The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3365

Bashtovoi, V.

Klimovich, S.

Motsar, A.

Reks, A.

Ryapolov, P.

Shabanova, I.

Storozhenko, A.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 5 No 4, 04028(3pp) (2013) Том 5 № 4, 04028(3cc) (2013) 
 
 
The article was reported at the International Conference «Physics and Technology of Nanomaterials and Structures», Kursk, 21-22 November, 2013 
2077-6772/2013/5(4)04028(3) 04028-1  2013 Sumy State University 
Short Communication 
 
Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid 
 
V. Bashtovoi1,*, A. Reks1, S. Klimovich1, А. Motsar1, P. Ryapolov2, A. Storozhenko2, I. Shabanova2 
 
1 UNESCO Chair, Belarussian National Technical University, 65, Nezavisimosti Ave., 220013Minsk, Belarus 
2 Department of Nanotechnology and Engineering Physics, Southwest State University, 305040 Kursk, Russia 
 
(Received 27 October 2013; published online 10 December 2013) 
 
The present work deals with experimental investigation of the levitation of magnetic and non-magnetic 
bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It 
is established that the point of levitation of bodies in a magnetic fluid varies with time. 
 
Keywords: Magnetic fluid, Brownian diffusion, Levitation. 
 
 PACS numbers: 47.65.Cb, 47.57.eb 
 
 
                                                          
* bashv@rambler.ru 
1. INTRODUCTION 
 
As theoretically shown [1, 2], the processes of mag-
netophoresis and Brownian diffusion in a magnetic 
fluid under inhomogeneous magnetic fields can essen-
tially influence a static pressure distribution in it due 
to a redistribution of magnetic particle concentration. 
Accordingly, the statics of a magnetic fluid and, partic-
ularly, conditions for levitation of magnetic and non-
magnetic bodies in it can, to a considerable extent, be 
specified by these processes.  
This fact is of special importance for magnetic fluid 
devices based on the levitaton of permanent magnets in 
the magnetic fluid: suspensions in measuring devices 
[3], dynamic shock absorbers [4], etc. for which the sta-
bility of parameters, in particular suspension elasticity, 
is significant. 
Among the fundamental parameters responsible for 
mass transfer processes in the magnetic fluid are:  
– mobility of magnetic particles b that for spherical 
particles is determined through the viscosity of the 
carrier fluid η and through their radius R: b = 16ηR;  
– diffusivity D that in Einstein’s classical theory of 
Brownian diffusion of particles is related to the mobili-
ty by / 6D kTb kT R  ; 
– dimensionless criterion 0 0 /mU m H kT  that is 
the ratio of the potential energy of a particle with a 
magnetic moment mm under a magnetic field H0 to its 
thermal energy kT. Here 0 is the magnetic permeabil-
ity of vacuum, k is the Boltzmann constant, T is the 
temperature. 
– characteristic dimension of concentration inhomo-
geneity l, at which the particle concentration changes e 
times. It is determined by the value U  1. In this case, 
as a characteristic value of a magnetic field one should 
choose a product of a characteristic value of its gradi-
ent G  |gradH| and a characteristic dimension: 
H0  Gl. Then l  kT/0 mm G.  
– characteristic diffusion time, τ , of particles in the 
magnetic fluid. It is determined as follows: 
τ  l2/D  RkT/(0 mm G)2. 
 
2. EXPERIMENT 
 
Experiment is carried out with magnetic fluids based 
on transformer oil and kerosene with magnetite parti-
cles. Their properties are presented in a table below.  
 
Table 1 – Physical properties of used magnetic fluids 
 
Carrier fluid 
Transform-
er oil 
Kerosene 
Magnetic fluid 
name 
MOT-31 MK-28 MK-44 
Magnetisation 
of saturation 
MS, kA/m 
31,2 28,3 43,8 
Density , kg/m3 1270 1158 1305 
Magnetic fluid 
viscosity , Pa·s 
0,0356 0,0025 0,0066 
Carrier fluid 
viscosity , Pa·s 
0,02 0,0008 
Magnetic parti-
cles volume con-
centration, % 
6,6 5,9 9,1 
Magnetic parti-
cle diameter, dm 
7,6-12 8-12 8,4-12 
 
The mean magnetic moment of magnetite particles 
is mm  2.5·10 – 19 J/T. 
 
2.1 Levitation of a Permanent Magnet in Mag-
netic Fluid 
 
The influence of mass transfer processes in the 
magnetic fluid on the levitation of a permanent magnet 
in it is studied by the example of an object typical for 
the above-mentioned magnetic fluid devices. It repre-
sented a magnet inside a large magnetic fluid drop held 
on a horizontal solid base, as shown in Fig. 1. 
Rectangular ferrite-barium magnets with magneti-
zation along the shortest side are used. Their size is 
10 × 20 × 5 mm, and mass is 4,7 g. 
At the initial time moment, the permanent magnet 
placed into a homogeneous magnetic fluid occupies 
some equilibrium position at a distance h0 from the 
 V. BASHTOVOI, A. REKS, S. KLIMOVICH, ET AL. J. NANO- ELECTRON. PHYS. 5, 04028 (2013) 
 
 
04028-2 
base. With time, because of the processes of magneto-
phoresis and Brownian diffusion, the concentration of 
magnetic particles in the vicinity of the magnet in-
creases and near the base decreases. As a result, the 
magnet when acted upon by the gravity moves closer to 
the base and finally occupies a new equilibrium posi-
tion. In experiment, this movement Δh is fixed by 
means of a cathetometer with an accuracy of 0.01 mm. 
 
1
2
3
4
S
N
 
 
Fig. 1 – Scheme of experimental cell on permanent magnet 
levitation. 1 – solid base, 2 – magnetic fluid, 3 – permanent 
magnet, 4 – transparent cover 
 
It should be noted that such variations also result 
in enhancing the stiffness of the system. 
Data for the one magnet will be presented below.  
Maximum magnetic field intensity at the surface of it is 
65 kA/m, and the corresponding gradient of the field 
intensity at this point is equal to 15000 kA/m2. 
The values of the criterion U corresponding to this 
magnetic field is 5,1. 
The magnetic fluid volume V is varied from 3000 to 
5000 mm3.  
Time variations of the positions of levitation of the 
magnet in the magnetic fluid are shown in Figs. 2 and 3. 
 
 
 
Fig. 2 – A relative displacement Δh/h0 of the levitation point 
of the magnet in the kerosene based magnetic fluid in time 
 
The comparison of the data in Figs. 2 and 3 first of 
all attracts attention to an essentially different time of 
attaining a new equilibrium position by the magnet for 
different fluids.  
As seen from the presented in Introduction expres-
sion for the characteristic diffusion time, τ, of magnetic 
particles in the magnetic fluid, it is directly proportion-
al to the viscosity of the carrier fluid. For the conditions 
of the experiment described it is 220 min for kerosene 
based magnetic fluids and 5500 min for transformer oil 
based fluids. This is consistent with the order of magni-
tudes for the results plotted in Figs. 2 and 3.  
 
 
 
Fig. 3 – A relative displacement Δh/h0 of the levitation point of 
the magnet in the transformer oil based magnetic fluid in time 
 
2.2 Levitation of a Non-magnetic Body in  
Magnetic Fluid 
 
A plexiglas disc 7 mm in height and 23 mm in diame-
ter is used as a non-magnetic body. A coaxially magnet-
ized circular ferrite-barium magnet 20 mm in height, 
with inner and outer diameters equal to 84 and 40 mm,  
 
1
2
3
4
S
N
S
N
 
 
Fig. 4 – Scheme of experimental cell on levitation of 
nonmagnetic disk. 1 – circular permanent magnet, 2 – 
magnetic fluid, 3 – non magnetic disc, 4 – transparent vessel 
 
 
 
Fig. 5 – Absolute displacement Δh of the levitation point of a non-
magnetic disc in the transformer oil based magnetic fluid in time 
 
respectively, is used as a source of an inhomogeneous 
magnetic field. Maximum values of the magnetic field 
intensity and its vertical gradient on the magnet axis 
are equal to 22 kA/m and 3000 kA/m2. Because of its 
small density, the disc was floating over the magnetic 
fluid surface. The fluid filled a cylindrical vessel located 
inside the magnet ring, as presented in Fig. 4. 
 INFLUENCE OF BROWNIAN DIFFUSION ON LEVITATION… J. NANO- ELECTRON. PHYS. 5, 04028 (2013) 
 
 
04028-3 
In this case, the buoyancy force acting upon the disc 
decreases with time and it more submerged into the 
fluid [2]. In experiment, this movement Δh was also 
fixed by means of the cathetometer. The results are 
presented in Fig. 5.  
As seen from Fig. 5, the characteristic diffusion 
time is of the order of 4000 min and corresponds to the 
identical experimental data on the floating of the mag-
net in the transformer oil based magnetic fluid, Fig. 3. 
ACKNOWLEDGEMENT 
 
The study was supported by The Ministry of educa-
tion and science of Russian Federation, project № 
14.В37.21.0906 "The research on interaction of physical 
fields in acoustomagnetic effect on nanodispersed mag-
netic fluid". 
 
 
REFERENCES 
 
1. V.G. Bashtovoi, V.K Polevikov, A.E. Suprun, A.V. Stroots, 
S.A. Beresnev, Magnetohydrodynamics 43, 17 (2007). 
2. V.G. Bashtovoi, V.K  Polevikov, A.E. Suprun, A.V. Stroots, 
S.A. Beresnev, Magnetohydrodynamics 44, 121 (2008). 
3. A. Suprun, D.V. Simonenko D, Yu. Romanov. US Patent, 
6, 731, 268, (2004). 
4. V. Bashtovoi, A. Reks, P. Kuzhir, G. Bossis, A. Vikulenkov, 
A. Moisheev, N. Markachev Patent FR 2 894 004 –A1, 
01.06.07, Bulletin 07/22. 
 


English

Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 5 No 4, 04028(3pp) (2013) Том 5 № 4, 04028(3cc) (2013)   The article was reported at the International Conference «Physics and Technology of Nanomaterials and Structures», Kursk, 21-22 November, 2013 2077-6772/2013/5(4)04028(3) 04028-1  2013 Sumy State University Short Communication  Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid  V. Bashtovoi1,*, A. Reks1, S. Klimovich1, А. Motsar1, P. Ryapolov2, A. Storozhenko2, I. Shabanova2  1 UNESCO Chair, Belarussian National Technical University, 65, Nezavisimosti Ave., 220013Minsk, Belarus 2 Department of Nanotechnology and Engineering Physics, Southwest State University, 305040 Kursk, Russia  (Received 27 October 2013; published online 10 December 2013)  The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.  Keywords: Magnetic fluid, Brownian diffusion, Levitation.   PACS numbers: 47.65.Cb, 47.57.eb                                                             * bashv@rambler.ru 1. INTRODUCTION  As theoretically shown [1, 2], the processes of mag-netophoresis and Brownian diffusion in a magnetic fluid under inhomogeneous magnetic fields can essen-tially influence a static pressure distribution in it due to a redistribution of magnetic particle concentration. Accordingly, the statics of a magnetic fluid and, partic-ularly, conditions for levitation of magnetic and non-magnetic bodies in it can, to a considerable extent, be specified by these processes.  This fact is of special importance for magnetic fluid devices based on the levitaton of permanent magnets in the magnetic fluid: suspensions in measuring devices [3], dynamic shock absorbers [4], etc. for which the sta-bility of parameters, in particular suspension elasticity, is significant. Among the fundamental parameters responsible for mass transfer processes in the magnetic fluid are:  – mobility of magnetic particles b that for spherical particles is determined through the viscosity of the carrier fluid η and through their radius R: b = 16ηR;  – diffusivity D that in Einstein’s classical theory of Brownian diffusion of particles is related to the mobili-ty by / 6D kTb kT R  ; – dimensionless criterion 0 0 /mU m H kT  that is the ratio of the potential energy of a particle with a magnetic moment mm under a magnetic field H0 to its thermal energy kT. Here 0 is the magnetic permeabil-ity of vacuum, k is the Boltzmann constant, T is the temperature. – characteristic dimension of concentration inhomo-geneity l, at which the particle concentration changes e times. It is determined by the value U  1. In this case, as a characteristic value of a magnetic field one should choose a product of a characteristic value of its gradi-ent G  |gradH| and a characteristic dimension: H0  Gl. Then l  kT/0 mm G.  – characteristic diffusion time, τ , of particles in the magnetic fluid. It is determined as follows: τ  l2/D  RkT/(0 mm G)2.  2. EXPERIMENT  Experiment is carried out with magnetic fluids based on transformer oil and kerosene with magnetite parti-cles. Their properties are presented in a table below.   Table 1 – Physical properties of used magnetic fluids  Carrier fluid Transform-er oil Kerosene Magnetic fluid name MOT-31 MK-28 MK-44 Magnetisation of saturation MS, kA/m 31,2 28,3 43,8 Density , kg/m3 1270 1158 1305 Magnetic fluid viscosity , Pa·s 0,0356 0,0025 0,0066 Carrier fluid viscosity , Pa·s 0,02 0,0008 Magnetic parti-cles volume con-centration, % 6,6 5,9 9,1 Magnetic parti-cle diameter, dm 7,6-12 8-12 8,4-12  The mean magnetic moment of magnetite particles is mm  2.5·10 – 19 J/T.  2.1 Levitation of a Permanent Magnet in Mag-netic Fluid  The influence of mass transfer processes in the magnetic fluid on the levitation of a permanent magnet in it is studied by the example of an object typical for the above-mentioned magnetic fluid devices. It repre-sented a magnet inside a large magnetic fluid drop held on a horizontal solid base, as shown in Fig. 1. Rectangular ferrite-barium magnets with magneti-zation along the shortest side are used. Their size is 10 × 20 × 5 mm, and mass is 4,7 g. At the initial time moment, the permanent magnet placed into a homogeneous magnetic fluid occupies some equilibrium position at a distance h0 from the  V. BASHTOVOI, A. REKS, S. KLIMOVICH, ET AL. J. NANO- ELECTRON. PHYS. 5, 04028 (2013)   04028-2 base. With time, because of the processes of magneto-phoresis and Brownian diffusion, the concentration of magnetic particles in the vicinity of the magnet in-creases and near the base decreases. As a result, the magnet when acted upon by the gravity moves closer to the base and finally occupies a new equilibrium posi-tion. In experiment, this movement Δh is fixed by means of a cathetometer with an accuracy of 0.01 mm.  1234SN  Fig. 1 – Scheme of experimental cell on permanent magnet levitation. 1 – solid base, 2 – magnetic fluid, 3 – permanent magnet, 4 – transparent cover  It should be noted that such variations also result in enhancing the stiffness of the system. Data for the one magnet will be presented below.  Maximum magnetic field intensity at the surface of it is 65 kA/m, and the corresponding gradient of the field intensity at this point is equal to 15000 kA/m2. The values of the criterion U corresponding to this magnetic field is 5,1. The magnetic fluid volume V is varied from 3000 to 5000 mm3.  Time variations of the positions of levitation of the magnet in the magnetic fluid are shown in Figs. 2 and 3.    Fig. 2 – A relative displacement Δh/h0 of the levitation point of the magnet in the kerosene based magnetic fluid in time  The comparison of the data in Figs. 2 and 3 first of all attracts attention to an essentially different time of attaining a new equilibrium position by the magnet for different fluids.  As seen from the presented in Introduction expres-sion for the characteristic diffusion time, τ, of magnetic particles in the magnetic fluid, it is directly proportion-al to the viscosity of the carrier fluid. For the conditions of the experiment described it is 220 min for kerosene based magnetic fluids and 5500 min for transformer oil based fluids. This is consistent with the order of magni-tudes for the results plotted in Figs. 2 and 3.     Fig. 3 – A relative displacement Δh/h0 of the levitation point of the magnet in the transformer oil based magnetic fluid in time  2.2 Levitation of a Non-magnetic Body in  Magnetic Fluid  A plexiglas disc 7 mm in height and 23 mm in diame-ter is used as a non-magnetic body. A coaxially magnet-ized circular ferrite-barium magnet 20 mm in height, with inner and outer diameters equal to 84 and 40 mm,   1234SNSN  Fig. 4 – Scheme of experimental cell on levitation of nonmagnetic disk. 1 – circular permanent magnet, 2 – magnetic fluid, 3 – non magnetic disc, 4 – transparent vessel    Fig. 5 – Absolute displacement Δh of the levitation point of a non-magnetic disc in the transformer oil based magnetic fluid in time  respectively, is used as a source of an inhomogeneous magnetic field. Maximum values of the magnetic field intensity and its vertical gradient on the magnet axis are equal to 22 kA/m and 3000 kA/m2. Because of its small density, the disc was floating over the magnetic fluid surface. The fluid filled a cylindrical vessel located inside the magnet ring, as presented in Fig. 4.  INFLUENCE OF BROWNIAN DIFFUSION ON LEVITATION… J. NANO- ELECTRON. PHYS. 5, 04028 (2013)   04028-3 In this case, the buoyancy force acting upon the disc decreases with time and it more submerged into the fluid [2]. In experiment, this movement Δh was also fixed by means of the cathetometer. The results are presented in Fig. 5.  As seen from Fig. 5, the characteristic diffusion time is of the order of 4000 min and corresponds to the identical experimental data on the floating of the mag-net in the transformer oil based magnetic fluid, Fig. 3. ACKNOWLEDGEMENT  The study was supported by The Ministry of educa-tion and science of Russian Federation, project № 14.В37.21.0906 "The research on interaction of physical fields in acoustomagnetic effect on nanodispersed mag-netic fluid".   REFERENCES  1. V.G. Bashtovoi, V.K Polevikov, A.E. Suprun, A.V. Stroots, S.A. Beresnev, Magnetohydrodynamics 43, 17 (2007). 2. V.G. Bashtovoi, V.K  Polevikov, A.E. Suprun, A.V. Stroots, S.A. Beresnev, Magnetohydrodynamics 44, 121 (2008). 3. A. Suprun, D.V. Simonenko D, Yu. Romanov. US Patent, 6, 731, 268, (2004). 4. V. Bashtovoi, A. Reks, P. Kuzhir, G. Bossis, A. Vikulenkov, A. Moisheev, N. Markachev Patent FR 2 894 004 –A1, 01.06.07, Bulletin 07/22.  

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Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid

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