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

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

3 4 7

Q1

8

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

9 10

a r t i c l e

1 2 2 3 13 14 15 16 17

i n f o

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

18 19 20 21 22

Keywords: Magnetic fluid Ultrasonic wave propagation Nanofluid

a b s t r a c t Ultrasound wave propagation in nanofluids and its rheological behavior has been studied as a function of solid volume fraction, temperature and magnetic field for magnetic nanofluids synthesized in kerosene and transformer oil. Ultrasonic velocity decreases while viscosity increases with increasing volume fraction. The attenuation of ultrasonic wave is explained using dipolar coupling co-efficient which favors oligomer structures with increasing number density of particles. The structure formation increases further with increase in magnetic field which is prominent in transformer oil compared to kerosene. This difference can be due to the structural difference between these two carriers. Ó 2014 Published by Elsevier B.V.

24 25 26 27 28 29 30 31 32 33

34 35

1. Introduction

36

Magnetic nanofluids represent a technologically important material because of its wide scope of tuning the macroscopic behavior under different environment. Recent experiments and analysis show that magnetic dipole force and strong magnetic field expels nanoparticles to form chains and aggregates that can greatly affect the macroscopic properties of ferrofluids even for low concentration [1–6]. The formation of structural pattern in the magnetic fluid and its thin film under the influence of magnetic field can be investigated by optical microscopy, strong light diffraction image, electron microscopy, nuclear magnetic resonance (NMR) technique, small-angle neutron scattering (SANS), acoustical study and rheological studies [7–16]. This clustering has a significant influence on the properties of magnetic fluid and hence its further use. In 1975, Hayes had reported needle-like clusters or aggregates of the magnetic particles in nanofluids through optical microscopic observations under the influence of an external magnetic field [7]. Though magnetic nanofluids is an opaque liquid when it is sandwiched by two glass slides and pressed to a thin film of a few tens of micron thickness, visible light can be transmitted through the magnetic nanofluids film. The alternate study is to project the transmitted light on screen and obtain a peculiar scattering light pattern. Haas and Adams [8] observed a peculiar projection of the transmitted light from the diluted magnetic nanofluid’s film when the field was perpendicular to the light propagation. The

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Q2

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

needle-like clusters in the magnetic nanofluids play a role of grating of an optical diffraction grating. The strong diffraction effect is due to the periodical spacing between the needlelike clusters. On the contrary, by measuring the diffraction light intensity as a function of the diffraction angle, one can calculate the spacing of the clusters by Fourier transform [9]. The lower limit of an ordinary optical microscope’s resolution is about a micron. Therefore, if the clusters are lesser than the micron size then it cannot be distinguished by the optical microscope. Although, nanometer-size objects can be investigated by an electron microscope; it has a fatal disadvantage of an evacuated sample room. The solvent has to evaporate before observation and that limits the investigation as the drying process exceeds the aggregations of particles. Donselaar et al. [10] succeeded in observing clusters of submicron scale in the magnetic nanofluids in a frozen state by an electron microscope. However, from a more critical viewpoint, even these sub-micron clusters might be formed during the quenching process. When one studies the magnetic colloidal particle behavior in the Magnetic nanofluids, it is necessary to know how strong the magnetic field is at the particle position. The so-called local magnetic field at the particle position, Hloc, is different from an external field, H. In addition to H, there are magnetic fields generated by the permanent magnetic moments of all other surrounded magnetic particles. If the colloidal particles are uniformly distributed, the problem is not so difficult, but the existence of clusters in the nanofluids together with the colloidal particles makes the problem more complicated. The local field, Hloc, inside the cluster should be much stronger than that at the rest of the system. However, as the cluster is micron size it is difficult to measure Hloc with ordinary

http://dx.doi.org/10.1016/j.ultras.2014.08.017 0041-624X/Ó 2014 Published by Elsevier B.V.

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

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equipment however, such measurements can be done with the nuclear magnetic resonance (NMR) method [11,12]. By NMR experiment, not only the local field of the magnetic nanofluids were measured, but also the magnetization and particle concentration in the cluster can be obtained. The small-angle neutron scattering (SANS) is quite sensitive to the aggregation processes in magnetic fluids [13]. Wide possibilities of the contrast variation (hydrogen/deuterium isotopic substitution) in neutron experiments allow us to ‘look’ inside the aggregates. Also, the additional magnetic scattering of neutrons can be used for studying magnetic correlations in nano-systems with magnetic inclusions. SANS distinguishes between magnetic and nonmagnetic components of ferrofluids allowing density, composition, and magnetization profiles to be precisely determined. Ultrasonic propagation in magnetic fluid is a simplest nondestructive method to investigate the structure formation without any prior modifications of the sample. Several studies have been performed to investigate the properties of ultrasonic propagation in magnetic fluid prepared in polar or non-polar carrier [14–21]. In order to use this method for velocity profile measurement, it is important to have an accurate measurement of sound velocity in a magnetic fluid. In the present paper we report the variation in ultrasound velocity, t, as a function of solid volume fraction for different temperature and magnetic field of magnetic fluids prepared in two different carriers. These carriers are widely used in many engineering devices. Using the results of ultrasonic velocity profile, rheological and density measurement, various acoustic parameters were derived to understand the effect of temperature and magnetic field. This helps to understand the mechanism of cluster formation and or interaction between particles in the magnetic fluids.

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2. Experimental

123

Co-precipitation technique followed by digestion was used to prepare magnetic nanoparticles. The ratio of Fe2+ and Fe3+ was kept as 1:2. The particles were coated with oleic acid and then dispersed in kerosene and transformer oil [22]. The system is labeled as MFK and MFT respectively for kerosene base and transformer oil based fluid. The density of fluid was measured using specific gravity bottle of 10 ml capacity. The Bruker powder X-ray diffractometer model D2 Phaser with LYNEX EYE detector was used for the structural investigation of particles. The data were collected at 2h angle from 10° to 80° with 0.02° steps. Philips Tecnai F20 was used to study the morphology of the particles. The magnetic properties of fluids were measured using Polytronic magnetometer model BCS-100 using the principle of extraction method. The ultrasonic sound velocity in the fluids was measured using the continuous wave ultrasonic interferometer (Mittal Enterprises) working at 2 MHz frequency with the accuracy of ±2 m/s. A digital micrometer screw (least count 0.001 mm) is used to lower or raise the reflector plate connected to the cell. An experimental set-up is shown in Fig. 1. The specially designed jacketed measuring cell was used to maintain the uniform temperature of the sample. The inlet and outlet of the cell is connected to constant temperature bath with the accuracy of ±0.1 K. The measuring cell containing approximately 3 ml of the sample is connected to the frequency generator using co-axial wire. The generator was fixed at 2 MHz frequency. The readings were noted by moving the micrometer screw, when current meter shows maximum deflection. The measuring cell was placed between the pole pieces of an electromagnet. The direction of magnetic field is perpendicular to the direction of ultrasonic wave propagation. The data were taken after 20 min of the application of magnetic field so as the system reach to the equilibrium [23].

124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153

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

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

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3. Results and discussion

158

The X-ray diffraction pattern shown in Fig. 2 represents a single phase cubic spinel structure without any impurity phases. The broadness of all peaks indicates a typical characteristic of nanosize particles. Enhancements in intensity of peaks reveal the good crystallinity of the particles. Lattice parameter calculated from the pattern analysis is found as 0.8404 ± 0.0002 nm. This value is close to the bulk value for Fe3O4 system (0.8396 nm) [24]. The size of the particles calculated using Scherer’s formula for the most intense (3 1 1) reflection plane is 11.5 nm. The morphology of the particles as seen from TEM image shows spherical shape particles. The particle diameter was measured from the different portion of the image and then plotted in histogram. The distribution of particle size thus observed is fitted with the log-normal diameter distribution function as described in Eq. (1). From the fit, the particle size is found as 11.6 nm with size distribution, r as 0.25.

159

!

 ln ðD=Dm Þ2 dD f ðDÞdðDÞ ¼ pffiffiffi exp 2r 2 2prD 1

155 156 157

160 161 162 163 164 165 166 167 168 169 170 171 172 173

174

ð1Þ 176

Here, f(D)d(D) is the log-normal diameter distribution function with median diameter Dm and r is size distribution in ln(D). The solid volume fraction of the particles was determined using the actual density of carrier qc, density of particles, qp (5 g/cc) and the density of the fluid, qf. The formula used to calculate the solid volume fraction from the density is given in Eq. (2). Total five samples in kerosene and four samples in transformer oil were prepared with different volume fractions. The solid volume fraction of these samples is reported in Table 1. All the figures were drawn by considering the solid volume fraction of the particles.

177 178 179 180 181 182 183 184 185 186

187

u¼

ðqf  qc Þ ðqp  qc Þ

ð2Þ

The magnetic measurement of all fluid samples was investigated using extraction method. Fig. 3 shows the magnetic response of the fluid under the influence of magnetic field. The fluid magnetization of samples was calculated using fluid density and quantity of sample taken for the measurement. It is seen that as the volume fraction of the fluid increases the magnetization increases from 116 to 312 kA/m for transformer oil based fluid while for

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

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Intensity (a. u.)

(311)

(220)

(333) (440)

(400)

(111) (622)

(422)

20

40

(622)

60

80

f(D) dD

2θ (degree)

0

5

10

15

20

D (nm) Q4

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

Table 1 Density, 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 MFK2 MFK3 MFK4 MFK5 MFT1 MFT2 MFT3 MFT4

0.882 0.995 1.108 1.223 1.337 0.944 1.016 1.120 1.214

0.0238 0.0506 0.0774 0.1057 0.1317 0.0283 0.0455 0.0704 0.0929

2.17 2.87 3.72 5.00 6.49 14.4 17.4 24.2 30.3

136 210 270 390 543 116 159 237 312

600

MFT

MFluid (kA/m)

300

600

MFK MFK5

500

MFT4

MFK MFT

500

400 400

MFT3

200

MFK4

300

100

200

MFK2

MFT1

200

100 0 0.0

300

MFK3

MFT2

MFK1

0 0.3

0.6

0.9

100 0.0

H (T)

0.3

0.6

H (T)

0.9

5

10

15

φ (%)

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

197 198 199 200 201 202

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

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

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η (mPa.s)

6.5 6.0 5.5 MFK5

20

5.0

15

4.5 280

300

320

120 100

40

T.Oil MFT1 MFT2 MFT3 MFT4

30 20

80

10

τ (Pa)

τ (Pa)

25

Kerosene MFK1 MFK2 MFK3 MFk4 MFK5

7.0

30

η (mPa.s)

4

340

T (K)

60

MFT4

280

300

20

5

T=303 K

T = 303 K

0

0 1000

2000

3000

0

4000

1000

-1

212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231

232

234 235 236 237 238 239

4000

-1

behavior. Similar results were observed by other researchers for rheological study of magnetic fluid carried out in absence of magnetic field [20,21,25,26]. The temperature dependent viscosity was measured in the range of 303–338 K temperature. A typical figure of g versus T for concentrated fluid sample is shown in the inset of Fig. 4. The decrement in viscosity with rise in temperature follows the Arrhenius’s equation from which the activation energy is calculated (fitting not shown). The activation energy for MFK system, found to decrease from 4.28 to 1.51 kcalk1 mol1 with increasing particle volume fraction. While for MFT system, it decreases from 5.97 to 5.76 kcalk1 mol1 from pure carrier to 4.55% volume fraction (MFT2) and then it increases to 5.97 kcalk1 mol1 for MFT4. The exact reason for such behavior can not be known but we suspect it due to the cluster formation at higher concentration in transformer oil, which results into the increase in activation energy. Fig. 5 shows the viscosity of fluid samples with different volume fraction and temperature. It is seen that viscosity increases as volume fraction increases irrespective of the carrier. Viscosity of fluid as a function of volume fraction increases non-linearly (symbol) and it follows the Einstein Eq. (3) modified for hydrodynamic volume fraction [6] considering the surfactant layer around magnetic particles (dotted line).

"

 2 # g / ¼ 1  2:5/h þ ð2:5/c  1Þ h g0 /c

ð3Þ

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

6

transformer oil as well as in kerosene. For transformer oil base fluids, this difference is more compared to that of kerosene base fluid. This observation can be attributed to the effect of carrier, since the thermal expansion co-efficient for transformer oil is one order of magnitude higher compared to that of kerosene. In addition to this, it is observed that the difference in viscosity as a function of temperature is lower for lower volume fraction as compared to viscosity difference at higher volume fractions (MFK5). This observed variation can be attributed to the magnetic dipolar interaction which increases when volume fraction increases. Fig. 6 shows the ultrasonic velocity propagation in magnetic fluid as a function of volume fraction and temperature from 303 to 333 K for both the systems. It is seen that ultrasonic velocity decreases non-linearly as the particle volume fraction increases (symbol). The ultrasound velocity in transformer oil is 1.388 km/s while that for kerosene is 1.262 km/s. The ultrasound velocity in transformer oil based fluid decreases from 1.298 km/s to 1.200 km/s as volume fraction increases from 0.0283 to 0.0929 at 303 K. This velocity further decreases to 1.200–1.108 km/s as temperature increases from 303 to 333 K. This decrease follows second order polynomial function (dotted line). The similar trend is observed for kerosene based fluid. For kerosene based fluid ultrasound velocity decreases from 1.2 km/s to 1.052 km/s as volume fraction increases from 0.0238 to 0.1317 at 303 K. This velocity further decreases to 1.088–0.952 km/s as temperature increases from 303 to 333 K. The observed results are qualitatively agrees with macroscopic theory that predict a parabolic relationship between the ultrasonic velocity of magnetic fluid and the concentration of the particles [20]. Ultrasonic velocity of water based magnetic fluid reported by Nabeel Rashin and Hemalatha [17,18] shows increase in velocity with increase in temperature. This is because of the thermal rupture of the open packed structure of water, which in turn enhances 30

MFK

25

η (mPa.s)

211

3000

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

η (mPa.s)

210

2000

Shear rate (s )

Shear rate (s )

209

340

40

10

Q5

320

T (K)

4

T= 303 K

T= 333 K

2

MFT

20 15

T= 303 K

10

T= 333 K

5 0 0

5

10

φ (%)

15

0

5

10

φ (%)

Fig. 5. Viscosity, g, as a function of volume fraction, / for 303, 313, 323 and 333 K temperature.

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

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1.3

MFK

T= 303 K

T= 303 K υ (km/s)

υ (km/s)

1.2

1.4

1.1

MFT

1.3

1.2

1.0

T= 333 K

T= 333 K

1.1

0.9 0

5

10

15

0

5

φ (%)

10

φ (%)

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

284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299

MFK

T= 333 K

7.7

T= 333 K

MFT

10 -1

283

Pa )

282

9 8 7

7.0

-10

281

β (10

280

T= 303 K

6.3

T= 303 K 5.6

MFK

T= 333 K

MFT

T= 333 K

3.5

5.6

-2

279

resulted into increase of mean free path and adiabatic compressibility. In order to enhance the understanding of the system it is necessary to calculate the attenuation of sound wave in medium. Earlier, several researchers [19–21] have reported the study of ultrasonic propagation velocity and attenuation in a magnetic fluid. They have used the pulse generator as a source of ultrasonic wave. In our case the ultrasonic interferometer is a continuous source of ultrasound wave with defined frequency. Moreover, the attenuation coefficient is a measure of spatial rate of decrease in the intensity level on ultrasonic waves in a medium hence it depends on the characteristic of the medium. Treating the propagation of sound as an adiabatic phenomenon and following Stoke’s theory, absorption may be taken as being proportional to the viscosity of the medium (g) and the square of the frequency [28] which is described as a/f2 = (8k2g)/(3qv3). Fig. 8 represents the variation in attenuation as a function of volume fraction for different temperatures. It is seen that the attenuation of sound wave increases non-linearly with increasing volume fraction as expected for both the systems. However, the effect of temperature in kerosene base fluid and transformer oil base fluid is drastically different. For MFK system the attenuation data overlap for all temperatures making temperature insensitive system whereas for the case of MFT system the attenuation decreases with increasing temperature. In addition to this, for transformer oil based fluid, the difference in attenuation for lower volume fraction is less compared to that for higher volume fraction. The possible reason for the first observation can be explained by considering the structural difference between the carriers.

L mfp (10 nm)

278

-1

277

Pa )

276

-10

275

β (10

274

the cohesion of water molecules and less compressible closed packed structure leading to an increase in the ultrasonic velocity. In the present work, the non-polar carrier, kerosene and transformer oil, is used which shows decrease in ultrasound velocity with increasing temperature. This is due to the increase in collision between the carrier molecules as temperature increases which consequently reduces the velocity of sound wave propagation. Similar trend is observed in magnetic fluid prepared in these two carriers. The results are in agreement with those observed by other researchers [14,16,20,21]. The decrement in ultrasonic velocity at higher temperature and higher volume fraction can be explained by considering the variation of adiabatic compressibility (b = 1/qv2) and mean free path (Lmfp = K(b)1/2) between particles. Here, K is temperature dependent Jacobson’s constant calculated as K = (93.875 + (0.345 * T)) * 108 [27]. Fig. 7 shows the plot of the adiabatic compressibility and mean free path. The volume fraction is corrected for the thermal expansion of carrier as it is relatively large. After correction, both parameters, b and Lmfp, were plotted which shows decrement with increase in volume fraction and increment with increasing temperature. The variation in adiabatic compressibility and mean free path with increase in volume fraction and temperature can be attributed to the change in number density of the particles. Since the number density of particles increases at higher volume fraction, the particles come closer and making the system denser which inhibits the sound wave propagation. Increase in temperature will reduces the number density of particles and hence

-2

273

L mfp (10 nm)

272

3.0

T= 303 K

5.2

T= 303 K

4.8 2.5 0

5

10

φ (%)

15

0

5

10

φ (%)

Fig. 7. Mean free path, Lmfp, and adiabatic compressibility, b, as a function of / for 303, 313, 323 and 333 K temperature.

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

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T= 303 K

-1

sm )

-1

sm )

MFK

α /f (10

-14

-14

T= 303 K

T= 333 K

2.0

2

α /f (10

2

MFT

3.0

2

2

1.0

0.5

0

5

10

T= 333 K

1.0

15

0

5

10

φ (%)

φ (%)

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

MFK5 T= 308 K 8.0

30.0

MFT4

T= 308 K

MFK3

6.0

24.0

MFT3

21.0

2

α /f (10

-14

m)

27.0

MFK2

MFT2

18.0 4.0

MFK1

MFT1

15.0

1.20

υ (km/s)

MFK1 1.15

T= 308 K

1.30

MFT2

MFK2

MFT3

1.25 1.10

MFT4

MFK3 1.05

MFK5 0

200

400

600

800 1000

H (kA/m)

MFT1

1.20

T= 308 K 0

200

400

600

800 1000

H (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.

328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352

Kerosene is a light hydrocarbon liquid comprising of C12 to C15 carbon. The molecular formulas can range from C12H26 to C15H32. While, transformer oil is a highly refined mineral oil consisting of light mixtures of alkanes in the C15 to C40 range and cyclic paraffin. As a result, when oleic acid (C17H33COOH) coated particles are dispersed in kerosene the tail of oleic acid is quite compatible with the kerosene medium compared to transformer oil. So the probability of homogeneous dispersion of oleic acid coated particles is more in kerosene compared to transformer oil. Hence, transformer oil leads to form aggregates even if the volume fraction is low. As a result, the attenuation of ultrasonic wave in transformer oil based fluid is more compared to that in kerosene base fluid. With increasing volume fraction the probability of structure formation increases. Similar observation has been reported by Jozefczak et al. [20] in their study of temperature dependent ultrasonic measurement of transformer oil based fluid. They explained the variation in attenuation data using the concept of visco-inertial and thermal processes by considering the model proposed by Vinogradov-Isakovich [29]. From the fitting of ultrasonic data with particle size distribution function they confirm the breaking of aggregates or clusters at large temperature. The similar argument can be applied in the present case also. The argument of structure formation can be further substantiate by considering the concept of dipolar interactions and coupling constant, k of the system. In the present case the value of coupling constant k, defined by

k = l0M2dV/24kBT is found as 1.97 for magnetite particles. Since the number densities of particles increases at higher volume fraction and particles are magnetic in nature they form some kind of oligomer structures due to van der Waal’s and magnetic dipolar interactions among them. This structure can be reversible in nature and can be completely broken if enough thermal energy is provided. At 333 K temperature, the thermal energy starts breaking the structure of particles making the system homogeneous dispersion of nanomagnetic particles. This leads to increase the free space between the particles helping sound waves to propagate easily. As a result, the attenuation of sound wave propagation decreases at higher temperature. The same concept is applicable to system of low concentration. The only difference at low volume fraction is the lesser probability of structures formation and hence increase of free space with increasing temperature is also less. So the difference in attenuation is less. The application of magnetic field leads to enhance structure formation in the system. The type of structure formation depends on the carrier matrix, type and nature of particles as well as the field strength and temperature. These systems were placed under magnetic field where the direction of magnetic field is perpendicular to the ultrasonic wave propagation direction. Fig. 9 shows the velocity of ultrasound wave for transformer oil based and kerosene based fluid. It is seen that kerosene base fluid shows slight increase in velocity at certain field strength and then it remains almost

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

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constant with the field up to 1000 kA/m. Whereas in transformer oil based fluid, the ultrasound velocity continuously increases with the increase in field. The magnetic response of the fluid will be defined by its initial susceptibility which is derived from the value of coupling constant as vi = 8uk. As volume fraction increases, the probability of structure formation (clusters and or chain) increases. So for magnetite, even for small u the value of vi is high enough to form a long chain or clusters. As a result, they leave free space in the medium helping sound wave to propagate faster compared to zero magnetic field. If this clusters or chains are close enough then it helps to transfer the heat and as a result the thermal conductivity of nanofluids increases. These results are helpful to enhance the thermal conductivity of nanofluids as it is observed that cluster formation in magnetic nanofluids drastically enhances the thermal conductivity [29,30]. From the results of ultrasonic velocity the attenuation is calculated and same is illustrating in Fig. 9. It is seen that for kerosene base fluid attenuation remains constant for all concentrations. While for transformer oil based fluid attenuation decreases with increase in magnetic field. As the attenuation reveals the information of cluster formation in the system, one can say that the decrease in attenuation with increasing field is due to the inhomogeneous distribution of particles in medium, leading to increase the free space. As a result the attenuation decreases at higher field strength.

403

4. Conclusion

404

414

The ultrasonic velocity in magnetic fluid has been investigated for different concentration of particles in kerosene and transformer oil based fluid. The decrease in ultrasonic velocity with increase in volume fraction can be explained using increasing number density of particles, which leads to form structures of particles. These structures start collapses at higher temperature leading decrement of sound wave attenuation. Moreover, the possibility of structure formation is more in transformer oil compared to kerosene. The probability of field induced structure formation is more in transformer oil compared to kerosene because of its chemical structural difference.

415

5. Uncited reference

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405 406 407 408 409 410 411 412 413

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Q3

[31].

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Acknowledgments

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Authors would like to thank Prof. R.V. Upadhyay, Changa for constructive suggestions. The work is carried out under GUJCOST sponsored project.

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