced non-exponential relaxation in mag-netic nanofluids. In this matter tunable refractive index

∗Author to whom correspondence should be addressed.Email: [email protected]: 3 April 2013Accepted: 17 April 2013

mediated intensity correlation is one of the importantparameter to study photonic property of the material.42

Refraction of light and retroreflection techniques was usedto study the magnetic field dependent variation of refrac-tive index in ferrofluids.43–45 It was observed that when anexternal magnetic field is applied, the refractive index ofthe ferrofluid changes, stronger the magnetic field higherthe refractive index. This behaviour was attributed to themagnetically induced structure in ferrofluids.44 Anotherremarkable magneto-optical effect of magnetic fluid ismagnetochromatics,46 in which a white light is dispersedinto various colors, as light passes through a ferrofluidpossessing an ordered structure under externally appliedmagnetic field. Similarly, magnetically tunable structurallithographic printing is demonstrated by modulating theperiodicity of structures using magnetic field3 and withdifferent field strengths all the spectrum colors from vio-let to red are demonstrated with a simple technique.1 Formagneto-optical study the ferrofluid should be diluted fortwo reasons (a) to allow light transmission and (b) toreduce the dipolar energy less than thermal energy. Themagnetization of magnetic fluid is very well described bythe Langevin’s theory of paramagnetism for noninteract-ing single domain magnetic particles dispersed in a suit-able liquid carrier.47 But optical property of magnetic fluiddrastically changes when micron sized magnetic particlesare dispersed in a ferrofluid. Our group has demonstratedmagnetically induced zero forward scattering, enhanceback scattering, storage and retrieval of light, which are

188 J. Nanofluids 2013, Vol. 2, No. 3 2169-432X/2013/2/188/006 doi:10.1166/jon.2013.1058

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Bhatt and Patel Optical Transport in Bidispersed Magnetic Colloids with Varying Refractive Index

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LEexplained on the basis of magnetically induced Mie reso-nance and scattering by magnetic scatterers.6�24�33–36 It isalso observed that for small particle size (typically lessthan 10 nm) the transmitted intensity increases with theexternally applied magnetic field but decreases for the par-ticle size greater than 10 nm this is explained on the basisof competition between van der Waals and dipole–dipoleinteractions.48 A dramatic decrease in the transmission oflight at critical magnetic field, which follows the powerlaw dependence with volume fraction of nano particles isobserved and explain on the basis Mie resonance withinthe magnetic scatterers.33–36�38�39 Most of the above sitedreferences show magneto optical effect explained on thebasis of magnetically induced structures of magnetic nanoparticles of ferrofluid or light scattering by the magneticparticles, i.e., a macroscopic explanation. A better insightinto the origin of optical transport in magnetic colloids canbe studied microscopically via induced intensity correla-tions due to tunable refractive index. Correlations, whichare inherent property of the material, provide importantinformation about transport parameters. In past, correla-tions have been measured in time49 and frequency50 fordetermining the diffusion constant of light. Recently, anew approach for measuring both effective medium andthe transport properties of the light propagation in hetero-geneous media by varying the effective refractive index instrongly scattering material is studied.42 In this paper weanalyze intensity correlation using Green’s theorem as afunction of magnetically tunable effective refractive index.The same is compared with normalized transmitted inten-sity as a function of applied magnetic field in transverseconfiguration. Experimental results are in good agreementwith the theoretical predictions. The sample used in thisexperiment is designed specifically and purposefully withthe following aim.(a) The magnetic nanoparticles of the ferrofluid willbehave as a Rayleigh scatterer and the suspended micronsize magnetic particles will behave as a Mie scatterer. Fur-ther, modulating the refractive index of magnetic nanofluid(ferrofluid) by external magnetic field will change the rel-ative refractive index of the micron size magnetic spheressuspended in ferrofluid, consequently changing the scat-tering efficiency of the scatterer.(b) Nanoparticles restricts the dipolar induced largeaggregation of micron size magnetic particles, and givesmore stability to the bidispersed system.

The observed decrease in magnetic field dependent opti-cal transport is explained on the basis of Mie resonancewithin the scatterer, which is supported by observed reso-nance in forward-backward anisotropy factor < cos� > asa function of applied magnetic field.

2. THEORY

The correlations using generalized transport is wellexplained in Ref. [51, 52]. The effective refractive index

shows up in early stages where the average amplitudeGreen’s function is given as,42

G�r�nscatt� ls�=−e��inscatt�/c�−�1/2ls �r

4r(1)

where, nscatt is the refractive index of the scatterer (heremicron size particles, suspended in ferrolfuid), ls is thescattering mean free path, given as ls = l/�1−< cos� >).The anisotropy factor < cos� > and l = 1/�� can beexpressed as a function of Mie coefficient an and bn. Here� is the number density of the scatterer and � is the totalscattering cross section. The refractive index tuning can begiven as,42

= 1nf

�nscatt

�nf

(2)

This shows the relative change in refractive index ofscatterer with respect to the change in refractive indexof the ferrofuid, controlled by an external magnetic field.Here, nf is the refractive index of the fluid, nf = n0 +n� F ��; n0 is the refractive index of the ferrofluid atzerofield, n� is the refractive index of the ferrofluid at aninfinite field (saturation value), F ��= �L2��/�−L��,L��= coth�−�−1, �=�H/kBT , � is magnetic momentand, H is applied field, kB is Boltzmann constant and T isabsolute temperature. F �� is derived using effective fieldmedium.53 Here, can be easily controlled by the externalmagnetic field as L�� and consequently F �� is a func-tion of applied magnetic field. In this case the intensitycorrelation function can be used as,18

C�nf �nf +�nf �=� �nf

cosh√� �nf − cos

√� �nf

(3)

where, � = 2� L2/D, � is the frequency, L is the opticalpath length, D is the diffusion constant. We have also con-sidered the effective wave number k = 2/�e + i�1/2ls�,�e is the effective wave length, magnetically modulatedby change in refractive index of the ferrofluid. Further,ls depends on < cos� >, is a function of Mie scatter-ing parameters an and bn, with field dependent refractiveindex. The anisotropy factor for the lowest order term inka (where, a is radius of the scatterer) is,

< cos� >= Re�a1b∗1�

��a1�2+�b1�2�(4)

The periodic function p�n�ka�= ka tan�nka�, where n=nscatt/nf and nf depend on magnetic field and conse-quently < cos� > is field dependent. This theoreticalprediction is used to analyze the field dependent lighttransmission in magnetic colloids. This concept is notexploited much because of the experimental difficulties,42

but we have made it simple by designing the sampleaccordingly and with moderate magnetic field tunability.

J. Nanofluids, 2, 188–193, 2013 189



Optical Transport in Bidispersed Magnetic Colloids with Varying Refractive Index Bhatt and Patel

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LE3. EXPERIMENTAL DETAILS

Magnetic nanocrystals of Fe3O4 were prepared by classi-cal co-precipitation method. A mixture of solution con-taining ferric (Fe3+� chloride and ferrous (Fe2+� sulphatewas introduced in alkaline solution. Since ferrous chlo-ride degrades and forms hydroxide of ferrous in humidenvironment in the present synthesis we have replacedferrous chloride (Fe2+� with ferrous sulphate to maintainstoichiometric proportion of Fe2+/Fe3+ =1:2. 8 M solu-tion of ammonium hydroxide was used as an alkalinesource to obtain crystallite size ∼10 nm. Upon mixingof salt solutions of iron with ammonia, black precipitatesof Fe3O4 were instantly formed at 10.5 pH. The mix-ture was continuesly stirred for 20 min. at constant pH of10.5 to allow nanocrystallites to grow in size. Nanocrys-tallites were magnetically decanted and washed severaltimes with double distilled water to remove water-solubleimpurities. To obtain stable ferrofluid these nanocrystal-lites were coated with oleic acid and dispersed in kerosene.The fluid was centrifuged @12,000 rpm for 20 minutes toremove aggregates if any.Commercially available magnetite powder was obtained

from Alchemie Research Centre, Mumbai, India. Mag-netite powder was ball milled in a planetary monomill(Pulverisette 6, Fritch GMbH), in the presence of oleicacid and kerosene. The weight ratio of Fe3O4/Oleic acid=1 � 5. The particles are subjected to grinding @300 rpm for36 h. The charge to ball ratio was kept as 1:3. Using frac-tional sedimentation, suspensions of 3–5 �m-sized parti-cles were obtained.To obtain bidispersed magnetic dipolar fluid, magnetic

nano fluid of known volume fraction (1015/m3� is mixedwith a suspension containing micron size magnetic parti-cles of known volume fraction (105/m3� homogenized byultrasonication for 10 minutes.The Experiment was carried out for three different opti-

cal path lengths L= 40, 60 and 80 �m, illuminated by aHe-Ne laser (uniphase) with a wavelength of 633 nm and10 mW output power. The magnetic field (up to 0.1 T)was generated using an electromagnetic coil. The propa-gation of light is transverse to the direction of the appliedmagnetic field. The transmitted intensity was recorded viaphoto detector and the storage oscilloscope (Tektronix-TDS-2024) see Figure 1.

Fig. 1. (Color online) Schematic of the experimental set up. E is theelectric field vector, k is the wave vector and B is the magnetic fieldvector. The sample is illuminated by He-Ne laser. The light transmissionis detected by the photodetector.

4. RESULT AND DISCUSSION

The magnetic particles in a suitable carrier liquid acquiredipole moments in the presence of externally applied mag-netic field. The magnitude of the induced dipole momentis given as, m= �/6�d3�H , d is the diameter of the par-ticle, � is the effective susceptibility, H is the magnitudeof the externally applied magnetic field. The anisotropicinteraction energy between the particles is given as,

Uij =1

4�0

[mi ·mj

r3ij− 3�mi · rij ��mj · rij �

r3ij

](5)

where, rij is the displacement vector of the two particlesand �0 is the vacuum permeability, m is the respectivedipole moments. The coupling constant, which is a ratioof maximum magnitude of the interaction energy to thethermal energy, can be given as,

x = m2

4d3�0kBT(6)

where, kB is the Boltzmann constant and T is absolutetemperature. If x >> 1, the magnetic particles assembledinto chain like structure under the application of magneticfield. In such magnetic suspension (ferrofluid) in kerosene,the absorption study in visible range (wavelength 400 nm–800 nm) exhibits no characteristic visible absorption peakaround �= 633 nm for a typical 10 nm particle size.38 Ear-lier, it was shown that the optical transmission in ferrofluidis due to magnetic field dependent structures. This struc-tural behaviour depends upon the competition between vander Waal and dipole–dipole interactions of the particles.For particles greater than 10 nm, magnetic interaction ismore important and for less than 10 nm, van der Waalis more important. Hence it was shown that for 7 and9 nm particles in ferrofluid, transmission of light increaseswith increasing magnetic field and for 12 nm particles inferrofluid, transmission of light decreases with increasingmagnetic field.48 It was explained on the basis of magnet-ically induced structural transition, but not considering thechange in the effective refractive index of the medium byexternal magnetic field.Figure 2 shows the magnetically modulated refractive

index of ferrofluid sample. The line corresponds to theequation nf = n0 + n� F ��. The refractive index mea-surement was carried out by placing a small electromagnetand a sample cell on one arm of Michelson Interferometer.It is observed that as the field value increases the refrac-tive index of the ferrofluid increases and tends to saturatesat higher field. This is similar to that observed using othertechniques.43–45 Earlier this was explained on the basis ofmagnetically induced structure formation. But in a dilutefluids the field induced large structures may not be possi-ble, in that case, the observed effects can be explained onthe basis of magnetically modulated dielectric constant �f

of the ferrofluid and consequently in terms of refractive

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Fig. 2. (Color online) Variation of refractive index as a function ofexternally applied magnetic field in ferrofluid sample. The zerofieldrefractive index n0 is 1.401 and at 0.05 T field it reaches 1.465.

index nf =√�f , �f ∼ 1 at optical frequency. It is known

that �f of the ferrofluid can be tuned by external mag-netic field.44�54 When micron size magnetic spheres (∼3–5 �m, of same family, i.e., iron oxide) are dispersed in aferrofluid, the scattering property of the sample changesdrastically.33–35 In this case the magnetic nanoparticles ofmagnetic nanofluid will behave as a Rayleigh scatterers asd << �, whereas the micron size magnetic particles sus-pended in magnetic nanofluid will behave as a Mie scat-terer as d > �. The scattering efficiency will be tuned via,magnetic nanofluid’s magnetic field dependent refractiveindex using the above mentioned equation for refractiveindex nf . The relative refractive index of the scatterer canbe given as n = nscatt/nf which suggest that the relativerefractive index of the scatterer depend on the nf and con-sequently it depends on the external magnetic field.Figure 3 shows a plot of correlation function (C) versus

�nf (a magnetically induced change in ferrofluid refractive

Fig. 3. (Color online) Intensity correlation as a function of magneti-cally varying refractive index is plotted for magnetic spheres (3–5 �m)suspended in a ferrofluid (optical path length L =40, 60 and 80 �m).Solid line is fit to the Equation (3) is compared with the magnetic fielddependent normalized transmitted intensity for transverse magnetic fielddirection. Suggesting, importance of refractive index tuning in opticaltransport through magnetic colloids.

index) and a plot of transmitted intensity as a function ofapplied magnetic field H. This shows that, as the mag-netic field changes, the ferrofluid refractive index changes,consequently the relative refractive index of the scattererchanges which correspondingly changes the transmittedlight intensity. This is compared with the intensity corre-lation function. The result matches well with the theory.It is also observed that as the magnetic field increasesthe transmitted intensity decreases due to magneticallyinduced structure formation and magnetic field dependentMie resonance within the scatterer. This decrease in trans-mitted intensity is compared with the intensity correla-tion function as a function of magnetically induced changein ferrofluid refractive index. This suggests that the mag-netic field dependent light transmission can be explainedon the basis of magnetically varying effective refractiveindex and consequently with intensity correlations. Thenon-exponential behaviour may be due to dipolar interac-tions (Eq. (5)) of the particles and Brownian rotation ofmicron size particles in a magnetically interacting medium.Magnetic field induced oscillations in light transport andreduction in transmission is theoretically and experimen-tally observed due to Mie resonance.5�37 Figure 4 showsthe variation of scattering anisotropy factor < cos� > asa function of size parameter ka. The oscillatory behav-ior of < cos� > as a function of size parameter confirmsthe presence of resonance phenomena. It assumes nega-tive as well as positive oscillations, suggesting forward aswell as predominant backward scattering. Figure 5 shows< cos� > as a function of applied magnetic field. In theMie scattering parameters an and bn, the Riccati–Besseland Hankel functions are 2r/� and nscatt�, the rela-tive refractive index can be given as n = nscatt/nf wherenf is a function of applied magnetic field. From Equa-tion (4) < cos� > contains the Mie scattering parametersa1 and b1. This shows that < cos� > can be correlatedwith the applied magnetic field as shown in Figure 5. Itis observed that in this case < cos� > posses only pos-itive values. Suggesting typical Mie resonant preferential

Fig. 4. (Color online) The scattering anisotropy factor < cos� > plottedas a function of size parameter ka. The oscillatory behavior shows thepredeominent forward and backward resonance.

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Optical Transport in Bidispersed Magnetic Colloids with Varying Refractive Index Bhatt and Patel

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Fig. 5. (Color online) The scattering anisotropy factor < cos� >, plot-ted as a function of magnetic field for ka=30, where k is a wave vectorand a is the radius of the scatterer. Here � ∼ 1. The oscillations inthe anisotropy factor, suggests magnetic field dependent Mie resonancewithin the scatterer.

forward direction scattering. Thus field dependent mag-netic scattering exhibits a characteristic resonance behavioreven at moderate magnetic field and introduces an extratime delay in the light propagation, which can cause thedecrease in the transmitted intensity.

5. CONCLUSION

This study shows an interesting comparison between theintensity correlation function derived using generalizedtransport theory as a function of magnetically varyingrefractive index of specifically designed magnetic colloid-which consists of micron size magnetic spheres suspendedin a ferrofuid. Here, the importance of magnetic tuningof refractive index in optical transport in magnetic colloidis discussed. A decrease in normalized transmitted inten-sity as a function of externally applied magnetic field isobserved. This decrease in transmittance is explained onthe basis of morphology-dependent Mie resonance in thescatterer, which produces a standing wave and causes thereduction in light transport. Mie resonance inside the scat-terer is confirmed by magnetic field dependent oscillationsin forward-backward anisotropy factor. The study helpsto design novel magneto optical and photonic devices, inwhich the light transport can be controlled by magneticallyvarying refractive index.

References and Notes

1. F. Leal Calderon, T. Stora, O. M. Monval, and J. Bibette, Phys. Rev.Lett. 72, 2959 (1994).

2. R. Dreyfus, D. Lacoste, J. Bibbet, and J. Baudry, Eur. Phys. J. E.28, 113 (2009).

3. H. Kim, J. Ge, J. Kim, S. Choi, H. Lee, H. Lee, W. Park, Y. Yin,and S. Kwon, Nat. Photon. 3, 534 (2009).

4. J. Ge, Y. Hu, Y. Yin, Angrew. Chem. Int. Ed. 46, 7428 (2007).5. H. Bhatt, R. Patel, and R. V. Mehta, J. Opt. Soc. Am. A 27, 873

(2010).6. R. V. Mehta, R. Patel, B. Chudasama, and R. V. Upadhyay, Opt.

Lett. 33, 1987 (2008).

7. Y. Zhao, Y. Zhang, R. Lv, and Q. Wang, J. Magn. Magn. Mater.323, 2987 (2011).

8. C.-Y. Hong, J.-J. Chieh, S.-Y. Yang, H.-C. Yang, and H.-E. Horng,Appl. Opt. 48, 5604, (2009).

9. S. Pu, X. Chen, Y. Chen, W. Liao, L. Chen, and Y. Xia, Appl. Phys.Lett. 86, 171904, (2005).

10. J. Li, X. Qiu, Y. Lin, X. Liu, J. Fu, H. Miao, Q. Zhang, and T. Zhang,Appl. Opt. 50, 5780 (2011).

11. J. Li, Y. Huang, X. Liu, Y. Lin, Q. Li, and R. Gao, Phys. Lett. A372, 6952 (2008).

12. C. Z. Fan, E. J. Liang, and J. P. Huang, J. Phys. D: Appl. Phys.44, 325003 (2011).

13. S. Pu, X. Bai, and L. Wang, J. Magn. Magn. Mater. 323, 2866(2011).

14. L. Zhang and J. Huang, Chin. Phys. B 19, 024213 (2010).15. S. Pu and M. Liu, J. Alloys Compd. 481, 851 (2009).16. A. Candiani, W. Margulis, C. Sterner, M. Konstantaki, and

S. Pissadakis, Opt. Lett. 36, 2548 (2011).17. S. Pu, X. Chen, L. Chen, W. Liao, Y. Chen, and Y. Xia, Appl. Phys.

Lett. 87, 021901 (2005).18. W. Yuan, C. Yin, P. Xiao, X. Wang, J. Sun, S. Huang, X. Chen, and

Z. Cao, Microfluid. Nanofluid. 1 (2011).19. Q.-F. Dai, H.-D. Deng, W.-R. Zhao, J. Liu, L.-J. Wu, S. Lan, and

A. V. Gopal, Opt. Lett. 35, 97 (2010).20. P. Zu, C. C. Chan, L. W. Siang, Y. Jin, Y. Zhang, L. H. Fen, L. Chen,

and X. Dong, Opt. Lett. 36, 1425 (2011).21. X. Bai, S. Pu, and L. Wang, Opt. Commun. 284, 4929 (2011).22. X. Bai, S. Pu, L. Wang, X. Wang, G. Yu, and H. Ji, Chin. Phys. B

20, 107501 (2011).23. T.-Z. Zhang, J. Li, H. Miao, Q.-M. Zhang, J. Fu, and B.-C. Wen,

Phys. Rev. E 82, 021403 (2010).24. R. Patel and R. V. Mehta, Appl. Opt. 50, G17 (2011).25. S. Pu, L. Yao, F. Guan, and M. Liu, Opt. Commun. 282, 908

(2009).26. H. Wu, X. Li, M. Zhang, D. Stade, and H. Schau, Proceedings of

IEEE Conference on Transactions on Components and PackagingTechnology 32, 572 (2009).

27. L.-X. Chen, X.-G. Huang, J.-H. Zhu, G.-C. Li, and S. Lan, Opt. Lett.36, 2761 (2011).

28. Y. Miao, Y. Liu, B. Liu, K. Zhang, H. Zhang, and Q. Zhao, Proc.SPIE 7753, 775347 (2011).

29. J. Dai, M. Yang, X. Li, H. Liu, and X. Tong, Opt. Fiber Technol.17, 210 (2011).

30. P. Childs, A. Candiani, and S. Pissadakis, Proceedings of IEEE Con-ference on Photonics Technology Letters 23, 929 (2011).

31. T. Hu, Y. Zhao, X. Li, J. Chen, and Z. Lv, Chin. Opt. Lett. 8, 392(2010).

32. H. Ji, S. Pu, X. Wang, and G. Yu, Appl. Opt. 51, 1010 (2012).33. R. V. Mehta, R. Patel, R. Desai, R. V. Upadhyay, and K. H. Parekh,

Phys. Rev. Lett. 96, 127402 (2006).34. R. V. Mehta, R. Patel, and R. V. Upadhyay, Phys. Rev. B. 74, 195127

(2006).35. R. Patel and R.V. Mehta, Eur. Phys. J. Appl. Phys. 52, 30702

(2010).36. R. Patel and R. V. Mehta, J. Nano Photon. 6, 069503 (2012).37. Hem Bhatt, R. Patel, and R. V. Mehta, Phys. Rev. E 86, 011401

(2012).38. J. M. Laskar, J. Philip, and B. Raj, Phys. Rev. E 82, 021402

(2008).39. J. Philip and J. M. Laskar, Journal of Nanofluids 1, 3 (2012).40. S. Brojabasi and J. Philip, J. Appl. Phys. 113, 054902 (2013).41. R. Patel, Journal of Nanofluids 1, 71 (2012).42. S. Faez, P. M. Johnson, and Ad. Lagendijk, Phys. Rev. Lett.

103, 053903 (2009).43. S. Pu, X. Chen, Y. Chen, W. Liao, L. Chen, and Y. Xia, Appl. Phys.

Lett. 86, 171904 (2005).

192 J. Nanofluids, 2, 188–193, 2013




ARTIC

LE44. S. Y. Yang, J. J. Chieh, H. e. Horng, C.-Y. Horng, and H. C. Yang,

Appl. Phys. Lett. 84, 5204 (2004).45. Y. F. Chen, S. Y. Yang, W. S. Tse, H. E. Horng, C. Y. Hong, and

H. C. Yang, Appl. Phys. Lett. 82, 3481 (2003).46. H. E. Horng, C. Y. Hong, W. B. Yeung, and H. C. Yang, Appl. Opt.

37, 2674 (1998).47. R. E. Rosensweig, Ferrohydrodynamics Cambridge University Press,

Cambridge (1985).48. G. N. Rao, Y. D. Yao, Y. L. Chen, K. T. Wu, and J. W. Chen, Phys.

Rev. E 72, 031408 (2005).

49. W. Cai, B. B. Das, F. Liu, M. Zavellos, M. Lax, and R. R. Alfano,Proc. Natl. Acad. Sci. U.S.A. 93, 13561 (1996).

50. A. Z. Geneck, Phys. Rev. Lett. 58, 2043 (1987).51. S. Feng, C. Kane, P. A. Lee, and A. D, Stone, Phys. Rev. Lett.

61, 834 (1988).52. P. Sheng, Introduction to wave scattering. Localization and Meso-

scopic Phenomena Academic Press, New York (1995).53. F. A. Pinheiro, A. S. Martinez, and L. C. Sampaio, Phys. Rev. Lett.

84, 1435 (2000).54. S. Taketomi, J. J. Appl. Phys. 22, 1137 (1983).

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