Download Determination of Sound Speed in a Magnetic Fluid Using

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 23 (2016) pp. 11171-11175
© Research India Publications. http://www.ripublication.com
Determination of Sound Speed in a Magnetic Fluid Using
Acoustomagnetic Effect
Irina Aleksandrovna Shabanova, Anastasia Mikhaylovna Storozhenko and Vyacheslav Mikhaylovich Polunin
Southwest State University, 94, 50 let Oktyabrya, Kursk 305040, Russia.
Abstract
This paper describes the interferometric methodology for
determining the speed of ultrasonic wave’s propagation in a
magnetic fluid. The technique uses acoustomagnetic effect,
which can be observed in a magnetized magnetic fluid, when
elastic oscillations inside it. We describe the experimental
setup and the measurement technique in detail. We
determined the speed of ultrasonic waves propagation in the
system Magnetic Fluid - Cylindrical Shell for two samples of
nanodispersed magnetic fluids. The samples are colloidal
solutions of single-domain magnetite particles in a
hydrocarbon (kerosene, mineral oil) medium stabilized by
oleic acid. We got the values of the sound speed in the system
Magnetic Fluid - Glass Tube for different frequencies of
sound introduced into the system. Estimation of the sound
speed in the not-limited samples, held by the Korteweg
formula, correlates with the previously obtained values. One
can use our experimental data to calculate physical (magnetic
and geometric) parameters of magnetic nanoparticles, which
are dispersed in a magnetic fluid, by acoustogranulometric
analysis.
EXPERIMENTAL SETUP
To determine the speed of ultrasonic waves in a magnetic
fluid, we applied special experimental setup, which is
schematically shown in Figure 1.
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When simultaneously in a magnetic and ultrasound fields,
nanodispersed magnetic fluid (MF) broadcasts an
electromagnetic wave, which is a unique property of MF. This
effect called acoustomagnetic was first detected by Polunin
and it is described in detail in [1-2]. During the process of
acoustic wave propagation in magnetized MF, perturbations
of magnetization and demagnetizing field in a carrier fluid
occur due to fluctuations in concentration of ferroparticles and
temperature, as well as due to the kinetics of aggregates [3-6].
Because of their competition, one can observe the
acoustomagnetic effect (AME). It is an emitting of EMF in an
induction coil that is pressed to glass tube filled with a
magnetic fluid. This effect allows recording the acoustic
oscillations and exploring the acoustic field in the MF using
induction method.
The vast majority of scientists, who study AME
experimentally, use a cylindrical tube from non-magnetic and
non-conductive material [4]. The tube filled with MF is placed
into the transversal or longitudinal magnetic field either
partially or completely. After that, a sound wave is introduced
into the liquid. The alternating magnetic field in a magnetic
fluid induces voltage in the measuring induction coil. A
variable EMF from the coil is supplied to processing.
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Keywords: magnetic fluid, magnetic field, sound speed,
acoustomagnetic effect, standing sound wave, interferometer
INTRODUCTION
11
2
Figure 1. Experimental setup
The signal from sound oscillation generator 1 comes in
parallel to frequency meter 2, voltmeter 3, and piezo plate 4
mounted in acoustic cell 5. The sound signal forms a standing
wave when propagating through the MF confined in glass tube
6. The variable EMF from inductance coil 7 closely adjoining
the tube with the MF comes to selective amplifier 8, and then
in parallel to oscilloscope 9 and analog-to-digital converter 10
combined with computer 11. The inductance coil 7 is rigidly
fixed on the cinematic unit of a cathetometer 12. The
magnetic field is produced by a strong permanent magnet 13.
The magnetic fluid fills the glass tube, the bottom of which is
located between the poles of our permanent magnet. The
height of MF column is 200 mm.
Here are the parameters of our glass tube: glass brand - NS-3;
E  7.26 1010 Pa , Poisson ratio 0.21,
3
density  t  2400 kg/m , longitudinal wave velocity
Young's modulus
c p  5500 m/s ; outer and inner radii R1  8 mm ,
R2  6.9 mm , wall thickness h  1.1 mm , tube length
200 mm.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 23 (2016) pp. 11171-11175
© Research India Publications. http://www.ripublication.com
We carry out the experiment taking into account the optimal
conditions, i.e. noise-proof, control of temperature
T  31  0.2 C , and constant voltage on piezoelectric
element U  40  0.5 V . The acoustic cell with MF is set to
pole gap in a such way that magnetic field lines are
perpendicular to the tube axis.
The sensor moves along the tube with an accuracy of 0.01 mm
due to using a cathetometer. Its distance is the central area of
the pole gap and the adjacent areas of non-uniform field.
It is known that the amplitude of the excited oscillation modes
in the tube (normal modes) depends on the methodic of
excitation. In case of point-source, there are different
oscillation modes in the system Fluid – Tube. At the same
time, the piezo plate pressed to the bottom contributes to the
excitation of zero (piston) oscillation modes. That is why we
introduce the sound into the tube from its bottom, unlike [4].
When preparing the experiment to determine the sound speed
in the system MF - Cylindrical Shell, we act according to the
algorithm:
1.
Fill the acoustic cell up with MF;
2.
Fix it in the field of a permanent magnet;
3.
Select a sound frequency.
We fill the acoustic cell up with MF the day before the start of
the measurement to let all air bubbles leave the liquid through
its surface. To avoid the curve surface of the MF under the
influence of the normal component of the magnetic field we
carry out a forced stabilization of the liquid surface. For this
purpose, the upper end of the tube after the filling up to the
top is hermetically sealed by thin polyethylene film.
The measurements were performed as follows. At certain
frequencies of input sound oscillations in the system MF Cylindrical Shell standing waves occur. When moving the
measuring coil along the tube axis in a magnetic field, the
oscilloscope screen shows periodically alternating maxima
and minima of the amplitude of the received signal
corresponding to the nodes and anti-nodes of the standing
wave. The measuring coil is set in the antinode position of the
standing wave in the region of the most homogeneous
magnetic field, and then we select the sound frequency to
achieve a maximum of the signal amplitude.
After wide-band amplification and analog-to-digital
conversion, the signal from the inductive coil was applied to a
PC, where NI LabView made its decomposition to spectrum.
We carried out the measurements with this selected frequency
only if the amplitude of the signal is more than twice bigger
than the amplitude of the signal of other frequencies (traveling
wave component or noise). We switched the amplifier to a
selective mode only after checking the mentioned conditions.
MEASURING TECHNIQUE
It is known that in a cylindrical tube various modes of waves
can exist. If the frequency of oscillations is less than critical
[3-5], then only the plane waves can exist inside a tube and
they propagate with the phase speed
cT .
The following
expression [7] is a criterion of propagation of the plane waves
in a circular tube
RT  0.61 ,
(1)
Here RT is a tube radius, [lambda] is the length of sound
wave.
The sound speed is calculated using the following methodic of
ultrasound interferometer [5]. At some distance from the
bottom of the tube, which is not smaller than 3 / 2 , we fix
amplitude minimum of sound oscillations and then we
measure its coordinate Z d several times. After determination
of the lower minimum coordinates
Z d , we move the
induction coil up to a certain upper minimum amplitude of
EMF Z u , and during this process, we count the number of
half-waves N between
Z u and Z d as well as coordinates of
nodes in a standing wave. In case of external synchronization
mode of an oscilloscope, we see the phase change on the
screen when the coil is passing through the nodes of the
standing wave. The upper coordinate of minimum is also
determined several times.
Using the measured values of the coordinates
Z u and Z d we
calculate a sound wavelength by a simple formula:
  2(Z u  Z d ) / N ,
(2)
Its absolute accuracy is
 Z u
Z d
    

 Zu  Zd Zu  Zd

2Z
   
Zu  Zd

(3)
When we determine the coordinates of standing wave
minimum, there are some difficulties. The first is the fact that
near the minimum, sine wave changes a little. Secondly, the
inaccuracy of observation on the oscilloscope screen plays the
important role. These factors contribute the most significantly
to the measurement error.
We calculate the sound speed c in a magnetic fluid filling the
tube according to the vivid formula
c   ,
(4)
Here [nu] is the frequency of sound oscillations.
Error of measurement for sound speed is determined by the
formula for calculation of indirect measurements errors
c 
c  


.
с


(5)
According to our estimations, the error of the sound speed
value in MF filling a tube does not exceed 5%. This is also
confirmed by the range of c values, which were obtained on
the same sample but at different frequencies of oscillations
introduced into the system.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 23 (2016) pp. 11171-11175
© Research India Publications. http://www.ripublication.com
A limit of this methodology is that the tube containing the
fluid should be made from non-magnetic and non-conductive
material. This fact excludes the possibility of metal tubes
using, but allows experiments with almost all other materials.
We used glass tubes in this work.
single-domain magnetite
RESULTS AND DISCUSSION
The results for sound speed in the samples MF-58 and MF-56
at different frequencies are shown in Table 2.
The research described in this paper was carried out on
samples of magnetic fluid, which is a colloidal solution of
Fe3O4 particles in the hydrocarbon
medium (kerosene, mineral oil) stabilized by oleic acid [8-12].
Information about carrier liquids and the basic physical
parameters of the samples obtained at temperature
31  0.2C is presented in Table 1.
Table 1. Properties of MF samples
Sample
Medium
Density
Magnetization saturation
ρ [kg/m ]
Concentration of solid
state φ [%]
MF-56 mineral hydrocarbon oil
2036
29.7
33.6
MF-58
2075
31.4
35.1
3
kerosene
MS [kA/m]
Table 2. Sound speed values
Sample Frequency
[Hz]
MF-56
MF-58
The length of a
standing wave [mm]
Sound speed
[m/s]
46
11
1012
48
11
1056
50
10
1000
53
9
954
55
9
990
62
9
1116
64
8
1024
66
8
1056
36
13
936
39
12
936
43
13
1114
46
11
1012
48
9
864
51
8
816
53
8
848
56
8
896
59
8
944
64
9
1150
The mean value of
sound speed [m/s]
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The absolute error of The relative error of
sound speed
sound speed
1026
38
3,7%
952
85
4,9%
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 23 (2016) pp. 11171-11175
© Research India Publications. http://www.ripublication.com
The sound speed values in the system MF - Glass Tube were
calculated for different frequencies of sound oscillations, and
the dispersion of values is in the range of mentioned
measurement error.
One may fear that the presence of a constant magnetic field
would lead to a distortion of the data due to the dependence of
a sound speed in the MF on a magnetic field strength. The
mentioned fear is unnecessary, because [1] found that the
sound speed in a stable magnetic fluid does not depend on the
magnetic field strength up to ~ 500 kA/m within the
measurement error.
To estimate the experimental values of a sound speed in the
samples, we calculated the theoretical values using Korteweg
formula. For the speed of acoustic wave in the system Liquid Tube at low frequencies, it looks like:
c2 =
Here
c 02
,
2 R
1+
E h
(6)
c0 is the sound speed in an infinite medium, [betta] is
wide-spread type of magnetic fluids “magnetite particles in a
hydrocarbon medium stabilized by oleic acid”.
For sound frequencies from 35 Hz to 65 Hz, the values of
sound speed in the system Magnetic Fluid - Glass Tube and in
the not-limited samples correlate with the previously obtained
values.
The described experimental data can be further used for
calculating the physical (magnetic and geometric) parameters
of magnetic nanoparticles in MF by the acoustogranulometric
method [4].
ACKNOWLEDGES
This work was supported by the Grant of the President of the
Russian Federation for young Russian scientists, contract
#14.Z56.16.5703-MK. I.A.S. also acknowledges support from
Russian Foundation for Basic Research within research
project #16-32-50092\16.
REFERENCES
compressibility coefficient, R is an average radius of a tube,
h  R1  R2 is a thickness of a tube wall, E is an elastic
modulus of tube material, which is E   E (1  ) , E is
Young's modulus, and [nu] is Poisson's ratio of the material.
The compressibility coefficient [betta] could be got from the
expression с =
0
1 , where
f
f
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is a density of liquid.
After simple transformations of (6) we obtain:
c0  c
E h
E h  2 R f c 2
(7)
Substituting the parameters values in this formula, we find the
following values of the sound speed in an infinite medium
c0 :
For MF-56
c0  1460 m/s ,
For MF-58
c0  1277 m/s .
These values are close to the results obtained earlier in [1] for
the MFs of the same type.
CONCLUSIONS
This interferometric methodology for determining the sound
speed in a magnetic fluid is promising due to its simple
realization, i.e. experimental setup and the measurement
technique. The technique uses acoustomagnetic effect, which
can be observed when elastic oscillations are propagating in a
magnetized magnetic fluid.
We calculated the speed of ultrasonic waves propagation in
the system Magnetic Fluid - Cylindrical Shell for two samples
of nanodispersed magnetic fluids, which belong to the most
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 23 (2016) pp. 11171-11175
© Research India Publications. http://www.ripublication.com
[10]
V.E. Fertman, “Magnetic fluids: Reference Guide”.
Moscow: High education, pp. 184, 1988.
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S. Chikazumi, “Physics of Ferromagnetism” (2nd
edition). Oxford University Press, pp. 668, 1997.
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S. Odenbach (Ed.), “Colloidal Magnetic Fluids:
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Lect”. Notes Phys. Berlin: Springer, pp. 430, 2009.
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