effect of carrier and particle concentration on ultrasound properties of magnetic nanofluids

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Ultrasonics xxx (2014) xxx–xxx

ULTRAS 4902 No. of Pages 7, Model 5G

26 August 2014

Contents lists available at ScienceDirect

Ultrasonics

journal homepage: www.elsevier .com/locate /ul t ras

Effect of carrier and particle concentration on ultrasound propertiesof magnetic nanofluids

http://dx.doi.org/10.1016/j.ultras.2014.08.0170041-624X/� 2014 Published by Elsevier B.V.

⇑ Corresponding author.E-mail address: [email protected] (K. Parekh).

Please cite this article in press as: J.K. Patel, K. Parekh, Effect of carrier and particle concentration on ultrasound properties of magnetic nanUltrasonics (2014), http://dx.doi.org/10.1016/j.ultras.2014.08.017

Jay Kumar Patel, Kinnari Parekh ⇑Dr. KC Patel R & D Center, Charotar University of Science & Technology, Changa 388 421, Dist. Anand, Gujarat, India

a r t i c l e i n f o

242526272829303132

Article history:Received 3 June 2014Received in revised form 7 August 2014Accepted 12 August 2014Available online xxxx

Keywords:Magnetic fluidUltrasonic wave propagationNanofluid

a b s t r a c t

Ultrasound wave propagation in nanofluids and its rheological behavior has been studied as a function ofsolid volume fraction, temperature and magnetic field for magnetic nanofluids synthesized in keroseneand transformer oil. Ultrasonic velocity decreases while viscosity increases with increasing volume frac-tion. The attenuation of ultrasonic wave is explained using dipolar coupling co-efficient which favors oli-gomer structures with increasing number density of particles. The structure formation increases furtherwith increase in magnetic field which is prominent in transformer oil compared to kerosene. This differ-ence can be due to the structural difference between these two carriers.

� 2014 Published by Elsevier B.V.

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1. Introduction

Magnetic nanofluids represent a technologically importantmaterial because of its wide scope of tuning the macroscopicbehavior under different environment. Recent experiments andanalysis show that magnetic dipole force and strong magnetic fieldexpels nanoparticles to form chains and aggregates that can greatlyaffect the macroscopic properties of ferrofluids even for low con-centration [1–6]. The formation of structural pattern in the mag-netic fluid and its thin film under the influence of magnetic fieldcan be investigated by optical microscopy, strong light diffractionimage, electron microscopy, nuclear magnetic resonance (NMR)technique, small-angle neutron scattering (SANS), acoustical studyand rheological studies [7–16]. This clustering has a significantinfluence on the properties of magnetic fluid and hence its furtheruse.

In 1975, Hayes had reported needle-like clusters or aggregatesof the magnetic particles in nanofluids through optical microscopicobservations under the influence of an external magnetic field [7].Though magnetic nanofluids is an opaque liquid when it is sand-wiched by two glass slides and pressed to a thin film of a few tensof micron thickness, visible light can be transmitted through themagnetic nanofluids film. The alternate study is to project thetransmitted light on screen and obtain a peculiar scattering lightpattern. Haas and Adams [8] observed a peculiar projection ofthe transmitted light from the diluted magnetic nanofluid’s filmwhen the field was perpendicular to the light propagation. The

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needle-like clusters in the magnetic nanofluids play a role of grat-ing of an optical diffraction grating. The strong diffraction effect isdue to the periodical spacing between the needlelike clusters. Onthe contrary, by measuring the diffraction light intensity as a func-tion of the diffraction angle, one can calculate the spacing of theclusters by Fourier transform [9].

The lower limit of an ordinary optical microscope’s resolution isabout a micron. Therefore, if the clusters are lesser than the micronsize then it cannot be distinguished by the optical microscope.Although, nanometer-size objects can be investigated by an elec-tron microscope; it has a fatal disadvantage of an evacuated sam-ple room. The solvent has to evaporate before observation and thatlimits the investigation as the drying process exceeds the aggrega-tions of particles. Donselaar et al. [10] succeeded in observing clus-ters of submicron scale in the magnetic nanofluids in a frozen stateby an electron microscope. However, from a more critical view-point, even these sub-micron clusters might be formed duringthe quenching process.

When one studies the magnetic colloidal particle behavior inthe Magnetic nanofluids, it is necessary to know how strong themagnetic field is at the particle position. The so-called local mag-netic field at the particle position, Hloc, is different from an externalfield, H. In addition to H, there are magnetic fields generated by thepermanent magnetic moments of all other surrounded magneticparticles. If the colloidal particles are uniformly distributed, theproblem is not so difficult, but the existence of clusters in thenanofluids together with the colloidal particles makes the problemmore complicated. The local field, Hloc, inside the cluster should bemuch stronger than that at the rest of the system. However, as thecluster is micron size it is difficult to measure Hloc with ordinary

ofluids,

http://dx.doi.org/10.1016/j.ultras.2014.08.017

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http://www.elsevier.com/locate/ultras


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Fig. 1. Experimental set-up 1: (a) base to hold cell, (b) double jacketed measuringcell containing quartz crystal for generating 2 MHz frequency, (c) top part of the cellwith micrometer screw gauge which moves reflector plate up and down and (d)multifrequency ultrasonic waves generator. 2: electromagnet setup (a) electro-magnets, (b) DC power supply. 3: constant temperature bath.

2 J.K. Patel, K. Parekh / Ultrasonics xxx (2014) xxx–xxx


26 August 2014

equipment however, such measurements can be done with thenuclear magnetic resonance (NMR) method [11,12]. By NMRexperiment, not only the local field of the magnetic nanofluidswere measured, but also the magnetization and particle concentra-tion in the cluster can be obtained.

The small-angle neutron scattering (SANS) is quite sensitive tothe aggregation processes in magnetic fluids [13]. Wide possibilitiesof the contrast variation (hydrogen/deuterium isotopic substitu-tion) in neutron experiments allow us to ‘look’ inside the aggre-gates. Also, the additional magnetic scattering of neutrons can beused for studying magnetic correlations in nano-systems withmagnetic inclusions. SANS distinguishes between magnetic andnonmagnetic components of ferrofluids allowing density, composi-tion, and magnetization profiles to be precisely determined.

Ultrasonic propagation in magnetic fluid is a simplest non-destructive method to investigate the structure formation withoutany prior modifications of the sample. Several studies have beenperformed to investigate the properties of ultrasonic propagationin magnetic fluid prepared in polar or non-polar carrier [14–21].In order to use this method for velocity profile measurement, itis important to have an accurate measurement of sound velocityin a magnetic fluid.

In the present paper we report the variation in ultrasoundvelocity, t, as a function of solid volume fraction for different tem-perature and magnetic field of magnetic fluids prepared in two dif-ferent carriers. These carriers are widely used in many engineeringdevices. Using the results of ultrasonic velocity profile, rheologicaland density measurement, various acoustic parameters werederived to understand the effect of temperature and magnetic field.This helps to understand the mechanism of cluster formation andor interaction between particles in the magnetic fluids.

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2. Experimental

Co-precipitation technique followed by digestion was used toprepare magnetic nanoparticles. The ratio of Fe2+ and Fe3+ was keptas 1:2. The particles were coated with oleic acid and then dispersedin kerosene and transformer oil [22]. The system is labeled as MFKand MFT respectively for kerosene base and transformer oil basedfluid. The density of fluid was measured using specific gravity bot-tle of 10 ml capacity. The Bruker powder X-ray diffractometermodel D2 Phaser with LYNEX EYE detector was used for the struc-tural investigation of particles. The data were collected at 2h anglefrom 10� to 80� with 0.02� steps. Philips Tecnai F20 was used tostudy the morphology of the particles. The magnetic propertiesof fluids were measured using Polytronic magnetometer modelBCS-100 using the principle of extraction method.

The ultrasonic sound velocity in the fluids was measured usingthe continuous wave ultrasonic interferometer (Mittal Enterprises)working at 2 MHz frequency with the accuracy of ±2 m/s. A digitalmicrometer screw (least count 0.001 mm) is used to lower or raisethe reflector plate connected to the cell. An experimental set-up isshown in Fig. 1. The specially designed jacketed measuring cell wasused to maintain the uniform temperature of the sample. The inletand outlet of the cell is connected to constant temperature bathwith the accuracy of ±0.1 K. The measuring cell containing approx-imately 3 ml of the sample is connected to the frequency generatorusing co-axial wire. The generator was fixed at 2 MHz frequency.The readings were noted by moving the micrometer screw, whencurrent meter shows maximum deflection. The measuring cellwas placed between the pole pieces of an electromagnet. Thedirection of magnetic field is perpendicular to the direction ofultrasonic wave propagation. The data were taken after 20 min ofthe application of magnetic field so as the system reach to the equi-librium [23].

Please cite this article in press as: J.K. Patel, K. Parekh, Effect of carrier andUltrasonics (2014), http://dx.doi.org/10.1016/j.ultras.2014.08.017

Viscosity of the samples were measured using 18318 RheolabQC (Anton Paar) attached with DG 26.7 measuring cup under con-stant shear rate (CSR) mode. Temperature was controlled with theaccuracy of ±0.1 K using constant temperature bath.

3. Results and discussion

The X-ray diffraction pattern shown in Fig. 2 represents a singlephase cubic spinel structure without any impurity phases. Thebroadness of all peaks indicates a typical characteristic of nanosizeparticles. Enhancements in intensity of peaks reveal the good crys-tallinity of the particles. Lattice parameter calculated from the pat-tern analysis is found as 0.8404 ± 0.0002 nm. This value is close tothe bulk value for Fe3O4 system (0.8396 nm) [24]. The size of theparticles calculated using Scherer’s formula for the most intense(311) reflection plane is 11.5 nm. The morphology of the particlesas seen from TEM image shows spherical shape particles. The par-ticle diameter was measured from the different portion of theimage and then plotted in histogram. The distribution of particlesize thus observed is fitted with the log-normal diameter distribu-tion function as described in Eq. (1). From the fit, the particle size isfound as 11.6 nm with size distribution, r as 0.25.

f ðDÞdðDÞ ¼ 1ffiffiffi2p

prDexp

� ln ðD=DmÞ2

2r2

!dD ð1Þ

Here, f(D)d(D) is the log-normal diameter distribution functionwith median diameter Dm and r is size distribution in ln(D). Thesolid volume fraction of the particles was determined using theactual density of carrier qc, density of particles, qp (5 g/cc) andthe density of the fluid, qf. The formula used to calculate the solidvolume fraction from the density is given in Eq. (2). Total five sam-ples in kerosene and four samples in transformer oil were preparedwith different volume fractions. The solid volume fraction of thesesamples is reported in Table 1. All the figures were drawn by con-sidering the solid volume fraction of the particles.

u ¼ ðqf � qcÞðqp � qcÞ

ð2Þ

The magnetic measurement of all fluid samples was investi-gated using extraction method. Fig. 3 shows the magnetic responseof the fluid under the influence of magnetic field. The fluid magne-tization of samples was calculated using fluid density and quantityof sample taken for the measurement. It is seen that as the volumefraction of the fluid increases the magnetization increases from116 to 312 kA/m for transformer oil based fluid while for

particle concentration on ultrasound properties of magnetic nanofluids,


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0 5 10 15 20

2θθ (degree)

(622)(622)

(440)(333)(422)

(400)

(311)

(220)

Inte

nsity

(a. u

.)

D (nm)

f(D) d

D

(111)

Fig. 2. X-ray diffrQ4 action pattern for Fe3O4 particles. TEM image and histogram derived from the TEM image. Line in histogram is fit to log-normal distribution function.

Table 1Density, viscosity, volume fraction and fluid magnetization of kerosene based and transformer oil based nanofluid at 303 K temperature.

Sample code Density (q) (g/cc) Volume fraction (U) Viscosity (g) @ 303 K (Mpa s) Fluid magnetization (Ms) (kA/m)

MFK1 0.882 0.0238 2.17 136MFK2 0.995 0.0506 2.87 210MFK3 1.108 0.0774 3.72 270MFK4 1.223 0.1057 5.00 390MFK5 1.337 0.1317 6.49 543MFT1 0.944 0.0283 14.4 116MFT2 1.016 0.0455 17.4 159MFT3 1.120 0.0704 24.2 237MFT4 1.214 0.0929 30.3 312

0.0 0.3 0.6 0.90

100

200

300

5 10 15100

200

300

400

500

600

MFT4

MFT3

MFT2

MFT

H (T)0.0 0.3 0.6 0.9

H (T)

MFl

uid

(kA

/m)

MFT1

0

100

200

300

400

500

600

MFK5

MFK4

MFK3

MFK2

MFK1

MFK MFK MFT

φ ( % )

Fig. 3. Magnetic measurement of kerosene and transformer oil based fluid with solid volume fraction.

J.K. Patel, K. Parekh / Ultrasonics xxx (2014) xxx–xxx 3


26 August 2014

kerosene-based fluid it increases from 136 to 543 kA/m. The fluidmagnetization when plotted as a function of solid volume fractionit is found that it increases linearly irrespective of the types of car-rier used for the dispersion. This shows that fluid is dilution insen-sitive in both the carrier to the limit of volume fraction used for theinvestigation.


The viscosity of all the samples was investigated as a function ofshear rate and temperature. Fig. 4 illustrates the plot of shearstress, s versus shear rate for kerosene and transformer oil basedmagnetic fluid for different volume fractions measured at 303 Ktemperature. The linear plot shows that the carriers as well asmagnetic fluid with different volume fractions possess Newtonian



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τ(Pa)

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T.Oil MFT1 MFT2 MFT3 MFT4

MFT4ηη (m

Pa.s

)

T (K)

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7.0

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Kerosene MFK1 MFK2 MFK3 MFk4 MFK5

T = 303 K

η (m

Pa.s

)T (K)

MFK5

-1(s )Shear rate

Fig. 4. Shear stress versus shear rate for (a) kerosene based fluid and (b) transformer oil based fluQ5 id measured at 303 K. Inset figure shows viscosity as a function oftemperature for concentrated sample.



26 August 2014

behavior. Similar results were observed by other researchers forrheological study of magnetic fluid carried out in absence of mag-netic field [20,21,25,26]. The temperature dependent viscosity wasmeasured in the range of 303–338 K temperature. A typical figureof g versus T for concentrated fluid sample is shown in the inset ofFig. 4. The decrement in viscosity with rise in temperature followsthe Arrhenius’s equation from which the activation energy is calcu-lated (fitting not shown). The activation energy for MFK system,found to decrease from 4.28 to 1.51 kcalk�1 mol�1 with increasingparticle volume fraction. While for MFT system, it decreases from5.97 to 5.76 kcalk�1 mol�1 from pure carrier to 4.55% volume frac-tion (MFT2) and then it increases to 5.97 kcalk�1 mol�1 for MFT4.The exact reason for such behavior can not be known but we sus-pect it due to the cluster formation at higher concentration intransformer oil, which results into the increase in activationenergy.

Fig. 5 shows the viscosity of fluid samples with different volumefraction and temperature. It is seen that viscosity increases as vol-ume fraction increases irrespective of the carrier. Viscosity of fluidas a function of volume fraction increases non-linearly (symbol)and it follows the Einstein Eq. (3) modified for hydrodynamic vol-ume fraction [6] considering the surfactant layer around magneticparticles (dotted line).

gg0¼ 1� 2:5/h þ ð2:5/c � 1Þ /h

/c

� �2" #

ð3Þ

where /h = / [(d + 2s)/d] with s is thickness of surfactant layer and/c is maximum volume fraction. With the increase in temperaturefrom 303 to 333 K viscosity decreases. The only difference withthe two carriers with the temperature rise is that the change inviscosity at lower and higher volume fraction is different in

0 5 10 150

2

4

6

φ (%)

T= 333 K

η(m

Pa.s

)

T= 303 K

MFK

Fig. 5. Viscosity, g, as a function of volume fractio


transformer oil as well as in kerosene. For transformer oil base flu-ids, this difference is more compared to that of kerosene base fluid.This observation can be attributed to the effect of carrier, since thethermal expansion co-efficient for transformer oil is one order ofmagnitude higher compared to that of kerosene. In addition to this,it is observed that the difference in viscosity as a function of tem-perature is lower for lower volume fraction as compared to viscos-ity difference at higher volume fractions (MFK5). This observedvariation can be attributed to the magnetic dipolar interactionwhich increases when volume fraction increases.

Fig. 6 shows the ultrasonic velocity propagation in magnetic fluidas a function of volume fraction and temperature from 303 to 333 Kfor both the systems. It is seen that ultrasonic velocity decreasesnon-linearly as the particle volume fraction increases (symbol).The ultrasound velocity in transformer oil is 1.388 km/s while thatfor kerosene is 1.262 km/s. The ultrasound velocity in transformeroil based fluid decreases from 1.298 km/s to 1.200 km/s as volumefraction increases from 0.0283 to 0.0929 at 303 K. This velocityfurther decreases to 1.200–1.108 km/s as temperature increasesfrom 303 to 333 K. This decrease follows second order polynomialfunction (dotted line). The similar trend is observed for kerosenebased fluid. For kerosene based fluid ultrasound velocity decreasesfrom 1.2 km/s to 1.052 km/s as volume fraction increases from0.0238 to 0.1317 at 303 K. This velocity further decreases to1.088–0.952 km/s as temperature increases from 303 to 333 K.The observed results are qualitatively agrees with macroscopic the-ory that predict a parabolic relationship between the ultrasonicvelocity of magnetic fluid and the concentration of the particles [20].

Ultrasonic velocity of water based magnetic fluid reported byNabeel Rashin and Hemalatha [17,18] shows increase in velocitywith increase in temperature. This is because of the thermal rup-ture of the open packed structure of water, which in turn enhances

0 5 10

5

10

15

20

25

30

φ (%)

η(m

Pa.s

)

MFT

T= 333 K

T= 303 K

n, / for 303, 313, 323 and 333 K temperature.



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1.1

1.2

1.3

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1.4

T= 333 K

MFK

υ( k

m/s

)

υ( k

m/s

)

φ (%) φ (%)

T= 303 K MFT

T= 333 K

T= 303 K

Fig. 6. Ultrasonic velocity as a function of volume fraction, / for 303, 313, 323 and 333 K temperature.



26 August 2014

the cohesion of water molecules and less compressible closedpacked structure leading to an increase in the ultrasonic velocity.In the present work, the non-polar carrier, kerosene and trans-former oil, is used which shows decrease in ultrasound velocitywith increasing temperature. This is due to the increase in collisionbetween the carrier molecules as temperature increases whichconsequently reduces the velocity of sound wave propagation.Similar trend is observed in magnetic fluid prepared in these twocarriers. The results are in agreement with those observed by otherresearchers [14,16,20,21].

The decrement in ultrasonic velocity at higher temperature andhigher volume fraction can be explained by considering the varia-tion of adiabatic compressibility (b = 1/qv2) and mean free path(Lmfp = K(b)1/2) between particles. Here, K is temperature dependentJacobson’s constant calculated as K = (93.875 + (0.345 * T)) * 10�8

[27].Fig. 7 shows the plot of the adiabatic compressibility and mean

free path. The volume fraction is corrected for the thermal expan-sion of carrier as it is relatively large. After correction, both param-eters, b and Lmfp, were plotted which shows decrement withincrease in volume fraction and increment with increasing temper-ature. The variation in adiabatic compressibility and mean freepath with increase in volume fraction and temperature can beattributed to the change in number density of the particles. Sincethe number density of particles increases at higher volume frac-tion, the particles come closer and making the system denserwhich inhibits the sound wave propagation. Increase in tempera-ture will reduces the number density of particles and hence

2.5

3.0

3.5

MFK

φ (%)

T= 333 K

T= 303 K

7

8

9

10MFK

T= 303 K

T= 333 K

0 5 10 15

β (1

0-10 P

a-1)

L mfp

(10-2

nm

)

Fig. 7. Mean free path, Lmfp, and adiabatic compressibility, b, as


resulted into increase of mean free path and adiabatic compress-ibility. In order to enhance the understanding of the system it isnecessary to calculate the attenuation of sound wave in medium.Earlier, several researchers [19–21] have reported the study ofultrasonic propagation velocity and attenuation in a magneticfluid. They have used the pulse generator as a source of ultrasonicwave. In our case the ultrasonic interferometer is a continuoussource of ultrasound wave with defined frequency. Moreover, theattenuation coefficient is a measure of spatial rate of decrease inthe intensity level on ultrasonic waves in a medium hence itdepends on the characteristic of the medium. Treating the propa-gation of sound as an adiabatic phenomenon and following Stoke’stheory, absorption may be taken as being proportional to the vis-cosity of the medium (g) and the square of the frequency [28]which is described as a/f2 = (8k2g)/(3qv3). Fig. 8 represents the var-iation in attenuation as a function of volume fraction for differenttemperatures. It is seen that the attenuation of sound waveincreases non-linearly with increasing volume fraction as expectedfor both the systems. However, the effect of temperature inkerosene base fluid and transformer oil base fluid is drastically dif-ferent. For MFK system the attenuation data overlap for all temper-atures making temperature insensitive system whereas for thecase of MFT system the attenuation decreases with increasing tem-perature. In addition to this, for transformer oil based fluid, the dif-ference in attenuation for lower volume fraction is less comparedto that for higher volume fraction.

The possible reason for the first observation can be explainedby considering the structural difference between the carriers.

β (1

0-10 P

a-1)

φ (%)

L mfp

(10-2

nm

)

0 5 10

4.8

5.2

5.6

MFTT= 333 K

T= 303 K

5.6

6.3

7.0

7.7 MFT

T= 303 K

T= 333 K

a function of / for 303, 313, 323 and 333 K temperature.



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0.5

1.0

MFK

φ (%) φ (%)

T= 333 K

T= 303 K

α/f2 (1

0-14 s

2 m-1)

α/f2 (1

0-14 s

2 m-1)

0 5 10 15 0 5 10

1.0

2.0

3.0MFT

T= 333 K

T= 303 K

Fig. 8. Attenuation (a/f2) as a function of / for 30, 40, 50 and 60 �C temperature.

1.05

1.10

1.15

1.20

0 200 400 600 800 1000

1.20

1.25

1.30

4.0

6.0

8.0

15.0

18.0

21.0

24.0

27.0

30.0

T= 308 KMFK2

MFK3MFK5

MFK1

υ(k

m/s

)

H (kA/m)

T= 308 K

MFT3

MFT2

MFT4

MFT1

MFK3

MFK1

MFK2

α/f

2 (10-1

4 m)

T= 308 KMFK5 T= 308 K

MFT3

MFT2MFT1

MFT4

0 200 400 600 800 1000H (kA/m)

Fig. 9. Velocity profile and attenuation as a function of magnetic field for MFK and MFT system carried out at 308 K temperature.



26 August 2014

Kerosene is a light hydrocarbon liquid comprising of C12 to C15 car-bon. The molecular formulas can range from C12H26 to C15H32.While, transformer oil is a highly refined mineral oil consisting oflight mixtures of alkanes in the C15 to C40 range and cyclic paraffin.As a result, when oleic acid (C17H33�COOH) coated particles are dis-persed in kerosene the tail of oleic acid is quite compatible withthe kerosene medium compared to transformer oil. So the proba-bility of homogeneous dispersion of oleic acid coated particles ismore in kerosene compared to transformer oil. Hence, transformeroil leads to form aggregates even if the volume fraction is low. As aresult, the attenuation of ultrasonic wave in transformer oil basedfluid is more compared to that in kerosene base fluid. With increas-ing volume fraction the probability of structure formationincreases. Similar observation has been reported by Jozefczaket al. [20] in their study of temperature dependent ultrasonic mea-surement of transformer oil based fluid. They explained the varia-tion in attenuation data using the concept of visco-inertialand thermal processes by considering the model proposed byVinogradov-Isakovich [29]. From the fitting of ultrasonic data withparticle size distribution function they confirm the breaking ofaggregates or clusters at large temperature. The similar argumentcan be applied in the present case also. The argument of structureformation can be further substantiate by considering the conceptof dipolar interactions and coupling constant, k of the system.In the present case the value of coupling constant k, defined by


k = l0Md2V/24kBT is found as 1.97 for magnetite particles. Since

the number densities of particles increases at higher volume frac-tion and particles are magnetic in nature they form some kind ofoligomer structures due to van der Waal’s and magnetic dipolarinteractions among them. This structure can be reversible in natureand can be completely broken if enough thermal energy is pro-vided. At 333 K temperature, the thermal energy starts breakingthe structure of particles making the system homogeneous disper-sion of nanomagnetic particles. This leads to increase the free spacebetween the particles helping sound waves to propagate easily. Asa result, the attenuation of sound wave propagation decreases athigher temperature. The same concept is applicable to system oflow concentration. The only difference at low volume fraction isthe lesser probability of structures formation and hence increaseof free space with increasing temperature is also less. So the differ-ence in attenuation is less.

The application of magnetic field leads to enhance structure for-mation in the system. The type of structure formation depends onthe carrier matrix, type and nature of particles as well as the fieldstrength and temperature. These systems were placed under mag-netic field where the direction of magnetic field is perpendicular tothe ultrasonic wave propagation direction. Fig. 9 shows the veloc-ity of ultrasound wave for transformer oil based and kerosenebased fluid. It is seen that kerosene base fluid shows slight increasein velocity at certain field strength and then it remains almost



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26 August 2014

constant with the field up to 1000 kA/m. Whereas in transformeroil based fluid, the ultrasound velocity continuously increases withthe increase in field. The magnetic response of the fluid will bedefined by its initial susceptibility which is derived from the valueof coupling constant as vi = 8uk. As volume fraction increases, theprobability of structure formation (clusters and or chain) increases.So for magnetite, even for small u the value of vi is high enough toform a long chain or clusters. As a result, they leave free space inthe medium helping sound wave to propagate faster compared tozero magnetic field. If this clusters or chains are close enough thenit helps to transfer the heat and as a result the thermal conductiv-ity of nanofluids increases. These results are helpful to enhance thethermal conductivity of nanofluids as it is observed that clusterformation in magnetic nanofluids drastically enhances the thermalconductivity [29,30].

From the results of ultrasonic velocity the attenuation is calcu-lated and same is illustrating in Fig. 9. It is seen that for kerosenebase fluid attenuation remains constant for all concentrations.While for transformer oil based fluid attenuation decreases withincrease in magnetic field. As the attenuation reveals the informa-tion of cluster formation in the system, one can say that thedecrease in attenuation with increasing field is due to the inhomo-geneous distribution of particles in medium, leading to increasethe free space. As a result the attenuation decreases at higher fieldstrength.

4. Conclusion

The ultrasonic velocity in magnetic fluid has been investigatedfor different concentration of particles in kerosene and transformeroil based fluid. The decrease in ultrasonic velocity with increase involume fraction can be explained using increasing number densityof particles, which leads to form structures of particles. Thesestructures start collapses at higher temperature leading decrementof sound wave attenuation. Moreover, the possibility of structureformation is more in transformer oil compared to kerosene. Theprobability of field induced structure formation is more in trans-former oil compared to kerosene because of its chemical structuraldifference.

5. Uncited reference

[31].

Acknowledgments

Authors would like to thank Prof. R.V. Upadhyay, Changa forconstructive suggestions. The work is carried out under GUJCOSTsponsored project.

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effect of carrier and particle concentration on ultrasound properties of magnetic nanofluids

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