We have studied the discrete spectrum of the forced oscillation of microdroplet aggregates in magnetic fluid in magnetic field H(t) = H[0]sinwt with the frequency of 0,01-100 Hz

Drozdova, V.I.

Romanenko, M.G.

Shagrova, G.V.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 8 No 3, 03055(3pp) (2016) Том 8 № 3, 03055(3cc) (2016) 
 
 
2077-6772/2016/8(3)03055(3) 03055-1  2016 Sumy State University 
Short Communication 
 
Spectrum Features of Forced Oscillations of Microdroplet Aggregates in Magnetic Fluids  
 
V.I. Drozdova, G.V. Shagrova, M.G. Romanenko 
 
North-Caucasian Federal University, 1, Pushkin st., 355009 Stavropol, Russia 
 
(Received 22 May 2016; published online 03 October 2016) 
 
We have studied the discrete spectrum of the forced oscillation of microdroplet aggregates in magnetic 
fluid in magnetic field H(t)  H0sint with the frequency of 0,01-100 Hz. 
 
Keywords: Magnetic fluid, Microdroplet aggregate, Forced oscillations, Fourier analysis. 
 
DOI: 10.21272/jnep.8(3).03055 PACS numbers: 75.50.Mm, 02.60.Cb 
 
 
1. INTRODUCTION 
 
Magnetic fluids are artificial magnetizing 
nanodispersive environment, combining fluidity with 
the ability to be magnetized. Microdroplet aggregates 
are included in some of the samples of magnetic fluids 
type «magnetite in water» [1] and «magnetite in 
kerosene» [2], represent a field outside a spherical drop 
of highly concentrated magnetic fluid with size of about 
1 μm in the magnetic fluid of low concentration. High 
sensitivity microdroplet aggregates to the magnetic 
field is associated with high for artificial liquid medium 
values of magnetic permeability (~ 50) unique and low 
values of interfacial tension at the interface of 
microdroplet – ambient magnetic fluid ( ~ 10 – 7N/m). 
In a weak alternating magnetic field at  < 10 – 6 N/m 
possible forced oscillations of both the small and large 
amplitude [3]. The relevance of the study of oscillations 
of microdroplet aggregates are associated with a non-
contact determination of physical properties of 
individual units in the parameters of oscillations and 
the search for effective ways to control the properties of 
the samples containing the magnetizable ensembles of 
interacting micro-objects. Deformation [1] and 
oscillations [3] of microdroplet aggregates in a magnet 
field are of a hysteresis character, which changes the 
shape of the aggregates correspond to the critical fields 
of a strong stepwise elongation with increase of the 
field threshold (Н1) and abrupt reductions in elongation 
with decreasing field (H2), and H2  Н1. In this article 
we consider the discrete spectrum of forced oscillations 
of microdroplet aggregates in the field H(t)  Hosint 
when Ho  Н1. The characteristic time of deformation 
o ~ Ro/ for the studied samples is a few seconds, so 
the period change of the external field T in the 
frequency range 0,01 Hz ≤  f ≤ 100 Hz can be more or 
less o. Were previously studied forced oscillations, 
mainly during Т  o and Т  o. 
Less studied are the forced oscillations at frequency 
1-2 Hz when o ~ Т and a change in the nature of 
oscillations from hysteretic to anhysteretic.  
 
2. DESCRIPTION OF THE OBJECT AND 
METHODS OF INVESTIGATION 
 
In this article we investigate discrete spectrum of 
forced oscillations, the contribution of higher harmonics 
in the oscillations, as well as the applicability of the 
previously developed systems computer simulation [4] to 
describe the oscillations, when o ~ Т. Research methods 
based on field and numerical experiments. 
Experimental setup and methodology is described in 
[3]. Images of isolated microdroplet aggregates were 
obtained at high magnification with a microscope, and 
change their form in an alternating magnetic field were 
investigated by recording the light transmitted through 
the sample. In an alternating magnetic field changing 
the shape of the aggregates during oscillations lead to 
periodical changes of the luminous flux, passed through 
the slit diaphragm, on which was projected the image of 
the boundary between aggregates and the surrounding 
liquid. Luminous flux (signal PMT) and the signal 
proportional to the alternating magnetic field were 
recorded using a dual beam oscilloscope. Samples for 
testing consisted of a magnetic fluid type «magnetite in 
kerosene», were containing microdroplet aggregates with 
a size of ~ 1 μm. Interfacial tension did not exceed  
410 – 7 N/m, the permeability of the aggregates was ~ 50. 
The magnitude of the external field H(t)  Hosint 
experimentally selected so as to obtain a stepwise 
elongation of the aggregates, when the instantaneous 
value of the field exceeded the critical field stepwise 
elongation Н1, at the same time, the consolidation of 
aggregates into larger isn’t occurred. 
Oscillations microdroplet aggregates in the frequency 
range of 0.01-100 Hz can be divided into three types: 
steady state oscillations in Т  o the transition mode 
when Т~ o and steady-state mode when Т  o. 
Steady state oscillations at Т  o, described in the 
work [5], characterized by the fact that during the period 
of oscillation the ratio of the semiaxes of units (t) 
changes to the order from the value (t)  1 
corresponding spherical shape to the value (t)  10 
which corresponds to the needle-like shape of the 
aggregates. Such variations are of a hysteresis character, 
occurring when the frequency of the external field f 
changes from 0.01 to 0.1 Hz. 
The transition mode oscillations (Т ~ o) obtained 
when f ~ 1 Hz.  This mode corresponds to the transition 
from hysteretic nature of the oscillations to anhysteretic. 
Periodic curves corresponding to the luminous flux 
associated with the deformation of the shape of droplets 
are non-sinusoidal in nature. Oscillations occur 
 V.I. DROZDOVA, G.V. SHAGROVA, M.G. ROMANENKO J. NANO- ELECTRON. PHYS. 8, 03055 (2016) 
 
 
03055-2 
relatively elongated shape and the restoration of 
spherical shape does not occur. The shape of the curves 
of the light flux in the transition regime (Т ~ o) not 
stable in amplitude and resembles the letter «M». 
 
3. ANALYSIS OF THE RESULTS OF THE 
EXPERIMENT 
 
For oscillation analysis used a decomposition of the 
signal in the Fourier series (F), and wavelet transform 
of this signal using the wavelet Daubechies of the 4th 
order (G). The spectrogram resulting from a wavelet 
transformation Gk, and the Fourier transformation  
Fk see Figure 1(a).  
Figure 1 (b) shows a graph of the analyzed signal Si 
and the points obtained by the inverse wavelet 
transform AGi. 
From the obtained results it follows that the 
contribution of harmonics of the frequency f and the 2f in 
the transitional regimes are close in magnitude, an 
appreciable contribution to the oscillations also make 3 
and 4 harmonics. Wavelet transform in the analysis of 
forced oscillations can be used to detect the transition, as 
for other modes of oscillation the contribution of the 
wavelet functions are negligible. 
Steady state oscillations at Т << o characterized by 
the fact that the forced oscillations are relatively highly 
elongated needle-like shape and are reduced to 
fluctuations of the pointed ends, while the oscillations 
are of anhysteretic in nature [6]. At low values  
 ~ 10 – 7 N/m and high values of magnetic permeability  
 
 
a b 
 
Fig. 1 – Results of Fourier and wavelet analysis of a signal: a) Spectrogram of the direct Fourier transform Fk     
and a direct wavelet transformation Gk,  b) recovered as a result of the inverse wavelet transformation AGi of the analyzed 
signal Si 
 
oscillations are not completely terminated when the 
frequency of the external magnetic field f  20 Hz and 
you may receive small vibrations of the ends of highly 
elongated aggregates, despite the fact that during visual 
observations with a microscope the aggregates seem to 
be fixed. For harmonic components of the discrete 
spectrum the coefficients ki  Аi/А, representing the 
relationship of effective values of the harmonics (Аi) to 
the effective value of the whole curve (A) where i – the 
number of the harmonic were calculated. The 
dependences of the calculated values ki from the 
frequency are presented in Figure 2. Curve 1 
corresponds to the fundamental oscillation. The 
frequency of the fundamental harmonic of oscillations 
coincides with the frequency of driving force (2f). 
Curve 2 corresponds to the harmonic, the frequency of 
which coincides with the frequency of the external field f 
and is equal to half the frequency of the fundamental 
harmonic. Values ki, obtained at i  3, are shown by 
circles, at i  4 – triangles, at i  5 – stars. 
 
 
 
Fig. 2 – Dependence ki  Аi/А from the frequency to the 
harmonic frequency 2f (curve 1) and frequency f (2) 
 
 
 SPECTRUM FEATURES OF FORCED OSCILLATIONS… J. NANO- ELECTRON. PHYS. 8, 03055 (2016) 
 
 
03055-3 
4. CONCLUSION 
 
From the obtained results it follows that for 
strongly elongated aggregates with increasing 
frequency the contribution of the harmonic frequency f 
to the current value of the signal is increased, and the 
fraction of the harmonic of frequency 2f decreases. 
On changing the external field frequency from 10 to 
80 Hz, the relative fraction of higher harmonics is 
significantly lower than the fraction of harmonic 
frequency f. The relative fraction of the harmonic 
frequency 2f in oscillations of strongly elongated ends 
at f  60 Hz is less than 0.17 and the harmonic 
frequency 2f is merged into the noise. 
Thus, the pointed ends of the microdroplet 
aggregates can make the forced oscillations in the 
frequency range from 20 to 80 Hz, which are 
characterized by the presence mainly in the discrete 
spectrum of harmonic frequency f. Therefore, for highly 
elongated microdroplet aggregates in a weak 
alternating field the assumption of the linear nature of 
the magnetization, which should lead to a doubling of 
the oscillation frequency, is not performed. 
Computer simulation of forced oscillations of 
microdroplet aggregates [4] on the basis of 
mathematical model and systems computer simulation, 
constructed under the assumption about the linear 
nature of the magnetization and ellipsoid shape of 
aggregates can adequately describe the variation in 
Т  o, and Т  o. When Т ~ o to obtain a non-
sinusoidal periodic curves corresponding time 
dependences of the ratio of the semiaxes (t) it wasn't 
possible. At the same time, the shape of the curves (H) 
corresponding to dependence of  on the instantaneous 
field values corresponds to the shape of the experimental 
curves of the dependence of intensities of anisotropic 
scattered light on the instantaneous field values for the 
samples of magnetic fluids type «magnetite in kerosene» 
containing microdroplet aggregates [2]. Since the 
oscillations of the aggregates lead to fluctuations in 
intensity of scattered light, a system of computer 
simulation [4] can be useful in the analysis of oscillation 
regimes when Т ~ o. 
 
 
REFERENCES 
 
1. J.C. Bacri, D. Salin, J. Physique-Lett. 44, L415 (1983).  
2. V.I. Drozdova, G.V. Shagrova, J. Magn. Magn. Mater. 85, 
93 (1990).  
3. V.I. Drozdova, V.V. Kushnarev, G.V. Shagrova, Colloid J. 
68, 142 (2006). 
4. G.V. Shagrova, V.I.  Drozdova, M.G. Romanenko, J. Nano- 
Electron. Phys. 7 No 4, 04020 (2015). 
5. V.I. Drozdova, G.V. Shagrova, M.G. Romanenko, J. Nano- 
Electron. Phys. 6 No 3, 03013 (2014). 
6. V.I Drozdov, G.V. Shagrova, M.G. Romanenko, 2nd 
International scientific-practical conference – Physics and 
technology of nanomaterials and structures, 243 (Kursk: 
SWSU: 2015). 
 


Spectrum Features of Forced Oscillations of Microdroplet Aggregates in Magnetic Fluids

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Spectrum Features of Forced Oscillations of Microdroplet Aggregates in Magnetic Fluids

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SocioEconomic Challenges Journal (Sumy State University)