Bacri, Jean-Claude

Cabuil, Valérie

Perzynski, Regine

Rosensweig, Ronald E.

Sandre, Olivier

English

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HAL Id: hal-02336430
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New ferrofluid composites: Magnetism and optics
experiments
Olivier Sandre, Ronald E. Rosensweig, Jean-Claude Bacri, Valérie Cabuil,
Regine Perzynski
To cite this version:
Olivier Sandre, Ronald E. Rosensweig, Jean-Claude Bacri, Valérie Cabuil, Regine Perzynski. New fer-
rofluid composites: Magnetism and optics experiments. The 6th International Conference on Electro-
Rheological Fluids, Magneto-Rheological Suspensions and their Applications (ERMR’97), Jul 1997,
Yonezawa, Japan. ￿hal-02336430￿
NEW FERROFLUID COMPOSITES : MAGNETISM AND OPTICS EXPERIMENTS 
O. SANDRE†, R. E. ROSENSWEIG†, J.-C. BACRI†, V. CABUIL‡, R. PERZYNSKI† 
†Lab. LMDH, ‡Lab. LIIC "Ferrofluides", Universities Paris VI and VII, France 
 
 An ionic ferrofluid is an aqueous 
colloidal suspension of surface charged 
magnetic nanoparticles. Dispersion of the 
particles is ensured by the Coulomb forces. 
The effect of an added electrolyte is the 
screening of the electrostatic repulsions. 
Above a threshold ionic strength, a 
separation occurs between one phase rich 
in particles and another poor in particles 
[1]. Near the threshold, this ferrofluid 
composite consists of highly magnetic 
droplets (a few micrometers in diameter) 
surrounded by a dilute weakly magnetic 
medium. The nanoparticles are made of γ-
Fe2O3 (maghemite) and their 
polydispersity is high : their diameter 
follows a log-normal distribution with 
parameters D0=6.8nm and σ=0.5. Hence 
relatively large particles are present which 
favors phase separation. Iron titration of 
the concentrated phase gives a volume 
fraction of particles Φc=0.31.To 
characterise the microdroplets we use the 
method [2] which consists in measuring 
their ellipsoidal deformation (axisymmetric 
prolate ellipsoids with long semi-axis a and 
short semi-axis b) as a function of the 
magnetic field. 
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1
10
100
B
m
=m
0
H2R
0
/σ
a/b
 
(1) Aspect ratio a/b versus magnetic Bond number 
Bm for a droplet of initial radius R0=6.65mm : the 
best fit gives χ=63 and σ=7.5x10-7N.m-1. 
 
 The equilibrium shape results from the 
competition between magnetic and 
interfacial energy. Figure (1) shows the 
aspect ratio a/b for a droplet of given 
volume versus field intensity. The best fit 
gives the magnetic susceptibility χ=63 of 
the concentrated phase and the interfacial 
tension σ=7.5x10-7N.m-1 between the two 
phases. Because of the high value of χ and 
the small value of σ a magnetic induction 
so small as a few 10-4T induces a large 
deformation of the droplets. 
 
(2) Picture of an assembly of microdroplets in a 
magnetic field with intensity H=1280A.m-1 
rotating at frequency Ω=3.45Hz. 
 We study this magnetic composite 
material which consists in an assembly of 
magnetic and deformable microdroplets. 
We present here two complementary 
experiments in order to show the 
competition between the magnetic torque 
created by a field and the viscous torque 
due to a local vorticity. In the first 
experiment the assembly of microdroplets 
is submitted to a rotating magnetic field at 
frequency Ω and observed under an optical 
microscope. Figure (2) is a typical view for 
a field intensity H=1280A.m-1 and a 
frequency Ω=3.45Hz. The rotation is 
counter clockwise and the picture is taken 
at a moment when the field is along the 
vertical. 
 Thus there is a visible phase lag θ 
between the field and the droplets. The 
highest values of θ are found for the most 
elongated droplets. For a given droplet, θ 
increases with the frequency Ω. At a 
critical value Ωc the droplet breaks into 
two parts or more in order to minimize the 
total dissipation [3]. Figure (3) shows the 
mean aspect ratio a/b of the droplets 
distribution as a function of Ω at constant 
field intensity and for several values of the 
field. The decreasing of the average aspect 
ratio with increasing Ω is a consequence of 
the break up of the droplets. 
Simultaneously the mean volume of the 
droplets decreases and the number of 
droplets in the screen increases to keep the 
total volume of concentrated phase 
constant. 
5
10
15
20
25
30
0 1 2 3 4 5 6
640A.m-1
1280A.m-1
2240A.m-1
a/b
Ω  (Hz)  
(3) Aspect ratio a/b averaged on approximately 100 
droplets versus Ω. 
 The second experiment consists in a 
rotating sample at frequency Ω in a static 
field H (
  
 
H ⊥
 
Ω ).The solid rotation of the 
cell under a constant field is equivalent to 
the rotation of the field with a static 
sample. We study the diffraction pattern of 
a laser beam parallel to 
  
 
Ω in order to 
obtain a direct measurement of the phase 
lag θ averaged on a huge amount of 
droplets. Figure (4) is a picture of the 
scattering pattern for H=980A.m-1 and 
Ω=0.23Hz. There is a wide range of H and 
Ω where two scattering lines 
corresponding to two different values of θ 
are observed simultaneously. 
 
(4) Scattering pattern of an assembly of 
microdroplets in a sample rotating counter 
clockwise submitted to a static field. 
 Thus we deduce that the population of 
droplets is bi-modal, which can be a 
consequence of the break up of the droplets 
caused by the viscous torque. In a simple 
model for large aspect ratio and large χ, 
the balance between magnetic and viscous 
torques scales as : 
ηa3Ω ∝ m0χab
2H2 sin2θ  
where η is the viscosity of the dilute phase. 
As it is expected the upper limit of θ is 
45°. The plot on figure (5) of sin2θ versus 
Ω/H2 allows to superpose all the data on 
only two branches. 
0.1
1
0.0001 0.001 0.01
1970A.m-1
980A.m-1
770A.m-1
550A.m-1
Si
n2
θ
 ηΩ  / m
0
H2  
(5) Plot of sin2θ versus Ω/H2 for several H. 
 
References 
[1] J.-C. BACRI et al, J. Coll. Int. Sc. 132(1989). 
[2] J.-C. BACRI and D. SALIN, J. Phys. Lett. 43 
(1982) 649. 
[3] A. V. LEBEDEV and K. I. MOROZOV, JETP 
Lett. 65 2 (1997) 161. 
 


New ferrofluid composites: Magnetism and optics experiments

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New ferrofluid composites: Magnetism and optics experiments

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