Download Frequency dependence of metal

Frequency dependence of metal-particle/insulating oil electrorheological
fluids
Weijia Wen and Kunquan Lua)
Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
~Received 3 April 1995; accepted for publication 14 August 1995!
The frequency dependence of the shear stress of metal-particle/insulating oil electrorheological ~ER!
fluids under an ac electric field has been studied. The results show that the shear stress of the
metal-particle ER fluid under a fixed electric field increases with increasing frequency and then
tends to a saturated value at higher frequency. The shear stress at 103 Hz is much larger than that
under a dc field. The transition of the shear stress shifts to higher frequency when the conductivity
of the fluid is larger. The measurements are consistent with the theoretical model proposed by Davis
@J. Appl. Phys. 73, 680 ~1993!#. © 1995 American Institute of Physics.
It has been known for a long time that electrorheological
~ER! fluids are potential engineering materials, on account of
their reversible changes in rheological behavior when subjected to an external electric field. This phenomenon has attracted increasing attention from scientists and engineers.
The commonly believed mechanism is that the particles suspended in ER fluids are polarized in the electric field and the
interactions among them induce chains or columns which
give rise to increase of shear stress. Much experimental and
theoretical work has been done in the last few years,1–9 but
experiments performed by previous researchers focused
mostly on ER fluids consisting of polymer or inorganic compounds. Inoue10 observed the ER effect of a conductive core
with an insulating skin system under a dc and a 50 Hz ac
electric field, but did not report the frequency response of
metal particle ER fluid over a wide range. Davis11 proposed
a theoretical model and introduced a relationship between
the frequency f of the electric field and dipole moment p in a
metal-particle ER fluid. He predicted that the particle–
particle force F or the shear stress t is at least an order of
magnitude larger at high f then at f50. The transition frequency depends upon the fluid conductivity and usually
takes place in the region of 1–100 Hz, but this conclusion
has not been proven by experiment. The main difficulties of
the experiment are from breakdown between the metal particles and the electrodes even when the metal particles surfaces are coated with an oxide layer.
In this letter we report the results on the dependence of
the shear stress on the frequency of ac electric field in an
aluminum metal particle ER fluid. We find that the shear
stress under a fixed electric field increases with increasing
frequency in the region below a few thousand Hz and tends
to a saturated value at higher frequency. The measurement
results are consistent with the calculation according to the
model developed by Davis.11
Our ER fluid consisted of aluminum particles suspended
in two kinds of diffusion pump oil with a conductivity s f of
1.131027 and 1.531027 S/m, respectively. The spherical
aluminum particles of 20 mm in diameter were dried in an
oven at 200 °C for 48 h. There must be a thin oxide layer on
the surface of the particle. The volume fractions of particles
in the fluids were f50.1 and 0.3. The shear stress was meaa!
Electronic mail: [email protected]
Appl. Phys. Lett. 67 (15), 9 October 1995
sured with a viscometer, the electrodes of which were covered by 0.1 mm Kapton tape ~permittivity is about 3.0! to
prevent electrical shorting. The exact electric field applied on
the ER fluids should be deduced with the influence of the
insulating layers subtracted. Without the insulating film on
the surfaces of the electrodes, the maximum field strength
that could be applied was only 100 V/mm, when the metal
particle chains were formed. The distance between the two
electrodes was adjusted to be 1 mm, and the shear rate was
15.50 s21 in the measurements. The viscometer was standardized with a standard viscous oil. The whole system was
put in an oil bath, where the temperature could be controlled.
The power supply was specially designed to have a sinusoidal voltage output from 0 to 5000 V and frequency from
10 to 4000 Hz. The current output of the apparatus limited
the frequency in the measurements of the shear stress under
high field to be below about 2000 Hz; beyond that, the capacitance effect became more serious. Observation with an
optical microscope demonstrated that no electrical short occurred in the region of the applied electric field when the
metallic particles all lined up into chains. A microscopic pattern of the Al particle chains obtained under a 50 Hz ac field
of 1400 V/mm is shown in Fig. 1.
The measured results of the shear stress versus frequency at a fixed electric strength E5900 V/mm across the
electrodes are plotted in Fig. 2. Curves ~1! and ~2! show that
the shear stresses increase in the 10–103 Hz range and then
tend to a saturated value at high frequency. The shear stresses
FIG. 1. The microscopic pattern of the aluminum particle chains under 1400
V/mm field, f550 Hz. The gap of the electrodes is 0.5 mm.
0003-6951/95/67(15)/2147/2/$6.00
© 1995 American Institute of Physics
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FIG. 2. The shear stress vs frequency at 900 V/mm. Curve ~1! and ~2! are
measured, ~f50.3!. Curve ~3! is p 2 vs f calculated and copied from Ref. 11
for s f 51.031027 S/m.
under a dc field ~f50! were too low to be observed. It is
obvious that the shear stress at high frequency is much larger
than that at f50.
According to the analysis of the metal-particle system
based on the dipole approximation, the particle–particle
force and the shear stress which are proportional to p 2 , the
square of the dipole moment, should become larger when the
frequency is increased. The frequency dependence of p 2 calculated in Ref. 11 for the case of a fluid conductivity
s f 51027 S/m is copied in Fig. 2 with a dashed line @curve
~3!#, which has been normalized to the scale. Our measured
curves ~1! and ~2! match well with the predicted curve ~3!,
although the oxide layer on the aluminum sphere is very thin
~less than 0.1 mm! in our case. In addition, it can be seen in
Fig. 2 that the transition of shear stress would shift to higher
frequency when a fluid with larger conductivity is used in the
experiment. Again this is consistent with the calculation proposed by Davis.11
At a fixed frequency, the shear stress t follows the behavior of t }E 2 , when the field strength is lower than about
1200 V/mm, and then the rate of increment of the shear
stress will slow down as shown in Fig. 3. The gentle increment under higher field is due to a thermal effect. In this case
FIG. 4. The temperature dependence of the shear stress measured at 1000
V/mm and 1000 Hz ~f50.3!.
Joule heating from the current passing through the metal
particles becomes serious and even boiling of the oil could
be observed. To demonstrate the heating effect, we measured
the temperature dependence of the shear stress as shown in
Fig. 4, where the shear stress of the ER fluid decreases nearly
linearly with increasing temperature. This fact also rules out
the possibility that the increase of shear stress with frequency, as shown in Fig. 2, results from the temperature
effect.
In conclusion, the characteristics of metal-particle/
insulating oil ER fluids at different ac electric field frequencies have been investigated. To prevent electric shorting in
the experiments, the electrodes of the viscometer were covered with insulating films. The results show that the shear
stress of the metal-particle ER fluid under a fixed electric
field increases with increasing frequency and then tends to a
saturated value at higher frequency. The shear stress at 103
Hz is much larger than that at f50. The transition of the
shear stress shifts to higher frequency, when the conductivity
of the fluid is larger. The measurements are consistent with
the theoretical model proposed by Davis11 and demonstrate
that conductivity mismatch is important in the ER effect.
We are grateful to Xiao Nan for his help in our experiments. This work was supported by the Chinese National
Science Foundation and a Key Research Project grant of the
Climbing Program from the State Science and Technology
Commission of China.
FIG. 3. The shear stress vs field strength at f51000 Hz.
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Appl. Phys. Lett., Vol. 67, No. 15, 9 October 1995
W. Wen and K. Lu
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