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Temperature dependent acoustic properties of temperature sensitive magnetic fluid subjected to magnetic field
Accepted Manuscript Temperature dependent acoustic properties of temperature sensitive magnetic fluid subjected to magnetic field
Kinnari Parekh, Jaykumar Patel, R.V. Upadhyay PII: DOI: Reference:
S0167-7322(17)34038-2 doi:10.1016/j.molliq.2017.10.090 MOLLIQ 8052
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
1 September 2017 12 October 2017 18 October 2017
Please cite this article as: Kinnari Parekh, Jaykumar Patel, R.V. Upadhyay , Temperature dependent acoustic properties of temperature sensitive magnetic fluid subjected to magnetic field. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Molliq(2017), doi:10.1016/j.molliq.2017.10.090
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ACCEPTED MANUSCRIPT Temperature dependent acoustic properties of temperature sensitive magnetic fluid subjected to magnetic field Kinnari Parekha*, Jaykumar Patela, R V Upadhyaya,b a
Dr. K. C. Patel R & D Center, bP. D. Institute of Applied Sciences, Charotar University of Science & Technology, Changa-388421, Gujarat, India.
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*Corresponding Author’s e-mail: [email protected]
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Abstract
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The ultrasonic velocity of temperature sensitive magnetic fluid is investigated as a function of volume fraction, temperature and magnetic field. The ultrasonic velocity decreases
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with increasing volume fraction of magnetic nanoparticles. This is attributed to the particlecarrier interaction which leads to form shorter aggregates. The pre-aggregates in magnetic fluid
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break when temperature increases in the absence of a field. Magnetic field makes the system anisotropic to ultrasound wave propagation. The change in ultrasonic propagation velocity under
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the influence of magnetic field shows chain like alignment for low volume fraction of magnetic nanoparticles (1.6 %) which changes to short dipolar chains at an intermediate volume fraction
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(6.8 %). Above this volume fraction, short chains become thicker by aligning sidewise to the neighboring chains resulting in spherical drop like structures. The modified Tarapov’s theory fit
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to change in ultrasonic propagation velocity confirms the transformation from chains to aggregates with increasing magnetic nanoparticles volume fraction. The optical microscopy
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study also confirms the results. Upon increasing the temperature the field dependent velocity variation shows breaking of thick chain like aggregates. The modified Tarapov’s theory fit shows
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that this is attributed to decrease in magnetic moment with increasing temperature. The variation of magnetic moment with temperature obtained from the fitting gives the Curie temperature of fluid as 363 K. This value agrees with those obtained from other techniques.
Keywords: magnetic fluid; acoustic properties; nanoparticles structure; transformer oil
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ACCEPTED MANUSCRIPT 1.
INTRODUCTION Magnetic fluid represents a technologically important material because of its wide scope
of tuning the macroscopic behaviour 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 magnetic fluid even at low concentration [1–6]. In the absence of external magnetic field, magnetic fluid behaves like a
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normal suspension containing magnetic nanoparticles but the exposure of the magnetic field
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induces the dipole moment in particle as a result particles respond to the magnetic field either
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through Neel rotation or through Brownian rotation. In addition to the particle-field interaction, particles experience short-range van der Waals and magnetic dipolar attractive forces. The
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collective behavior of the same will produce different structures within the carrier matrix. Ultrasonic propagation in magnetic fluid is a non-destructive method to investigate the
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structure formation without any prior modifications of the sample such as thin film preparation, drying or freezing of the sample, etc., and have maximum sample recovery. In addition, the It offers an added advantage to
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study can be performed for a concentrated system too.
investigate the study under different magnetic field and temperature without changing the
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geometry of the experimental set-up. Moreover, it is possible to study the simultaneous effect of these parameters, i.e., particle concentration (φ), temperature (T), and magnetic field (H) using
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ultrasonic interferometer.
Several experimental and theoretical studies performed to investigate the properties of
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ultrasonic propagation in magnetic fluid prepared in polar and non-polar carrier [8-15]. The spatial ordering of magnetic nanoparticles influences the parameters of ultrasonic propagation
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and by analysing these; it is possible to understand the homogeneity of magnetic fluid. Experimental results of aggregation and structuring of dispersed ferromagnetic particles in magnetic fluid have been explained theoretically by Tarapov [15] using an ultrasound wavelength of the order of 10-4 m which is much greater than the dimension of the aggregates (~10-6 m). In such a high wavelength limit, the fluid behaves as if it is a homogeneous fluid, but the presence of aggregation can change the magnetic structure (due to dipole-dipole interactions) and the thermodynamic properties of fluid making the system anisotropic and inhomogeneous. This influences the collective behavior of magnetic particles under magnetic field.
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ACCEPTED MANUSCRIPT In our earlier paper [16], the enhancement of thermal conductivity as a function of the magnetic field is explained by considering the change in aspect ratio of particle aggregation. The results showed that the optimum volume fraction leads to form a chain like structure, which upon increasing concentration changes to a fictitious spherical drop like shape. The change in shape of particle aggregation leads to decrease the thermal conductivity value.
Since ultrasonic
velocity anisotropy can also be used to investigate the types of structure formation in the
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magnetic fluid [17-18], in the present study, we report results of ultrasonic wave propagation in
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the transformer oil based magnetic fluid (TSMF) which is sensitive to temperature in the range
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of 308-338 K. In the TSMF, the pyromagnetic co-efficient, i.e., change in fluid magnetization with temperature is high. The effect of temperature on TSMF subjected under magnetic field is
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investigated for the first time for the highly concentrated system (φ=10.3%) using ultrasonic wave propagation. The effect of magnetic particle volume fractions (1.6, 3.2, 6.8, and 10.3 %)
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and temperature (303 - 338 °K) on particle-carrier interaction and particle-particle interactions in the absence of magnetic field is investigated. The influence of magnetic field at 308 K is also
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studied for all volume fractions to investigate its influence on change in ultrasonic propagation velocity. The simultaneous effect of magnetic field and temperature were studied for the sample
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with the maximum magnetic volume fraction of 10.3 %. 2. Experimental
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Zn substituted Mn-ferrite nanoparticles dispersed in transformer oil (density at 303 K is 817 kg/m3, thermal expansion co-efficient is 0.00084 K-1, viscosity at 303 K is 9 mPa.s) with the
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1.6, 3.2, 6.8, and 10.3 % of particle volume fractions have been investigated for the study [16]. The density of magnetic fluid was measured using specific gravity bottle of 10 ml capacity. The
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crystalline structure of these particles measured using X-ray diffractometer (XRD, D2 Phaser, Bruker) shows characteristic peaks of spinel ferrite structure (Figure 1a) with the crystallite size of 8.0 ± 0.5 nm. Transmission Electron Microscopy (TEM) image (Figure 1b) shows that the particles are nearly spherical with a median diameter, D = 9.5 nm and size distribution in ln(D) : σ = 0.43. The ultrasonic velocity propagation in the fluid was measured using the continuous wave ultrasonic interferometer (Mittal Enterprises, India) working at 2 MHz frequency with a 0.3% measuring accuracy of velocity.
A digital micrometer screw (least count 0.001 mm) was
connected to the cell for lowering or raising the reflector plate. The specially designed jacketed 3
ACCEPTED MANUSCRIPT measuring cell was used to maintain the uniform temperature of the sample. The inlet and outlet of the cell were connected to a constant temperature bath with the accuracy of ± 0.1 °K. The measuring cell was placed between the pole pieces of an electromagnet. The direction of the magnetic field was perpendicular to the direction of ultrasonic wave propagation. The data were acquired after 20 min of the diligence of the magnetic field so as the system passes to the
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AN
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T
equilibrium [19]. Figure 2 shows the experimental set-up.
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Figure 1: (a) XRD pattern of Zn substituted Mn-ferrite nanoparticles (b) TEM image of fluid.
Figure 2:
Ultrasonic
interferometer
setup
with
temperature
controller
bath
and
electromagnet.
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ACCEPTED MANUSCRIPT 3. Results & Discussion 3.1 Influence of volume fraction on structure formation (H= 0) Figure 3a shows the influence of particle volume fractions on the ultrasonic velocity propagation in transformer oil measured at 308 °K. The ultrasonic velocity propagation in the magnetic fluid shows decrement as volume fraction (symbol) increases. The increase in volume fractions from 0 to 10.3 % decreases the ultrasonic velocity from 1.355 ± 0.002 km/s to 1.170 ±
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0.002 km/s. Initial ultrasonic velocity decreases linearly from 0 to 3.2 % volume fraction then it
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deviates at higher concentration. The decrease in velocity follows second order polynomial
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function (red line). This decrement is a qualitative measure of particle-fluid interactions, which are predominantly at low volume fraction. The higher volume fraction leads to increase the particle-particle interaction resulting in the non-linear behavior. Moreover, with the particle
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loading, the rate of Brownian motion of particles decreases along with the formation of a
a
Figure 3:
4
6
8
10
0
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2
b
2
4
1.20
c
1.10 6
8
10
0
2
4
6
8
10
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0
5.8
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6.0
1.30
6
6.2
1.20
1.40
3
M
ad (10
1.25
1.15
6.4
-10
(km/s)
1.30
Z (10 Pa-s/m )
6.6
-1
Pa )
1.35
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resistive surface layer that can persuade a decrease in ultrasonic velocity [20].
Plot of (a) ultrasonic velocity (b) adiabatic compressibility and (c) acoustic
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impedance as a function of volume fraction at 308 °K.
The observed variation in ultrasonic velocity can be explained using the parameters such as adiabatic compressibility (
) and acoustic impedance (Z
) which is plotted as
a function of volume fraction respectively in Figure 3b and 3c. The greater the attractive force among the molecules of a liquid, the smaller will be the compressibility [21]. Figure 3b shows that the adiabatic compressibility decreases with increasing volume fraction confirming the predominance of particle-fluid interaction over particle-particle interaction. With the increase in volume fraction, the number density of particles increases, which restricts the Brownian motion 5
ACCEPTED MANUSCRIPT of the carrier molecules as well as particles, this leads to decrease the adiabatic compressibility. Figure 3c shows that the acoustic impedance increases with increasing volume fraction. The increase in the value of acoustic impedance indicates that there is a significant interaction between the particles and carrier molecules.
From this variation it can be concluded that
transformer oil forms loose aggregates due to the combined effect of short range van der Waal’s interaction, strong dipole-dipole attraction (due to the presence of a small fraction of large
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particles), and carrier-surfactant interaction.
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3.2 Influence of temperature on structure formation (H = 0)
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Figure 4a shows the velocity profile as a function of temperature for all volume fractions. The ultrasonic velocity decreases with increasing temperature irrespective of volume fractions
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used in the present study, following the trend of the carrier, i.e., transformer oil ( = 0 %). The observed behavior can be explained by considering the temperature effect on the movement of
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suspended molecules in the liquid matrix and the amount of time they spend in contact with their nearest neighbor. Increasing temperature leads to the weakening of the intermolecular adhesive
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and cohesive forces [22] thereby, improving the compressibility (Figure 4b), which in turn, decreases the ultrasonic velocity.
The acoustic impedance decreases with increase in
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temperature as shown in Figure 4c. This shows that the high temperature weakens the particle– fluid interaction. A similar trend is observed in magnetic fluid prepared in non-polar carriers.
1.15 1.10
310
320
T K
7.0
6.0
330
340
c
1.4
3
-1
6.5
1.05 300
7.5
1.5
5.5 300
1.3 1.2
6
1.20
b
Z (10 Pa-s/m )
1.25
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(km/s)
1.30
Pa )
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1.35
-10
8.0
a
ad (10
1.40
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The results are in agreement with those observed by other researchers [8, 10, 14, 15].
310
320
T K
330
340
1.1 1.0 300
310
320
330
340
T K
Figure 4: Influence of temperature on (a) ultrasonic velocity, (b) adiabatic compressibility (c) and acoustic impedance in magnetic fluid for all volume fractions.
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ACCEPTED MANUSCRIPT 3.3 Influence of magnetic field on structure formation (H ≠ 0, T = 308 °K) Many researchers have reported theoretically as well as experimentally the morphologies of the field-assisted structures in the last few decades [23-29]. With the application of magnetic field (H), particles in the magnetic fluid aligned in the field direction leading to enhance the length of the structures. With increasing field strength, the structure can be extended up to the dimension of the cell, thus making the system anisotropic in nature. The morphology of the
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structures depends on particle-particle interactions characterized by dcc (= μ0μ2/4πD3kBT), as
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well as particle-field interactions characterized by α, where α =μH/kBT, known as an energy ratio
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or Langevin’s parameter where H is the strength of applied magnetic field. In practice, when the characteristic dipole energy falls within the range of 2 to8 kBT, the structures can assemble and
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disassembled through the application or removal of an external magnetic field, although the interactions are still weak to induce self-assembled structures [30]. In presence of a magnetic
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field, polarization of magnetic fluid takes place and fluctuating dipole moments of individual nanoparticles get aligned in the field direction. The particle-field interactions become strong
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enough to overcome the thermal energy when α >1. Under such conditions, the dipole-dipole interactions are also intensified due to preferential alignment of the individual dipoles, resulting
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in the formation of field-induced structures such as chains and columns. Both; concentration and coupling to the magnetic field are responsible for the transition from dipolar short chains to
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columnar ordering and to the thick bundles. In the present system, the direction of the magnetic field is perpendicular to the ultrasonic
propagation.
Therefore, the anisotropic structures hinder the sound wave
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wave propagation direction.
The types of structures, whether aggregates or a one dimensional chain like
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structures, will decide the change in velocity of sound waves upon an increase in field strength. Since, the direction of the magnetic field is perpendicular to the direction of sound wave propagation, chain like structures will reduce the velocity upon an increase in the field. Whereas, aggregates may increase the velocity propagation upon an increase in the field compared to that at zero field. So, the change in ultrasonic propagation velocity defined as , (where
,
parameters
and
is the ultrasonic velocity at zero field and
with field, respectively, as a function of magnetic field), will be either negative (for chain formation) or positive (for aggregate formation).
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ACCEPTED MANUSCRIPT Figure 5 shows the change in ultrasonic propagation velocity for transformer oil based magnetic fluid for various volume fractions as a function of magnetic field (0 to 0.1 T) at 308 °K temperature. A distinct behavior is seen for all the volume fractions. The change in ultrasonic propagation velocity is negative for the magnetic fluid with 1.6 % magnetic particles volume fraction that means it is decreasing with increasing field, reaches a minimum and then saturate at higher field (above 0.05 T). With increasing volume fraction of particles (φ = 3.2 %), the change
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in ultrasonic propagation velocity shows slight decrease in lower field strength and then
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increases with the increase in field and becomes positive. While for magnetic fluid with 6.8 %
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particle volume fraction, it shows positive value for the entire field range. With increasing the particle volume fraction from 6.8 % to 10.3 %, the magnetic fluid shows once again decrease and
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has a negative value in the entire field range following the trend of the lowest volume fraction (1.6%). The magnitude of the change in ultrasonic propagation velocity at the highest volume
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fraction is deeper than that observed at lower volume fraction of 1.6 %.
0.010
=6.8 % =3.2 %
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/0
0.005
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0.015
0.000
-0.005
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=1.6 %
-0.010
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-0.015
-0.020 0.00
0.02
0.04
0.06
0.08
0.10
Change in ultrasonic propagation velocity as a function of applied magnetic field
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Figure 5:
T= 308 K
=10.3 %
for various volume fractions (1.6 to 10.3 %) at a 308 °K temperature. The solid symbols are experimental data points and dash line is to guide to the eye.
At a low volume fraction, the application of the magnetic field induces short chains like aggregates which are loose (i.e., are easier to break) and flexible due to the fluctuating moments of the individual particles within the chain. The schematic of this alignment is shown in the Figure 6a. The formation of chain like aggregates hinders the sound wave propagation in the 8
ACCEPTED MANUSCRIPT medium, hence, the velocity of the sound wave decreases upon an increase in the field, making change in ultrasonic propagation velocity negative. Thus, change in ultrasonic propagation velocity decreases with increasing field for 1.6 % volume fraction. With increasing volume fraction there exist greater fractions of short dipolar chains that are stable as compared to the low volume fraction, as shown in Figure 6b, making the system as if it is a distribution of small aggregates in the medium. So, the hindrance to sound waves to propagate in such a medium is
With further increase in volume fraction, the density of small
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velocity becomes positive.
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less as compared to presence of chain like aggregates. Thus, change in ultrasonic propagation
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aggregates increases. For a certain volume fraction such as 6.8 % in the present case, dense aggregates formed by the application of the magnetic field, which upon increasing field strength
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align in field directions and grow in size, leaving more space for ultrasonic velocity propagation (Figure 6c). The growth of these aggregates depends on field strength. With further increase in
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concentration, the previously formed zero-field structures in magnetic fluid (Figure 6d) elongates and align in field direction making chains of the aggregates. The thickness and the length of
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such chains, increase with increase in field strength, making change in ultrasonic propagation velocity once again minimum. At higher magnetic field, the interaction of these chains results in
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the spherical drop like structure (fractal) creating free space and hence ultrasonic velocity
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increases.
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ACCEPTED MANUSCRIPT Figure 6: Change in ultrasonic propagation velocity for all volume fractions along with a schematic of structure formation (inset of the graph) in magnetic fluid as a function of applied magnetic field for various volume fractions (a=1.6 %, b=3.2 %, c= 6.8 % and do = 10.3 %). The change in ultrasonic propagation velocity in magnetic fluid upon application of the Tarapov’s theory is useful in explaining the change in ultrasonic propagation
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interaction.
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magnetic field is due to the aggregate formation, i.e., chain or clusters due to the particle-field
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velocity in magnetic fluid in the presence of the magnetic field. In this theory, it is considered that though the attenuation of ultrasonic wavelength in magnetic fluids (~10-4 m) is much greater
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than the aggregate size (~103 nm) [31, 32], the thermodynamic characteristics of the fluid changes significantly. An equation for the velocity of weak perturbation propagation (wave) is
)…(1)
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(
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derived, which can be expressed as
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Where, as is the initial value of the velocity, θ is the angle between the magnetic field and propagation direction, which in the present case, is 90º. So considering this, the equation (1)
(
)…(2)
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-
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reduces to
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L0, L1 and L2 are defined as (
*
[
)
*
,
( )
-+ *
+ …(3)
+…(4)
]…(5)
10
ACCEPTED MANUSCRIPT Where, q, ψ, ξ,
, N, α, , and 1 are dimensionless parameters which, along with a0,
a1, a2 and a3, defined as
,
)*
(
,
)+ ,
,
,
,
( ),
(
),
),
(
),
( ),
(
)
CR
(
IP
T
(
,
Where, Ms is saturation magnetization of fluid, ρ is the density of the fluid, T is the
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absolute temperature, cp and cv, are heat capacities at constant pressure and volume and an unperturbed state of the medium (Ts and Tp) values remain constant. For α<< 1, the series
)…(6)
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(
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expansion of equation (2) gives [33]
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The equation (6), qualitatively describes the experimental results of normalized change in
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ultrasonic propagation velocity as reported by Chung et al [34]. Accordingly, it is
)
…(7)
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(
The term α and q relates to the dipole-dipole interaction while α relates to the ratio of
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magnetic energy to thermal energy. L0, L1, and L2 are function of concentration of magnetic particles, fluid magnetization, field, and temperature. Since the fluid magnetization and the response to the magnetic field are sensitive to particle size, it is very important to precisely plug the value of particle size. Chung et al [34-35] and Tarapov et al [15] have reported that the magnitude of normalized velocity decreases initially with field, reaches a minimum and thereafter it increases. At a higher field, it exhibits the saturation behavior. Tarapov’s theory does not consider the effect of polydispersity and the frequency of sound wave propagation. However, the magnetic particles dispersed in the magnetic fluids are usually poly-dispersed following lognormal 11
ACCEPTED MANUSCRIPT distribution function.
Kruti et al [36] recently emphasized this point, where the existing
Tarapov’s equation was modified by the lognormal moment distribution function. The modified
( ) ( )…(8)
( )
( ) ( )…(9)
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( )
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equations (3), (4) and (5) can be described as
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( ) ( )…(10)
(
)
√
(
(
)
)
…(11)
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( ) ( )
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Where, P(μ)d(μ) is log-normal moment distribution function
Where, σ is magnetic moment distribution and m is mean magnetic moment. Using
( )(
)…(12)
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( )
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these modified term equation (2) changes to
In the present case, equation (12) used to fit experimental data. The theory line of
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is generated for the modified L0', L1', and L2' terms. The experimental data of change in ultrasonic propagation velocity for all volume fractions were fitted with the modified Tarapov’s theory using equation (12). Figure 6 (a to d) shows the experimental data fitted to the modified
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Tarapov’s theory for the 6.8 % and 10.3 % volume fractions. It is seen that at 6.8 % volume fraction, the aggregates formed which respond to the direction of the magnetic field. Whereas, for 10.3 % volume fraction, chain like structures observed due to the complete alignment of these aggregates in the field direction. The fitted parameters, i.e., the mean magnetic moment (), moment distribution (σ) and the number density of particles (n), for all the volume fractions are given in the Table 1. Table 1: Parameters obtained from the modified Tarapov’s theory fit to the experimental data for all the volume fractions. 12
ACCEPTED MANUSCRIPT T= 308 °K Sr.
φ
No
(±0.02 %)
n x 1022
μ
σμ
(0.02 ± 10-19A/m2)
(± 0.05)
m-3 (± 0.1)
1.6
4.7
0.2
2.5
2
3.2
2.7
0.6
5.1
3
6.8
1.75
0.8
4
10.3
1.5
0.6
7.5
19.8
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T
1
The mean magnetic moment, , decreases from 4.7± 0.02 x 10-19A/m2 to 1.5 ± 0.02 x 10A/m2 with increasing volume fraction from 1.6 % to 10.3 %. In addition, the magnetic moment
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19
distribution increases from 0.2 ± 0.05to 0.8 ± 0.05 with increasing volume fraction and then
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reduced to 0.6 ± 0.05 with further increase in the volume fraction to 10.3 %. This shows that the Zeeman energy (magnetic field energy - .H) leads to form structures, which extends upon
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increasing volume fractions. The effective moment of these aggregates is lower as compared to that of individual particles. Also, the overall size of the aggregates is different throughout the The observed decrease in the mean magnetic moment and increase in moment
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medium.
distribution and number density of particles (n) supports this argument. At higher volume
these aggregates.
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fraction, i.e. 10.3 %, these pre-aggregates align in the field direction and forming long chains of At higher field, inter-chain interactions increases to form columnar like
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structure and hence, change in ultrasonic propagation velocity increases. Figure 7 shows the optical microscopy images for various volume fractions after 5 min
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and 20 min exposure to 0.1 T magnetic fields. The image shows the chain like alignment of particles in the direction of the field for all volume fractions. However, the number of chains like structures increases with increase in concentration.
This chain like structure starts
associating as time progresses and form coarse structures after 5 min. The diluted system shows comparatively thinner chain structures (Figure 7a and 7d) which joins together and forms a continuous rod like structure. Thus, the aspect ratio of diluted system is high compared to concentrated system. An increase in concentration leads to inter-chain interaction and forms the columnar structure (Figure 7b and 7e). The concentrated system (=10.3 %) shows a large number of chains associate together forming thick fibril of particle chains (Figure 7c). Such 13
ACCEPTED MANUSCRIPT structure may be ascribable to the high particle concentration and carrier viscosity.
The
coarsening of chains slowly forms spherical drop like structures, which grow with time (Figure 7f). Hayes [38] has reported similar coalescent of chains into a spherical drop like structure in magnetic fluid using optical microscopy. With increasing the concentration, the chain–chain interaction increases, which decrease the aspect ratio. Hence, the optical microscopic images
Optical microscopic images for fluid of different concentrations measured under
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Figure 7:
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M
AN
US
CR
IP
T
show similar outcomes as observed in ultrasonic results.
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the application of 0.1 T field after 5 min and 20 min. 3.4 Simultaneous effects of temperature and magnetic field for φ =10.3%
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The application of magnetic field induces the long-range structures in magnetic fluid. This structure can be disturbed by increasing the temperature of the system.
Increase in
temperature increases the thermal energy and Brownian motion of the particles which leads to break these aggregates thus making the system homogeneous. Hence, it will be interesting to study the simultaneous effect of the temperature and magnetic field on change in ultrasonic propagation velocity of the magnetic fluid.
14
ACCEPTED MANUSCRIPT 0.020 0.015
T= 338 K
0.010
T= 328 K T= 318 K
0.000
-0.005
T= 308 K
T
/0
0.005
-0.015 0.02
0.04
0.06
0.08
0.10
Change in ultrasonic propagation velocity as a function of applied magnetic field
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Figure 8:
=10.3 %
US
-0.020 0.00
CR
IP
-0.010
M
at different temperature for =10.3 %. The line shows the Tarapov’s theory.
It can be seen from Figure 8 that with increasing temperature the change in ultrasonic
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propagation velocity for max (=10.3 %) increases from negative to the positive. At 308 °K change in ultrasonic propagation velocity is negative and becomes positive only at the highest
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field of 0.1 T. With increase in temperature from 308 - 318 °K, the magnitude of change in ultrasonic propagation velocity reduces and shows the positive value at comparatively lower
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field strength (H = 0.05 T). Further increase in temperature to 328 °K, it shows a positive anisotropy in the whole range of the applied magnetic field. It has a peak at the lower field value
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(H = 0.015 T), becomes positive minimum of 0.02 T field and then increases with increasing field and attain saturation. For the 338 °K temperature, the change in ultrasonic propagation velocity is positive and it increases with increasing field and attains saturation after 0.04 T field. The temperature dependent change in ultrasonic propagation velocity data also fitted with the modified Tarapov’s theory. Line in Figure 8 shows the Tarapov’s theory fitting for two different temperatures 308 °K and 338 °K. The fitted parameters are reported in Table 2.
Table 2:
Parameters derived using modified Tarapov’s theory for φ = 10.3 % at different temperatures. 15
ACCEPTED MANUSCRIPT φ=10.3 % Sr.
T
No
(± 0.5 °K)
μ
n x 1022
σμ -19
(± 0.02 x 10
2
A/m )
(± 0.05)
m-3 (± 0.1)
308
1.5
0.6
19.8
2
318
1.2
0.8
21.4
3
328
0.9
0.95
4
338
0.7
1.35
23.5 28.5
CR
IP
T
1
It inferred from the Table 2 that the magnetic moment of the particle decreases from 1.5
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± 0.02 x10-19 A/m2 to 0.7 ± 0.02 x10-19 A/m2 with increasing temperature from 308 - 338 °K. The moment distribution and number density increases respectively from 0.6 to 1.35 ± 0.05 and
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19.8 to 28.5 upon increasing temperature. Actually the moment of particles should increase upon increasing temperature because the high temperature will break the aggregates. But in the present case, it is observed that the moment decreases even to that observed at room temperature.
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The decrease in magnetic moment with increasing temperature can be correlated to the
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temperature sensitive nature of the particles because the Curie temperature of the sample is low (380 °K) [39]. With increasing temperature, the chain like aggregates starts breaking due to two
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reasons (i) high thermal energy and (ii) reduced magnetic moment. The magnetic moment of aggregates decreases as temperature increases because Zn substituted Mn-ferrite is temperature
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sensitive, so the magnetic moment of particles reduces significantly with increasing temperature. The reduction in magnetic moment weakens the strength of Zeeman energy which is responsible
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for the chain formation. Hence, a prominent effect of breaking of chains into aggregates is seen with increasing temperature. In addition, the Curie temperature is calculated by extrapolating the reduction in magnetic moment with increase in temperature and it is found at 363 K. The value of Curie temperature, thus obtained is comparable to that obtained using another experiment [39]. 4. Conclusion The ultrasonic velocity of the magnetic fluid as a function of volume fraction, temperature and magnetic field is investigated for transformer oil based temperature sensitive 16
ACCEPTED MANUSCRIPT magnetic fluid. The ultrasonic velocity decreases with increasing volume fraction attributed to the particle-carrier interaction leading to form shorter aggregates.
The pre-aggregates in
magnetic fluid break when temperature increases in the absence of a field. Field dependent change in ultrasonic propagation velocity shows chain like alignment for low (1.6 %) volume fraction. With increasing volume fraction (6.8 %) there exist greater fractions of short dipolar chains, but large and stable compared to the low volume fraction creating a free space for sound
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waves to propagate and results in the increase in the ultrasonic velocity with increasing field. For
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still higher volume fractions (10.3 %) the change in ultrasonic propagation velocity shows a
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negative deep with increasing field. The negative deep shows chain like structures formed due to the presence of the large number of pre-aggregates, which decreases the ultrasonic velocity. In
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an appropriately high concentration, the chains become thicker by aligning sidewise to the neighboring chains. The change in ultrasonic propagation velocity data were fitted with the
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modified Tarapov’s theory which shows the presence of aggregates with increasing volume fraction. The optical microscopy study confirms the short chain like structure at low volume
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fractions. These structures extend with the increasing volume fraction and increasing magnetic field strength. At higher volume fraction the chain-chain interaction occurs and thick columnar
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like structures formed. For 10.3 % volume fraction, the chain like structure becomes a spherical drop like fractals. The ultrasonic velocity and optical microscopy studies also confirm the results
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of thermal conductivity data analysis.
The simultaneous effect of the temperature and magnetic field for 10.3 % volume fraction
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has also been studied. At 308 °K change in ultrasonic propagation velocity is a negative forming thick chain like aggregate formation with the applied field.
This aggregates break with
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increasing temperature, the systematic variation in change in ultrasonic propagation velocity from negative to positive upon an increase in temperature reflects the same. The experimental data were fitted with the modified Tarapov’s theory. The fit parameters show decrease in magnetic moment from 1.5± 0.02 x10-19 A/m2 to 0.7 ± 0.02 x10-19A/m2 with increasing temperature from 308 °K to 338 °K. From the variation of magnetic moment with temperature obtained from the fitting of change in ultrasonic propagation velocity, the Curie temperature of the sample is obtained which is found at 363 K. The value is near to the Curie temperature obtained from the fluid using different techniques.
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ACCEPTED MANUSCRIPT Acknowledgement: The authors would like to thank Department of Science & Technology, Government of India, New Delhi, for providing the financial support vide number; DST/TSG/2011/161-G project.
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Graphical Abstract
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ACCEPTED MANUSCRIPT Highlights
Acoustic property of magnetic fluid is investigated as a function of temperature and magnetic field.
In zero field, the pre-aggregates found in magnetic fluid which breaks when
Change in velocity shows transformation from chain like alignment to short dipolar
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temperature increases.
chains.
Tarapov’s theory confirms the presence of chains and aggregates with increasing
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volume fraction.
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These aggregates break with increasing temperature, also reflected from Tarapov’s
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fit.
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Kinnari Parekh, Jaykumar Patel, R.V. Upadhyay PII: DOI: Reference:
S0167-7322(17)34038-2 doi:10.1016/j.molliq.2017.10.090 MOLLIQ 8052
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
1 September 2017 12 October 2017 18 October 2017
Please cite this article as: Kinnari Parekh, Jaykumar Patel, R.V. Upadhyay , Temperature dependent acoustic properties of temperature sensitive magnetic fluid subjected to magnetic field. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Molliq(2017), doi:10.1016/j.molliq.2017.10.090
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ACCEPTED MANUSCRIPT Temperature dependent acoustic properties of temperature sensitive magnetic fluid subjected to magnetic field Kinnari Parekha*, Jaykumar Patela, R V Upadhyaya,b a
Dr. K. C. Patel R & D Center, bP. D. Institute of Applied Sciences, Charotar University of Science & Technology, Changa-388421, Gujarat, India.
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*Corresponding Author’s e-mail: [email protected]
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Abstract
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The ultrasonic velocity of temperature sensitive magnetic fluid is investigated as a function of volume fraction, temperature and magnetic field. The ultrasonic velocity decreases
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with increasing volume fraction of magnetic nanoparticles. This is attributed to the particlecarrier interaction which leads to form shorter aggregates. The pre-aggregates in magnetic fluid
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break when temperature increases in the absence of a field. Magnetic field makes the system anisotropic to ultrasound wave propagation. The change in ultrasonic propagation velocity under
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the influence of magnetic field shows chain like alignment for low volume fraction of magnetic nanoparticles (1.6 %) which changes to short dipolar chains at an intermediate volume fraction
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(6.8 %). Above this volume fraction, short chains become thicker by aligning sidewise to the neighboring chains resulting in spherical drop like structures. The modified Tarapov’s theory fit
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to change in ultrasonic propagation velocity confirms the transformation from chains to aggregates with increasing magnetic nanoparticles volume fraction. The optical microscopy
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study also confirms the results. Upon increasing the temperature the field dependent velocity variation shows breaking of thick chain like aggregates. The modified Tarapov’s theory fit shows
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that this is attributed to decrease in magnetic moment with increasing temperature. The variation of magnetic moment with temperature obtained from the fitting gives the Curie temperature of fluid as 363 K. This value agrees with those obtained from other techniques.
Keywords: magnetic fluid; acoustic properties; nanoparticles structure; transformer oil
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ACCEPTED MANUSCRIPT 1.
INTRODUCTION Magnetic fluid represents a technologically important material because of its wide scope
of tuning the macroscopic behaviour 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 magnetic fluid even at low concentration [1–6]. In the absence of external magnetic field, magnetic fluid behaves like a
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normal suspension containing magnetic nanoparticles but the exposure of the magnetic field
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induces the dipole moment in particle as a result particles respond to the magnetic field either
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through Neel rotation or through Brownian rotation. In addition to the particle-field interaction, particles experience short-range van der Waals and magnetic dipolar attractive forces. The
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collective behavior of the same will produce different structures within the carrier matrix. Ultrasonic propagation in magnetic fluid is a non-destructive method to investigate the
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structure formation without any prior modifications of the sample such as thin film preparation, drying or freezing of the sample, etc., and have maximum sample recovery. In addition, the It offers an added advantage to
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study can be performed for a concentrated system too.
investigate the study under different magnetic field and temperature without changing the
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geometry of the experimental set-up. Moreover, it is possible to study the simultaneous effect of these parameters, i.e., particle concentration (φ), temperature (T), and magnetic field (H) using
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ultrasonic interferometer.
Several experimental and theoretical studies performed to investigate the properties of
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ultrasonic propagation in magnetic fluid prepared in polar and non-polar carrier [8-15]. The spatial ordering of magnetic nanoparticles influences the parameters of ultrasonic propagation
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and by analysing these; it is possible to understand the homogeneity of magnetic fluid. Experimental results of aggregation and structuring of dispersed ferromagnetic particles in magnetic fluid have been explained theoretically by Tarapov [15] using an ultrasound wavelength of the order of 10-4 m which is much greater than the dimension of the aggregates (~10-6 m). In such a high wavelength limit, the fluid behaves as if it is a homogeneous fluid, but the presence of aggregation can change the magnetic structure (due to dipole-dipole interactions) and the thermodynamic properties of fluid making the system anisotropic and inhomogeneous. This influences the collective behavior of magnetic particles under magnetic field.
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ACCEPTED MANUSCRIPT In our earlier paper [16], the enhancement of thermal conductivity as a function of the magnetic field is explained by considering the change in aspect ratio of particle aggregation. The results showed that the optimum volume fraction leads to form a chain like structure, which upon increasing concentration changes to a fictitious spherical drop like shape. The change in shape of particle aggregation leads to decrease the thermal conductivity value.
Since ultrasonic
velocity anisotropy can also be used to investigate the types of structure formation in the
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magnetic fluid [17-18], in the present study, we report results of ultrasonic wave propagation in
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the transformer oil based magnetic fluid (TSMF) which is sensitive to temperature in the range
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of 308-338 K. In the TSMF, the pyromagnetic co-efficient, i.e., change in fluid magnetization with temperature is high. The effect of temperature on TSMF subjected under magnetic field is
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investigated for the first time for the highly concentrated system (φ=10.3%) using ultrasonic wave propagation. The effect of magnetic particle volume fractions (1.6, 3.2, 6.8, and 10.3 %)
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and temperature (303 - 338 °K) on particle-carrier interaction and particle-particle interactions in the absence of magnetic field is investigated. The influence of magnetic field at 308 K is also
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studied for all volume fractions to investigate its influence on change in ultrasonic propagation velocity. The simultaneous effect of magnetic field and temperature were studied for the sample
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with the maximum magnetic volume fraction of 10.3 %. 2. Experimental
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Zn substituted Mn-ferrite nanoparticles dispersed in transformer oil (density at 303 K is 817 kg/m3, thermal expansion co-efficient is 0.00084 K-1, viscosity at 303 K is 9 mPa.s) with the
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1.6, 3.2, 6.8, and 10.3 % of particle volume fractions have been investigated for the study [16]. The density of magnetic fluid was measured using specific gravity bottle of 10 ml capacity. The
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crystalline structure of these particles measured using X-ray diffractometer (XRD, D2 Phaser, Bruker) shows characteristic peaks of spinel ferrite structure (Figure 1a) with the crystallite size of 8.0 ± 0.5 nm. Transmission Electron Microscopy (TEM) image (Figure 1b) shows that the particles are nearly spherical with a median diameter, D = 9.5 nm and size distribution in ln(D) : σ = 0.43. The ultrasonic velocity propagation in the fluid was measured using the continuous wave ultrasonic interferometer (Mittal Enterprises, India) working at 2 MHz frequency with a 0.3% measuring accuracy of velocity.
A digital micrometer screw (least count 0.001 mm) was
connected to the cell for lowering or raising the reflector plate. The specially designed jacketed 3
ACCEPTED MANUSCRIPT measuring cell was used to maintain the uniform temperature of the sample. The inlet and outlet of the cell were connected to a constant temperature bath with the accuracy of ± 0.1 °K. The measuring cell was placed between the pole pieces of an electromagnet. The direction of the magnetic field was perpendicular to the direction of ultrasonic wave propagation. The data were acquired after 20 min of the diligence of the magnetic field so as the system passes to the
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equilibrium [19]. Figure 2 shows the experimental set-up.
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Figure 1: (a) XRD pattern of Zn substituted Mn-ferrite nanoparticles (b) TEM image of fluid.
Figure 2:
Ultrasonic
interferometer
setup
with
temperature
controller
bath
and
electromagnet.
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ACCEPTED MANUSCRIPT 3. Results & Discussion 3.1 Influence of volume fraction on structure formation (H= 0) Figure 3a shows the influence of particle volume fractions on the ultrasonic velocity propagation in transformer oil measured at 308 °K. The ultrasonic velocity propagation in the magnetic fluid shows decrement as volume fraction (symbol) increases. The increase in volume fractions from 0 to 10.3 % decreases the ultrasonic velocity from 1.355 ± 0.002 km/s to 1.170 ±
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0.002 km/s. Initial ultrasonic velocity decreases linearly from 0 to 3.2 % volume fraction then it
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deviates at higher concentration. The decrease in velocity follows second order polynomial
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function (red line). This decrement is a qualitative measure of particle-fluid interactions, which are predominantly at low volume fraction. The higher volume fraction leads to increase the particle-particle interaction resulting in the non-linear behavior. Moreover, with the particle
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loading, the rate of Brownian motion of particles decreases along with the formation of a
a
Figure 3:
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0
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2
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1.20
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(km/s)
1.30
Z (10 Pa-s/m )
6.6
-1
Pa )
1.35
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resistive surface layer that can persuade a decrease in ultrasonic velocity [20].
Plot of (a) ultrasonic velocity (b) adiabatic compressibility and (c) acoustic
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impedance as a function of volume fraction at 308 °K.
The observed variation in ultrasonic velocity can be explained using the parameters such as adiabatic compressibility (
) and acoustic impedance (Z
) which is plotted as
a function of volume fraction respectively in Figure 3b and 3c. The greater the attractive force among the molecules of a liquid, the smaller will be the compressibility [21]. Figure 3b shows that the adiabatic compressibility decreases with increasing volume fraction confirming the predominance of particle-fluid interaction over particle-particle interaction. With the increase in volume fraction, the number density of particles increases, which restricts the Brownian motion 5
ACCEPTED MANUSCRIPT of the carrier molecules as well as particles, this leads to decrease the adiabatic compressibility. Figure 3c shows that the acoustic impedance increases with increasing volume fraction. The increase in the value of acoustic impedance indicates that there is a significant interaction between the particles and carrier molecules.
From this variation it can be concluded that
transformer oil forms loose aggregates due to the combined effect of short range van der Waal’s interaction, strong dipole-dipole attraction (due to the presence of a small fraction of large
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particles), and carrier-surfactant interaction.
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3.2 Influence of temperature on structure formation (H = 0)
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Figure 4a shows the velocity profile as a function of temperature for all volume fractions. The ultrasonic velocity decreases with increasing temperature irrespective of volume fractions
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used in the present study, following the trend of the carrier, i.e., transformer oil ( = 0 %). The observed behavior can be explained by considering the temperature effect on the movement of
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suspended molecules in the liquid matrix and the amount of time they spend in contact with their nearest neighbor. Increasing temperature leads to the weakening of the intermolecular adhesive
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and cohesive forces [22] thereby, improving the compressibility (Figure 4b), which in turn, decreases the ultrasonic velocity.
The acoustic impedance decreases with increase in
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temperature as shown in Figure 4c. This shows that the high temperature weakens the particle– fluid interaction. A similar trend is observed in magnetic fluid prepared in non-polar carriers.
1.15 1.10
310
320
T K
7.0
6.0
330
340
c
1.4
3
-1
6.5
1.05 300
7.5
1.5
5.5 300
1.3 1.2
6
1.20
b
Z (10 Pa-s/m )
1.25
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(km/s)
1.30
Pa )
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1.35
-10
8.0
a
ad (10
1.40
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The results are in agreement with those observed by other researchers [8, 10, 14, 15].
310
320
T K
330
340
1.1 1.0 300
310
320
330
340
T K
Figure 4: Influence of temperature on (a) ultrasonic velocity, (b) adiabatic compressibility (c) and acoustic impedance in magnetic fluid for all volume fractions.
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ACCEPTED MANUSCRIPT 3.3 Influence of magnetic field on structure formation (H ≠ 0, T = 308 °K) Many researchers have reported theoretically as well as experimentally the morphologies of the field-assisted structures in the last few decades [23-29]. With the application of magnetic field (H), particles in the magnetic fluid aligned in the field direction leading to enhance the length of the structures. With increasing field strength, the structure can be extended up to the dimension of the cell, thus making the system anisotropic in nature. The morphology of the
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structures depends on particle-particle interactions characterized by dcc (= μ0μ2/4πD3kBT), as
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well as particle-field interactions characterized by α, where α =μH/kBT, known as an energy ratio
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or Langevin’s parameter where H is the strength of applied magnetic field. In practice, when the characteristic dipole energy falls within the range of 2 to8 kBT, the structures can assemble and
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disassembled through the application or removal of an external magnetic field, although the interactions are still weak to induce self-assembled structures [30]. In presence of a magnetic
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field, polarization of magnetic fluid takes place and fluctuating dipole moments of individual nanoparticles get aligned in the field direction. The particle-field interactions become strong
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enough to overcome the thermal energy when α >1. Under such conditions, the dipole-dipole interactions are also intensified due to preferential alignment of the individual dipoles, resulting
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in the formation of field-induced structures such as chains and columns. Both; concentration and coupling to the magnetic field are responsible for the transition from dipolar short chains to
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columnar ordering and to the thick bundles. In the present system, the direction of the magnetic field is perpendicular to the ultrasonic
propagation.
Therefore, the anisotropic structures hinder the sound wave
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wave propagation direction.
The types of structures, whether aggregates or a one dimensional chain like
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structures, will decide the change in velocity of sound waves upon an increase in field strength. Since, the direction of the magnetic field is perpendicular to the direction of sound wave propagation, chain like structures will reduce the velocity upon an increase in the field. Whereas, aggregates may increase the velocity propagation upon an increase in the field compared to that at zero field. So, the change in ultrasonic propagation velocity defined as , (where
,
parameters
and
is the ultrasonic velocity at zero field and
with field, respectively, as a function of magnetic field), will be either negative (for chain formation) or positive (for aggregate formation).
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ACCEPTED MANUSCRIPT Figure 5 shows the change in ultrasonic propagation velocity for transformer oil based magnetic fluid for various volume fractions as a function of magnetic field (0 to 0.1 T) at 308 °K temperature. A distinct behavior is seen for all the volume fractions. The change in ultrasonic propagation velocity is negative for the magnetic fluid with 1.6 % magnetic particles volume fraction that means it is decreasing with increasing field, reaches a minimum and then saturate at higher field (above 0.05 T). With increasing volume fraction of particles (φ = 3.2 %), the change
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in ultrasonic propagation velocity shows slight decrease in lower field strength and then
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increases with the increase in field and becomes positive. While for magnetic fluid with 6.8 %
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particle volume fraction, it shows positive value for the entire field range. With increasing the particle volume fraction from 6.8 % to 10.3 %, the magnetic fluid shows once again decrease and
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has a negative value in the entire field range following the trend of the lowest volume fraction (1.6%). The magnitude of the change in ultrasonic propagation velocity at the highest volume
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fraction is deeper than that observed at lower volume fraction of 1.6 %.
0.010
=6.8 % =3.2 %
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/0
0.005
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0.015
0.000
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=1.6 %
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-0.015
-0.020 0.00
0.02
0.04
0.06
0.08
0.10
Change in ultrasonic propagation velocity as a function of applied magnetic field
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Figure 5:
T= 308 K
=10.3 %
for various volume fractions (1.6 to 10.3 %) at a 308 °K temperature. The solid symbols are experimental data points and dash line is to guide to the eye.
At a low volume fraction, the application of the magnetic field induces short chains like aggregates which are loose (i.e., are easier to break) and flexible due to the fluctuating moments of the individual particles within the chain. The schematic of this alignment is shown in the Figure 6a. The formation of chain like aggregates hinders the sound wave propagation in the 8
ACCEPTED MANUSCRIPT medium, hence, the velocity of the sound wave decreases upon an increase in the field, making change in ultrasonic propagation velocity negative. Thus, change in ultrasonic propagation velocity decreases with increasing field for 1.6 % volume fraction. With increasing volume fraction there exist greater fractions of short dipolar chains that are stable as compared to the low volume fraction, as shown in Figure 6b, making the system as if it is a distribution of small aggregates in the medium. So, the hindrance to sound waves to propagate in such a medium is
With further increase in volume fraction, the density of small
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velocity becomes positive.
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less as compared to presence of chain like aggregates. Thus, change in ultrasonic propagation
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aggregates increases. For a certain volume fraction such as 6.8 % in the present case, dense aggregates formed by the application of the magnetic field, which upon increasing field strength
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align in field directions and grow in size, leaving more space for ultrasonic velocity propagation (Figure 6c). The growth of these aggregates depends on field strength. With further increase in
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concentration, the previously formed zero-field structures in magnetic fluid (Figure 6d) elongates and align in field direction making chains of the aggregates. The thickness and the length of
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such chains, increase with increase in field strength, making change in ultrasonic propagation velocity once again minimum. At higher magnetic field, the interaction of these chains results in
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the spherical drop like structure (fractal) creating free space and hence ultrasonic velocity
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increases.
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ACCEPTED MANUSCRIPT Figure 6: Change in ultrasonic propagation velocity for all volume fractions along with a schematic of structure formation (inset of the graph) in magnetic fluid as a function of applied magnetic field for various volume fractions (a=1.6 %, b=3.2 %, c= 6.8 % and do = 10.3 %). The change in ultrasonic propagation velocity in magnetic fluid upon application of the Tarapov’s theory is useful in explaining the change in ultrasonic propagation
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interaction.
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magnetic field is due to the aggregate formation, i.e., chain or clusters due to the particle-field
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velocity in magnetic fluid in the presence of the magnetic field. In this theory, it is considered that though the attenuation of ultrasonic wavelength in magnetic fluids (~10-4 m) is much greater
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than the aggregate size (~103 nm) [31, 32], the thermodynamic characteristics of the fluid changes significantly. An equation for the velocity of weak perturbation propagation (wave) is
)…(1)
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(
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derived, which can be expressed as
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Where, as is the initial value of the velocity, θ is the angle between the magnetic field and propagation direction, which in the present case, is 90º. So considering this, the equation (1)
(
)…(2)
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-
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reduces to
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L0, L1 and L2 are defined as (
*
[
)
*
,
( )
-+ *
+ …(3)
+…(4)
]…(5)
10
ACCEPTED MANUSCRIPT Where, q, ψ, ξ,
, N, α, , and 1 are dimensionless parameters which, along with a0,
a1, a2 and a3, defined as
,
)*
(
,
)+ ,
,
,
,
( ),
(
),
),
(
),
( ),
(
)
CR
(
IP
T
(
,
Where, Ms is saturation magnetization of fluid, ρ is the density of the fluid, T is the
US
absolute temperature, cp and cv, are heat capacities at constant pressure and volume and an unperturbed state of the medium (Ts and Tp) values remain constant. For α<< 1, the series
)…(6)
M
(
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expansion of equation (2) gives [33]
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The equation (6), qualitatively describes the experimental results of normalized change in
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ultrasonic propagation velocity as reported by Chung et al [34]. Accordingly, it is
)
…(7)
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(
The term α and q relates to the dipole-dipole interaction while α relates to the ratio of
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magnetic energy to thermal energy. L0, L1, and L2 are function of concentration of magnetic particles, fluid magnetization, field, and temperature. Since the fluid magnetization and the response to the magnetic field are sensitive to particle size, it is very important to precisely plug the value of particle size. Chung et al [34-35] and Tarapov et al [15] have reported that the magnitude of normalized velocity decreases initially with field, reaches a minimum and thereafter it increases. At a higher field, it exhibits the saturation behavior. Tarapov’s theory does not consider the effect of polydispersity and the frequency of sound wave propagation. However, the magnetic particles dispersed in the magnetic fluids are usually poly-dispersed following lognormal 11
ACCEPTED MANUSCRIPT distribution function.
Kruti et al [36] recently emphasized this point, where the existing
Tarapov’s equation was modified by the lognormal moment distribution function. The modified
( ) ( )…(8)
( )
( ) ( )…(9)
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( )
T
equations (3), (4) and (5) can be described as
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( ) ( )…(10)
(
)
√
(
(
)
)
…(11)
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( ) ( )
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Where, P(μ)d(μ) is log-normal moment distribution function
Where, σ is magnetic moment distribution and m is mean magnetic moment. Using
( )(
)…(12)
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( )
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M
these modified term equation (2) changes to
In the present case, equation (12) used to fit experimental data. The theory line of
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is generated for the modified L0', L1', and L2' terms. The experimental data of change in ultrasonic propagation velocity for all volume fractions were fitted with the modified Tarapov’s theory using equation (12). Figure 6 (a to d) shows the experimental data fitted to the modified
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Tarapov’s theory for the 6.8 % and 10.3 % volume fractions. It is seen that at 6.8 % volume fraction, the aggregates formed which respond to the direction of the magnetic field. Whereas, for 10.3 % volume fraction, chain like structures observed due to the complete alignment of these aggregates in the field direction. The fitted parameters, i.e., the mean magnetic moment (), moment distribution (σ) and the number density of particles (n), for all the volume fractions are given in the Table 1. Table 1: Parameters obtained from the modified Tarapov’s theory fit to the experimental data for all the volume fractions. 12
ACCEPTED MANUSCRIPT T= 308 °K Sr.
φ
No
(±0.02 %)
n x 1022
μ
σμ
(0.02 ± 10-19A/m2)
(± 0.05)
m-3 (± 0.1)
1.6
4.7
0.2
2.5
2
3.2
2.7
0.6
5.1
3
6.8
1.75
0.8
4
10.3
1.5
0.6
7.5
19.8
CR
IP
T
1
The mean magnetic moment, , decreases from 4.7± 0.02 x 10-19A/m2 to 1.5 ± 0.02 x 10A/m2 with increasing volume fraction from 1.6 % to 10.3 %. In addition, the magnetic moment
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19
distribution increases from 0.2 ± 0.05to 0.8 ± 0.05 with increasing volume fraction and then
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reduced to 0.6 ± 0.05 with further increase in the volume fraction to 10.3 %. This shows that the Zeeman energy (magnetic field energy - .H) leads to form structures, which extends upon
M
increasing volume fractions. The effective moment of these aggregates is lower as compared to that of individual particles. Also, the overall size of the aggregates is different throughout the The observed decrease in the mean magnetic moment and increase in moment
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medium.
distribution and number density of particles (n) supports this argument. At higher volume
these aggregates.
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fraction, i.e. 10.3 %, these pre-aggregates align in the field direction and forming long chains of At higher field, inter-chain interactions increases to form columnar like
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structure and hence, change in ultrasonic propagation velocity increases. Figure 7 shows the optical microscopy images for various volume fractions after 5 min
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and 20 min exposure to 0.1 T magnetic fields. The image shows the chain like alignment of particles in the direction of the field for all volume fractions. However, the number of chains like structures increases with increase in concentration.
This chain like structure starts
associating as time progresses and form coarse structures after 5 min. The diluted system shows comparatively thinner chain structures (Figure 7a and 7d) which joins together and forms a continuous rod like structure. Thus, the aspect ratio of diluted system is high compared to concentrated system. An increase in concentration leads to inter-chain interaction and forms the columnar structure (Figure 7b and 7e). The concentrated system (=10.3 %) shows a large number of chains associate together forming thick fibril of particle chains (Figure 7c). Such 13
ACCEPTED MANUSCRIPT structure may be ascribable to the high particle concentration and carrier viscosity.
The
coarsening of chains slowly forms spherical drop like structures, which grow with time (Figure 7f). Hayes [38] has reported similar coalescent of chains into a spherical drop like structure in magnetic fluid using optical microscopy. With increasing the concentration, the chain–chain interaction increases, which decrease the aspect ratio. Hence, the optical microscopic images
Optical microscopic images for fluid of different concentrations measured under
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Figure 7:
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IP
T
show similar outcomes as observed in ultrasonic results.
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the application of 0.1 T field after 5 min and 20 min. 3.4 Simultaneous effects of temperature and magnetic field for φ =10.3%
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The application of magnetic field induces the long-range structures in magnetic fluid. This structure can be disturbed by increasing the temperature of the system.
Increase in
temperature increases the thermal energy and Brownian motion of the particles which leads to break these aggregates thus making the system homogeneous. Hence, it will be interesting to study the simultaneous effect of the temperature and magnetic field on change in ultrasonic propagation velocity of the magnetic fluid.
14
ACCEPTED MANUSCRIPT 0.020 0.015
T= 338 K
0.010
T= 328 K T= 318 K
0.000
-0.005
T= 308 K
T
/0
0.005
-0.015 0.02
0.04
0.06
0.08
0.10
Change in ultrasonic propagation velocity as a function of applied magnetic field
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Figure 8:
=10.3 %
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-0.020 0.00
CR
IP
-0.010
M
at different temperature for =10.3 %. The line shows the Tarapov’s theory.
It can be seen from Figure 8 that with increasing temperature the change in ultrasonic
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propagation velocity for max (=10.3 %) increases from negative to the positive. At 308 °K change in ultrasonic propagation velocity is negative and becomes positive only at the highest
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field of 0.1 T. With increase in temperature from 308 - 318 °K, the magnitude of change in ultrasonic propagation velocity reduces and shows the positive value at comparatively lower
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field strength (H = 0.05 T). Further increase in temperature to 328 °K, it shows a positive anisotropy in the whole range of the applied magnetic field. It has a peak at the lower field value
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(H = 0.015 T), becomes positive minimum of 0.02 T field and then increases with increasing field and attain saturation. For the 338 °K temperature, the change in ultrasonic propagation velocity is positive and it increases with increasing field and attains saturation after 0.04 T field. The temperature dependent change in ultrasonic propagation velocity data also fitted with the modified Tarapov’s theory. Line in Figure 8 shows the Tarapov’s theory fitting for two different temperatures 308 °K and 338 °K. The fitted parameters are reported in Table 2.
Table 2:
Parameters derived using modified Tarapov’s theory for φ = 10.3 % at different temperatures. 15
ACCEPTED MANUSCRIPT φ=10.3 % Sr.
T
No
(± 0.5 °K)
μ
n x 1022
σμ -19
(± 0.02 x 10
2
A/m )
(± 0.05)
m-3 (± 0.1)
308
1.5
0.6
19.8
2
318
1.2
0.8
21.4
3
328
0.9
0.95
4
338
0.7
1.35
23.5 28.5
CR
IP
T
1
It inferred from the Table 2 that the magnetic moment of the particle decreases from 1.5
US
± 0.02 x10-19 A/m2 to 0.7 ± 0.02 x10-19 A/m2 with increasing temperature from 308 - 338 °K. The moment distribution and number density increases respectively from 0.6 to 1.35 ± 0.05 and
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19.8 to 28.5 upon increasing temperature. Actually the moment of particles should increase upon increasing temperature because the high temperature will break the aggregates. But in the present case, it is observed that the moment decreases even to that observed at room temperature.
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The decrease in magnetic moment with increasing temperature can be correlated to the
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temperature sensitive nature of the particles because the Curie temperature of the sample is low (380 °K) [39]. With increasing temperature, the chain like aggregates starts breaking due to two
PT
reasons (i) high thermal energy and (ii) reduced magnetic moment. The magnetic moment of aggregates decreases as temperature increases because Zn substituted Mn-ferrite is temperature
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sensitive, so the magnetic moment of particles reduces significantly with increasing temperature. The reduction in magnetic moment weakens the strength of Zeeman energy which is responsible
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for the chain formation. Hence, a prominent effect of breaking of chains into aggregates is seen with increasing temperature. In addition, the Curie temperature is calculated by extrapolating the reduction in magnetic moment with increase in temperature and it is found at 363 K. The value of Curie temperature, thus obtained is comparable to that obtained using another experiment [39]. 4. Conclusion The ultrasonic velocity of the magnetic fluid as a function of volume fraction, temperature and magnetic field is investigated for transformer oil based temperature sensitive 16
ACCEPTED MANUSCRIPT magnetic fluid. The ultrasonic velocity decreases with increasing volume fraction attributed to the particle-carrier interaction leading to form shorter aggregates.
The pre-aggregates in
magnetic fluid break when temperature increases in the absence of a field. Field dependent change in ultrasonic propagation velocity shows chain like alignment for low (1.6 %) volume fraction. With increasing volume fraction (6.8 %) there exist greater fractions of short dipolar chains, but large and stable compared to the low volume fraction creating a free space for sound
T
waves to propagate and results in the increase in the ultrasonic velocity with increasing field. For
IP
still higher volume fractions (10.3 %) the change in ultrasonic propagation velocity shows a
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negative deep with increasing field. The negative deep shows chain like structures formed due to the presence of the large number of pre-aggregates, which decreases the ultrasonic velocity. In
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an appropriately high concentration, the chains become thicker by aligning sidewise to the neighboring chains. The change in ultrasonic propagation velocity data were fitted with the
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modified Tarapov’s theory which shows the presence of aggregates with increasing volume fraction. The optical microscopy study confirms the short chain like structure at low volume
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fractions. These structures extend with the increasing volume fraction and increasing magnetic field strength. At higher volume fraction the chain-chain interaction occurs and thick columnar
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like structures formed. For 10.3 % volume fraction, the chain like structure becomes a spherical drop like fractals. The ultrasonic velocity and optical microscopy studies also confirm the results
PT
of thermal conductivity data analysis.
The simultaneous effect of the temperature and magnetic field for 10.3 % volume fraction
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has also been studied. At 308 °K change in ultrasonic propagation velocity is a negative forming thick chain like aggregate formation with the applied field.
This aggregates break with
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increasing temperature, the systematic variation in change in ultrasonic propagation velocity from negative to positive upon an increase in temperature reflects the same. The experimental data were fitted with the modified Tarapov’s theory. The fit parameters show decrease in magnetic moment from 1.5± 0.02 x10-19 A/m2 to 0.7 ± 0.02 x10-19A/m2 with increasing temperature from 308 °K to 338 °K. From the variation of magnetic moment with temperature obtained from the fitting of change in ultrasonic propagation velocity, the Curie temperature of the sample is obtained which is found at 363 K. The value is near to the Curie temperature obtained from the fluid using different techniques.
17
ACCEPTED MANUSCRIPT Acknowledgement: The authors would like to thank Department of Science & Technology, Government of India, New Delhi, for providing the financial support vide number; DST/TSG/2011/161-G project.
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39.
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Graphical Abstract
22
ACCEPTED MANUSCRIPT Highlights
Acoustic property of magnetic fluid is investigated as a function of temperature and magnetic field.
In zero field, the pre-aggregates found in magnetic fluid which breaks when
Change in velocity shows transformation from chain like alignment to short dipolar
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T
temperature increases.
chains.
Tarapov’s theory confirms the presence of chains and aggregates with increasing
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volume fraction.
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These aggregates break with increasing temperature, also reflected from Tarapov’s
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fit.
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23