Magnetically Induced Structural Difference in Ferrofluids And

Magnetically Induced Structural Difference in Ferroﬂuids and Magnetorheological Fluids

Hiral Virpura, Mayur Parmar, and Rajesh Patel∗ Department of Physics, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar 364002, India

We have prepared ferrofluid using magnetic nanoparticles (∼ 10 nm) and magnetorheological fluid (MR fluid) using micron size (∼ 10 m) magnetic particles. We have observed striking difference in magnetically induced structure formation in both the fluids although both are classifications of magnetic fluids in a broad way. A field induced structural difference in chain formation, labyrinthine pattern, spikes formation (Rosensweig surface instability) and optical diffraction pattern is observed. The induced structural difference is mainly due to the magnetically induced dipolar interaction, field induced viscosity and surface tension in both the fluids.

KEYWORDS: Magnetic Fluids, Induced Structures, Dipolar Interactions.

1. INTRODUCTION is between 10% to 40% to produce strong magnetorheo- ARTICLE Magnetic fluids can be classified in to two broad categories logical effect. In MR fluid the field induced aggregation [i] ferrofluid and [ii] magnetorheological fluids. Ferrofluid is a key factor for the magnetorheological behavior of is made up of a single domain magnetic nanoparti- the sample which is reversible. Particle sedimentation is cles (∼ 5–20 nm) dispersed in aIP: suitable 192.168.39.211 carrier liquid, On:1 Tue,one 28 ofSep the 2021 problems 22:21:30 with MR fluid whereas in ferrofluid whereas the MR fluid is made up ofCopyright: a micron size American mag- Scientificthe stability Publishers is long term. To overcome the particle sed- netic particles (∼ 2–20 m) dispersed in oilDelivered like car- byimentation Ingenta one can try to make bidispersed MR fluid.6–9 rier liquid.2 Magnetorheological fluid was introduced in Recently inversion of magnetic force between microparti- 1940’s2 whereas ferrofluid was introduced during 1960’s.3 cles and its effect on the magnetorheology in bidispersed Various applications of MR fluid includes Automotive magnetic fluid is studied.10 MR fluid is a yield stress fluid, clutches, brakes, polishing fluids, seat dampers, prosthetic ferrofluid is does not show field induced yield stress. MR knee damper, actuator systems, shock absorbers, etc.4 The fluid has strong dipolar interaction whereas ferrofluid has basic difference in MR fluid and ferrofluid starts with comparatively weak dipolar interactions as the magnetic their particle size. In ferrofluid the particle size range is susceptibility depends on the volume of the particles dis- about nanometer scale whereas for MR fluid the particle persed. In this paper we report striking difference in mag- size range is in micrometer scale. The magnetic nanopar- netic field induced structural difference such as particle ticles in ferrofluid are single domain whereas in MRF the aggregation behavior, labyrinthine pattern, spikes forma- magnetic particles can be multidomain. Consequently, the tion (Rosensweig surface instability) and optical diffrac- magnetic moment of micron size particles in MR fluid tion pattern and its field induced modulation. The observed is field induced and their Brownian motion is negligible, structural difference is due to the field induced strong dipo- while for ferrofluids the magnetic nanoparticles perform lar interactions, the field induced viscous behavior and sur- intense thermal motion. The field induced particle aggre- face tension in both the fluids. gation behavior in MR fluid is intense and under moderate magnetic field the fluid behaves like a solid due to large 2. EXPERIMENTAL DETAILS and thick aggregation of magnetic particles, in ferrofluid the field induced particle aggregation is less intense than Magnetic nanoparticles of Fe3O4 were prepared by classi- 1 MRF, it can produce magneto viscous effect5 butitdo cal co-precipitation method. The mixture of solution con- 3+ 2+ not behave like a solid the fluid behavior remains. The taining ferric (Fe ) chloride and ferrous (Fe ) sulphate volume concentration in MR fluid is generally high and was introduced in alkaline solution. The resulting mixture was continuously stirred for 20 min. at 10.5 pH to allow nanocrystallites to grow in size. Nanocrystallites were ∗Author to whom correspondence should be addressed. Emails: [email protected], [email protected] magnetically decanted and washed with distil water several Received: 18 December 2013 times to remove water-soluble impurities. To obtain sta- Accepted: 19 January 2014 ble ferrofluid these nanocrystallites were coated with oleic

J. Nanoﬂuids 2014, Vol. 3, No. 2 2169-432X/2014/3/121/006 doi:10.1166/jon.2014.1095 121 Magnetically Induced Structural Difference in Ferroﬂuids and Magnetorheological Fluids Virpura et al.

3. RESULTS AND DISCUSSION Magnetic fluids (MR fluids and ferrofluids) are composed of coated magnetic particles dispersed in a nonmagnetic liquid carrier. Under the effect of magnetic field they form head-to-toe chain like aggregation due to field induced dipolar interactions. The dipole moment of a magnetic particle is proportional to its magnetic core volume with the relation given by m = VH, where V = d3/6 volume of the particle, d is diameter of the particle, is the magnetic susceptibility of the particle, H is the applied magnetic field. The dipole–dipole interaction potential between particles i and j is given by, m · m 3m · r m · r dip = 1 i j − i ij j ij Uij 3 5 (1) 40 rij rij

where rij is the displacement vector of the two particles m m and 0 is the vacuum permeability, i and j is the respective dipole moments. The magnetic dipole moment Fig. 1. Microscopic and TEM images of micron size magnetic particles = 3 of the particles can be given as m 4/3am Ms where (Fe3O4 and magnetic nanoparticles (Fe3O4) respectively. am is radius of the magnetic core and Ms is the satura- acid and dispersed in kerosene. The fluid was centrifuged tion magnetization of the particle material. The maximum at 12,000 RPM for 20 min to remove aggregates if any. attraction between the particles is obtained when particle dipoles are oriented head to tail configuration, it is equal to From the magnetization measurements of the ferrofluid, particle size (10.4 nm) and saturation magnetization of the m2 U =−2 0 (2) fluid (250 Oe) were determined. For preparation of mag- max 4 r 3 neto rheological fluid (MRF), commerciallyIP: 192.168.39.211 available On: iron Tue, 28 Sep 2021 22:21:30 particles were used. The initial concentrationCopyright: of magneticAmerican ScientificThe formation Publishers of aggregates is opposed by Brownian nanoparticles in ferrofluid is 4.8% whereas theDelivered concen- by dispersionIngenta and as such, the potential for field induced tration of micron size magnetic particles in MRF it is aggregation versus Brownian dispersion can be expressed 15%. Figure 1 shows the microscopic and TEM images of in terms of a governing dimensionless parameter, known micron size magnetic particles and magnetic nanoparticles as coupling constant, respectively. The visualization of chain dynamics under ARTICLE 2H 2V rotating magnetic field is observed using Magnus MLX = 0 (3) 12k T microscope. The magnification used is 100×. CCD cam- B

era used is Samsung (BW-360CD) attached with the per- where 0 and H are free space permeability and applied sonal computer. The sample is placed at the centre of the magnetic field respectively. T and kB are absolute tem- pairs of Helmholtz coils to generate homogeneous mag- perature and Boltzmann constant. For 1 aggregation netic field up to 200 Oe in the plane of image. For spikes is highly favoured and 1 dispersion is favoured. Cal- formation (Rosensweig instability) and labyrinthine pat- culating its value for typical field strength of 10 kA/m tern observation, a layer of ferrofluid and MR fluid is and the susceptibility of iron particles with 10 m diam- mixed with miscible liquid and exposed to the perpendic- eter that is in the order of 108.5 Whereas for ferrofluid, ular magnetic field. An illuminating light is kept above it is approximately less than 5. The high value of makes the patter for the better visibility of the event. A capillary obvious that a strong tendency towards formation of chains viscometer having length 40 mm and diameter 0.5 mm and agglomerates is typical for a magnetorheological effect is calibrated at 25 C using three fluids: water, benzene, in MR fluids. and kerosene. Electromagnets were used to generate mag- Figure 2 shows the magnetic field induced chain for- netic field. The uncertainty involved in the viscosity mea- mation in ferrofluid and MR fluid at 500 Oe. It shows surement is ± 0.02 cP checked using standard samples. clear striking difference in a field induced aggregation in A He–Ne laser beam is passed through both the samples ferrofluid and MR fluid. It is visible that in ferrofluid the (after necessary dilution) for the detection and modulation size of the chain, distance between chains, formation of of diffraction pattern. For magnetic modulation of diffrac- multiple chain, shape of the chain like aggregate is quite tion pattern an electromagnet is used. The optical path different than that for MR fluid, for MR fluid the aggre- length of the sample is kept 2 mm. The observed on screen gation is caused by the association of multiple chains, diffraction pattern is recorded using CCD camera and a with structure of oblate shape in the direction of field, dis- computer. tance between chain is quite less, hence the dipolar forces

122 J. Nanoﬂuids, 3, 121–126, 2014 Virpura et al. Magnetically Induced Structural Difference in Ferroﬂuids and Magnetorheological Fluids

(a)

Fig. 2. Magnetic field induced chain formation in ferrofluid and MR fluid at 500 Oe. The chains in ferrofluid are much thinner and chain separation is more than that of in MR fluid suggesting that field induced aggregation dynamics is quite different. (b) between and within the chains will be quite different than that in ferrofluid. The shape fluctuations in parallel chains give rise to chain–chain interaction perpendicular to the field direction, causing the formation of thick sheets of particles due to lateral aggregation. The critical value for coupling constant or interaction parameter for ferrofluid is approximately 3–4,11 at this value the field induced aggre- ARTICLE gation in ferrofluid is prominent, whereas for MR fluid this value is quite large.12 It is generally known that the origin of internal structures in magnetic colloids is due to dipolar interactions between magneticIP: 192.168.39.211 particles dispersed On: Tue, 28 Sep 2021 22:21:30 in a nonmagnetic liquid carrier. The basicCopyright: features American of the Scientific Publishers effects of dipolar interactions in magnetic colloidsDelivered were by Ingenta outlined in the pioneering work of de Gennes and Pincus.13 Fig. 3. (a) Magnetic field dependent viscosity in ferrofluid through capillary. The direction of applied magnetic field is perpendicular to the They have shown the possibility of zerofield and field direction of flow. (b) Magnetic field dependent capillary viscosity in MR 3 induced structures in magnetic colloids. The dipole 1/r fluid. It is observed that there is a steap rise in the viscosity at 25 Oe pair potential, where r is the particle separation being aver- applied magnetic field. aged over the dipole orientations becomes and attractive 1/r 6–potential responsible for the van der Waals conden- sation. At high external fields the association phenomenon flow behavior and the viscosity is approximately 3.5 cP. should appear as the dipoles align along the field direction, For MR fluid the behavior is quite different. The vis- the head-to-tail configuration is energetically preferable cosity study for the MR fluid is carried out at very low and magnetic grains tend to form chains along the field field i.e., < 30 Oe. It is observed that the zero field cap- direction. illary viscosity is ∼ 3.7 cP, at 15 Oe it becomes ∼ 7cP, Figures 3(a) and (b) shows the field induced flow at 20 Oe it becomes ∼ 23 cP and at 25 Oe the viscosity behaviour of ferrofluid and MR fluid through capillary vis- rises sharply and becomes ∼ 350 cP, almost flow less. The cosity. The direction of the applied magnetic field was rise in the field induced viscosity of MR fluid is shown in kept perpendicular to the direction of the flow. The field Figure 3(b). A very sharp rise is observed between 20 and induced magnetoviscous effect is very well observed.5 25 Oe magnetic field, this suggest that the strong chain Recently, ferrohydrodynamic evaluation of rotational vis- formation takes place in such MR fluid in this field range cosity and relaxation in certain ferrofluids,14 effective vis- and the flow almost stops. cosity of magnetic nanofluids through capillaries,15 and The increase of viscosity of a ferrofluid is well effect of temperature on rotational viscosity in magnetic established.1 5 14–16 The effect was explained by hindrance nano fluids16 is carried out. The coefficient of viscosity of a of rotation of the particles due to the action of the mag- magneto-rheological fluid for different values of the magnetic field. The main peculiarity of ferrofluids is a spe- netic field and parameters at which the flow of the fluid cific relation between the magnetic and effective degrees through a capillary is stopped is determined.17 Here it is of freedom of suspended magnetic nanoparticles of which observed that at low field the ferrofluid viscosity increases the fluids are composed. Therefore, the concept of inter- and at higher field they tend to saturate. However even nal rotation first applied to the ferrofluids has proved to be at nearly 3000 Oe field value the ferrofluid exhibits the very useful. This model takes into account that the volume

J. Nanoﬂuids, 3, 121–126, 2014 123 Magnetically Induced Structural Difference in Ferroﬂuids and Magnetorheological Fluids Virpura et al.

density of the angular momentum of magnetic nanofluids horizontal layer of ferrofluid in a vertically applied mag- consists of both the orbital and spin parts. The orbital part netic field is characterized by the energy density,1 L = (r × v), is associated with the translational motion g h − 1 of magnetic grains and molecules of the solvent. The spin Ehx y = h2xy− dzB r Hxyz 2 0 2 part S, is caused by the rotation of the grains themselves and should be treated as an independent variable along the + 1 + hx y2 + hx y2 (4) = x y fluid velocity v, density , and pressure p. Here S I p, where p is the angular velocity of the particle. The dif- Here, and are the density and surface tension of − = ference between p , where 1/2 curl v, the local the ferrofluid, B is magnetic field induction, hx y the angular velocity of the fluid, gives rise to dissipation pro- local height of the liquid layer, H applied magnetic field. cesses due to redistribution of angular momentum between The three terms in the Eq. (4) represents the hydrostatic, − L and S. The difference p instantly decays where- magnetic and surface energy respectively. As the surface upon the hydrodynamic description is reduced to the com- profile deviates from the flat reference state, the first and mon set of hydrodynamic equations. This difference can be the last term grow whereas the magnetic energy decreases. maintained by applying an external magnetic torque that For sufficiently large B, this gives rise to the normal field − = acts directly upon the particle rotation 6 (p or Rosensweig surface instability. The spikes formation or M × H. Here, H is the magnetic field within the fluid and Rosesweig instability in a Fe3O4, kerosene based ferrofluid M is the magnetization of the fluid. In this model using is shown in Figure 4(A). The magnetic particle size in the concept of Fokker-Planck equation and effective field this fluid is nearly 10 nm and the fluid magnetization is concept. In dense ferrofluid the magnetic field induced 250 Oe. Surface tension of this fluid is measured using observed magnetoviscous effect is due to the chain for- sessile drop method, it is observed that the surface ten- mation of the particles.5 The field induced formation of sion decreases with the increasing particle concentration the chain is in the direction of the applied magnetic field and increases with applied magnetic field.18 Compare to and restricts the flow of the fluid, thus increases the vis- spikes formation in ferrofluid is quite different from MR cosity of the ferrofluid. This increment is larger than that fluid. The field induced surface instability in MR fluid is in dilute ferrofluid. In case of MR fluid the field induced shown in Figure 4(B). In MR fluid the concentration of large structure plays importantIP: role 192.168.39.211 for the magnetorheo- On: Tue,the 28 particlesSep 2021 are 22:21:30 more than that in ferrofluid, hence the logical effects. This structures inducesCopyright: plastic behavior American at Scientificdensity ofPublishers the fluid and dipolar interaction is larger. Fur- Delivered by Ingenta certain magnetic field and produces yield stress, which are ther, the MR fluid composed of iron particles whereas fer- not observed for ferrofluids. rofluid is composed of iron oxide particles hence the dipole Figure 4 shows the difference in field induced spikes moment of the iron particle will be larger, produces greater formation in ferrofluid and MR fluid. The direction of the dipolar interaction under the application of the magnetic

ARTICLE applied magnetic field is kept perpendicular to the fluid field. As the number concentration of the particles in MR surface. When an initially flat free surface of a ferrofluid fluid is more the surface tension is also more than that film is subjected to a perpendicular magnetic field, and in ferrofluid. Because of these reasons, under the applica- the magnetic surface force exceeds the stabilizing effects tion of magnetic field the surface as a sheet of comes up of gravity and surface tension, a stationary array of peaks instead of single spikes. This clearly shows the difference is formed also known as Rosensweig surface instability. in field induced surface instability in ferrofluid and MR Typically the thickness of the ferrofluid layer is on the fluid. This difference is mainly due to the field induced order of centimeters, being comparable to the wavelength strong dipolar interactions in MR fluid. of the unstable surface mode. This is a lossless system, a Figures 5(A) and (B) shows the difference between field induced labyrinthine patterns in ferrofluid and in MR fluid. A drop of ferrofluid in a magnetic field is one example of many systems, including amphiphilic mono- layers, thin magnetic films, and type I superconductors, that form labyrinthine patterns. When a two dimensional drop of ferrofluid is mixed with immiscible liquid in a Hele–Shaw cell and subjected to a magnetic field normal to the plates produces complex labyrinthine patterns.1 19 The induced labyrinthine pattern is due to competition between the ferrofluid-immissible fluid surface tension and bulk induced magnetic dipolar interactions. The motion Fig. 4. (A) Shows the spikes formation under the effect of perpendicu- satisfies a global constraint (fixed fluid volume) and is lar magnetic field in ferrofluid. (B) shows the flower like pattern in MR fluid is observed under perpendicular magnetic field. The viscosity of dominated by viscosity. The macroscopic nature of this the fluid and interparticle dipolar interactions plays important role in the system affords distinct experimental advantages, includ- pattern formation under magnetic field. ing ease of visualization and direct control of strength of

124 J. Nanoﬂuids, 3, 121–126, 2014 Virpura et al. Magnetically Induced Structural Difference in Ferroﬂuids and Magnetorheological Fluids

incident radiation 633 nm hence the particles behaves like a Mie scatterers and exhibits dominant forward scattering, due to this reason MR fluid shows the clear circular diffraction pattern. However, Philips and Laskar22 23 has shown ring like diffraction pattern in ferrofluid, which is due to field induced chain formation in ferrofluid. Rigor- ous solution of scattering of electromagnetic waves by a sphere of arbitrary size and refractive index was derived by Mie and Lorentz.24 According to Mie theory scattered intensity depends on two intensity functions

= Fig. 5. (A) Shows the magnetically induced labyrinthine pattern in fer- i12 S12mMMS (5) rofluid and (B) in MR fluid. Thickness and separation of the thread is quite different. This difference is also due to the viscosity of the fluid Here, suffix 1, 2 represent the two orthogonal states of lin- and interparticle dipolar interactions. ear polarization respectively, perpendicular and parallel to the scattering plane defined by the direction of propagation dipolar interaction. Figure 5(A) shows the magnetically and the direction of applied magnetic field. (= d/, induced labyrinthine pattern in ferrofluid and Figure 5(B) d is diameter) is the size parameter and is the scat- shows the field induced labyrinthine pattern in MR fluid. = tering angle. mMMS ( m↓s/m↓f is the relative refrac- For ferrofluid it is observed that the threads are thinner tive index of the scatterer (ms) with respect to that of and longer, the spacing between the threads are smaller. surrounding ferrofluids (mf ). The scattering coefficients Whereas for MR fluid the threads of the fluid is thicker and S12mMMS in turn depend on Mie coefficients an, shorter, the spacing between the threads are larger than that ARTICLE bn and partial derivatives of Legendre polynomials n of ferrofluid labyrinthine pattern. These differences are due (cos ) and n (cos ). Detailed expressions are given in to that the field induced dipolar interaction in MR fluid is Ref. [24]. The Mie coefficients depend on the size param- much larger than that in ferrofluid. Further due to strong eter and mMMS. dipolar interaction in MR fluid theIP: field192.168.39.211 induced viscosity On: Tue, 28 Sep 2021 22:21:30 is less than that in ferrofluid, hence theCopyright: labyrinthine American pattern Scientific Publishers in ferrofluid is quite different than that in MR fluid.Delivered by4. Ingenta CONCLUSION Figures 6(A) and (B) shows the transmitted diffraction In this work we have observed magnetically induced struc- pattern in ferrofluid and in MR fluid. It is clear that the tural difference in ferrofluid and MR fluid, though both are ferrofluid do not show the clear diffraction pattern whereas categories of magnetic fluid in general. It is observed that the MR fluid shows clear spherical diffraction pattern, due the magnetically induced chain formation in ferrofluid is to the micron size magnetic particles dispersed.20 21 In fer- short and thin, suggesting the particle aggregation is less, rofluid the dispersed particles are of nanosize (‘10 nm) whereas for MR fluid the chains are much more longer and the incident wavelength of the He–Ne laser light is and thick, suggesting association of large number of par- 633 nm, hence the size of the particles are much less than ticles in the chain formation. Due to strong behavior of the incident wavelength and the scatterer obeys Rayleigh chain formation it can easily produce magnetorheologi- scattering effect. In MR fluid the particles are of nearly cal effect like yield stress. For magnetic field dependent 3–10 m which is comparable with the wavelength of the ferrofluid viscosity it is observed that even at 3000 Oe field it does not saturate and the viscosity is nearly 3.4 cP, whereas for MR fluid the magnetically induced viscosity is nearly 350 cP at just 25 Oe field, shows potential for the MR effect. In the case of spikes formation (Rosesnweig surface instability) for ferrofluid under perpendicular magnetic field, well separated spikes are observed, however for MR fluid the pattern is completely different and it is like a flower pattern, not separate single spikes. In case of labyrinthine pattern, the ferrofluid patterns are thin, long and spacing is less, whereas for MR fluid the threads are thick, short and spacing is more. For light transmission it is observed that for ferrofluid the transmission do not show any diffraction as the magnetic nanoparticles are behaving Fig. 6. (A) Shows the transmitted light image on the screen through ferrofluid consisting magnetic nanoparticles where these particles behaves as a Rayleigh scatterer and do not contribute to the diffrac- like Rayleigh scatterers. (B) shows the optical diffraction pattern pro- tion of light, for micron size particles in MR fluid they duced by the micron size particles in MR fluid. obey Mie scattering and diffract light considerably, shows

J. Nanoﬂuids, 3, 121–126, 2014 125 Magnetically Induced Structural Difference in Ferroﬂuids and Magnetorheological Fluids Virpura et al.

clear diffraction pattern. The observed structural difference 10. M. T. Lopez-Lopez, G. Bossis, J. D. G. Duran, A. Gomez-Ramirez, is due to the field induced strong dipolar interactions, the P. Kuzhir, L. Iskakova, and A. Yu. Zubarev, J. Nanofluid 2, 85 field induced viscous behavior and surface tension in both (2013). 11. K. I. Morozov and M. I. Shliomis, Magnetic Fluid as an Assembly of the fluids. Flexible Chains, Stefan Odenbach (Ed.): LNP 594, Springer-Verlag, Berlin, Heidelberg (2002), pp. 162–184. Acknowledgment: Authors are thankful to Department 12. G. Bossis, O. Volkova, S. Lacis, and A. Meunier, Magnetorheology: of Science and Technology, India for providing finan- Fluids, Structures and Rheology, Stefan Odenbach (Ed.): LNP 594, Springer-Verlag, Berlin, Heidelberg (2002), pp. 202–230. cial support in terms of the projects DST-MRF and DST- 13. P. G. de Gennes and P. A. Pincus, Phys. Kondens. Materie 11, 189 AAOS. (1970). 14. Rajesh Patel, Phys. Rev. E 86, 016324 (2012). 15. Rajesh Patel, Phys. Rev. E 85, 026316 (2012). References and Notes 16. Rajesh Patel, Eur. Phys. J. E 35, 109 (2012). 1. R. E. Rosensweig, Ferrohydrodynamics, Cambridge University 17. A. Roszkowski, M. Bogdan, W. Skoczynski, and B. Marek, Mea- Press, Cambridge (1985). surement Science Review 8, 58 (2008). 2. J. Rabinow, AIEE Trans. 67, 1308 (1948). 18. Nishant Nair, Hiral Virpura, Vishakha Dave, and Rajesh Patel, 3. S. Papell (NASA), US Patent, 3,215,572 (1965). unpublished results. 4. J. de Vicente, D. J. Klingenberg, and R. Hidalgo-Alvarez, Soft Matter 19. A. J. Dickstein, S. Erramilli, R. E. Goldstein, D. P. Jackson, and 7, 3701 (2011). S. A. Langer, Science 261, 1012 (1993). 5. S. Odenbach, Magnetoviscous Effects in Ferrofluids, (Springer Lec- 20. R. V. Mehta, Rajesh Patel, Rucha Desai, R. V. Upadhyay, and ture Notes in Physics), Springer, Heidelberg (2003), p. 131. Kinnari Parekh, Phys. Rev. Lett. 96, 127402 (2006). 6. Rajesh Patel and B. Chudasama, Phys. Rev. E 80, 012401 (2009). 21. R. V. Mehta, Rajesh Patel, and R. V. Upadhyay, Phys. Rev. B 74, 7. Rajesh Patel, J. Magn. Magn. Mater. 323, 1360 (2011). 195127 (2006). 8. L. Felicia, R. John, and J. Philip, J. Nanofluid. 2, 75 (2013). 22. John Philip and Junaid M. Laskar, J. Nanofluids 1, 3 (2012). 9. N. M. Wereley, A. Chaudhuri, J.-H. Yoo, S. John, S. Kotha, 23. J. M. Laskar, J. Philip, and B. Raj, Phys. Rev. E 78, 031404 (2008). A. Suggs, R. Radhakrishnan, B. J. Love, and T. S. Sudarshan, 24. H. Bhatt, Rajesh Patel, and R. V. Mehta J. Opt. Soc. Am. A 27, 873 J. Intell. Mater. Syst. Struct. 17, 393 (2006). (2010).

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126 J. Nanoﬂuids, 3, 121–126, 2014