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Effect of frequency on a water-activated electrorheological fluid in an a.c. electric field
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 78 (1993) 167-175 0927-7757/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved.
167
Effect of frequency on a water-activated electrorheological fluid in an a.c. electric field T.Y. Chen, P.F. Luckham* Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, Prince Consort Road, London S W7 2BY, UK
(Received 10 August 1992; accepted 18 March 1993) Abstract The electrorheological (ER) behaviour of particulates in an external a.c. electric field can be explained by the structuring of dispersed particles caused by the oscillations of induced dipoles in the particles. In this work, the effect of an a.c. electric field on a water-activated ER fluid was investigated under both continuous and oscillatory shear. An a.c. frequency-dependent behaviour of a model ER fluid was found at large deformations (continuous shear). Specifically, it was observed that the Bingham yield value decreased as the a.c. frequency increased and above 500 Hz was independent of frequency, implying that the fluid has a response time of 2 ms. However, there was no significant dependence on the a.c. frequency at small deformations (oscillatory shear); the elastic modulus was found to be constant over the range lo-1500 Hz. This dichotomy has been resolved by recalling that the Bingham yield value is a measure of the energy needed to break the structure, whilst the elastic modulus is more a measure of the extent of structure. The data suggest that in the oscillatory experiments, which were obtained in the linear viscoelastic region, the structure is not destroyed, whilst in the continuous shear experiments the structure is broken and at high frequencies, above 500 Hz, the structure does not have time to reform. Key words: A.c. electric field; Continuous
shear; Oscillatory
shear; Water-activated
Introduction
Since Winslow [l] discovered the electrorheological (ER) phenomenon just before the Second World War, ER fluids have attracted increasing attention from scientists and engineers to this fascinating area, owing to their potential engineering applications in such diverse fields as torque transmission, braking systems, hydraulic valves, vibration absorbers, robotics joints, actuators [2-71 and gating of membrane channels [S] etc. For the past 50 years, many studies have been performed on these so-called “smart” fluids and the current state of the art of the properties of these materials has been outlined recently by *Corresponding
author.
electrorheological
fluid
Whittle and Bullough [9]. In general, the ER phenomenon is a fast and reversible phase change, from a viscous liquid to an elastic solid, as a consequence of an imposed electric field. In addition, this drastic change in the flow behaviour on the application of an external electric field is accompanied with the formation of chain-like aggregates, sometimes termed fibrinated structures, in the ER fluids. The viscosity can vary by several orders of magnitude [lo-131 and the change usually takes place in milliseconds [14]. This instantaneous phase shift, and hence the conversion of physical properties, provides simpler and more flexible options for the control of mechanical devices. However, many of the characteristics of ER fluids are still not clear. Further research is required for understanding their properties.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
168
Essentially,
ER
fluids
are
composed
of tiny
dielectric particles suspended in a non-conductive oil [lo-l 33. Despite the recent discovery of anhy-
167-175
attributed to the dipolar turnover of particles. He also indicated that particles may align perpendicu-
drous ER fluids [ 11,151, traditional water-activated ER fluids are by far the commonest; furthermore,
lar to the applied electric field at frequencies in the intermediate range while the particles always align parallel to the applied electric field to form a long
by changing the water content, the magnitude of the ER response may be varied. Absorbed water
chain across the electrodes at low and high frequencies. However, experimentally the a.c. frequency-
in dispersed
particles
increases
the dielectric
mis-
match between the disperse phase and the medium [ 133. This dielectric mismatch consequently causes the polarisation of dispersed particles in ER fluids when suspensions are subject to an external electric field. The polarisation induces interactions between particles and results in the formation of chains of particles between electrodes. This induced-dipolar force is well recognised by many researchers as the dominant force in the ER response of suspensions [lo-13,16-181. It is the presence of these structures which contributes to the enhancement of rheological properties of ER fluids. Despite the intensive study of the ER response of dispersions to an external electric field, the behaviour of ER fluids in an alternating current (ac.) electric field is still poorly understood. In early research on the frequency dependence of the ER effect, Klass and Martinek [19] measured the frequency dependence of the apparent viscosity of an insulating oil suspension of silica gel and calcium titanate by using a rotating viscometer cell. They reported a rapid drop in the electromechanical coupling above 1000 Hz and a 20% drop in the viscosity over a narrow a.c. frequency band around 500 Hz. This was attributed to the change in double-layer polarisation in an a.c. electric field. Furthermore, by examining the frequency response of ER fluids at different polarising voltages, Brooks [2] pointed out that the electrical permittivity of ER fluids decreases as the frequency increases. In other words, the dielectric mismatch may decrease as a.c. frequency increases. This effect was found to be most significant at ac. frequencies below 100 Hz. Recently, Jones [20] described the phenomenon in an a.c. electric field by using a frequency-dependent alignment model. In his mathematical model, this phenomenon could be
dependent
behaviour
of ER fluids in an external
a.c. electric field has not been well investigated. For example, the a.c. frequency dependences of apparent viscosity, yield stress and viscoelastic moduli of ER fluids are poorly understood. In this study, the ER behaviour in an external a.c. electric field was investigated for silica suspensions under both continuous and oscillatory shear. The frequency dependences of apparent viscosity, shear stress, yield stress, complex modulus, storage (elastic) modulus and loss (viscous) modulus are presented.
Experimental Rheological experiments were carried out to study the response of a model ER fluid under both continuous and oscillatory shear. This section describes the experimental system, apparatus and methods.
System The model ER suspensions used in the rheological measurements were made up of porous silica particles (standard TLC grade without binder) (Aldrich) and pure corn oil. The average diametric range and average pore diameter of the particles are 2-25 urn and 6 nm respectively. The pure corn oil is a Newtonian fluid with shear viscosity of 0.049 Pa s. Furthermore, an evaporation method was used to moisten the surface of the silica particles and the water content of the dispersed particles was determined gravimetrically. In all the experiments reported here, the water fraction in the silica particles was 0.0265 and the volume fraction of the silica particles was 0.1111.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
Apparatus All the modified
167-175
and procedure
i Computer Shows : i 1ShearStress. G’ . G” j Shear Rate ,‘Str& ,
measurements were performed on a Bohlin VOR rheometer (Bohlin
Viscosities (Tcmper;_fure, etcl.
Rheologie, Lund, Sweden) with a set of concentric cylinders. This is a fully computer-controlled rheological outer velocity selected
instrument. cup
rotates
During either
for steady shear angular frequency
measurements, at
a selected
169
_)
~
H--L-.
/Torque\
the angular
measurements or at a o for oscillatory shear
measurements. Under these conditions the sample, contained in the gap, induces a torque which is detected by the inner bob and measured by a torque bar. In addition, a temperature-controlling unit was used to provide constant temperature during measurement. The concentric cylinder set-up consists of a bob (25 mm outside diameter and 37.4 mm high) and a cup (27 mm inside diameter and 62 mm high). Consequently, the 1 mm annular gap was utilised to exert a high potential difference. The above setup is the standard concentric cylinder geometry for the Bohlin rheometer. In order to convert the instrument to an electrorheometer it was necessary to isolate the bob and cup from the rest of the rheometer (see Fig. 1). Thus an electrically insulated part made in Delrin (Du Pont) was designed for each cylinder to protect the rest of the rheometer from the high voltage. An electrical brush contact was used to supply the large a.c. potential difference to the cup and an electrical lead was applied to ground the bob. The whole apparatus was placed inside an isolating cabinet (see Fig. 1) containing a microswitch which interrupts the high voltage when the door of the cabinet is open. To produce the high ac. voltage the following set-up was assembled. A function generator (Thandar TG501 RS Components Ltd) supplied the wave form (5 V) which was amplified 10 times by an amplifier (model 762-1, Weir). This output was fed into a 10 kV EHT electrical modulator powered by a 30 kV high voltage power supply (Alpha Series II, Brandenburg). This assembly enabled the frequency to be varied from 0.005 Hz to 5 MHz at a maximum voltage of 10 kV.
Control Clutch Fig. 1. A schematic representation of the Bohlin VOR rheometer with a modified concentric cylinder assembly, revealing the insulation necessary to adapt the instrument to allow the application of high potentials.
In all the current experiments the electric field at the desired frequency was applied for 5 min before any rheological measurement was performed. Viscometric
measurements
Measurements were performed to study the structure of ER fluids at large deformation by means of continuous shear. In these measurements the flow behaviour of ER fluids can be examined because their structure is broken under this considerable deformation. A shear rate range of 1.4677146.7 s ’ was applied by increasing or decreasing the shear rate at a constant temperature of 25°C. The shear stress of the ER fluid can be obtained as a function of shear rate. Thus the apparent
v(P)= di)
viscosity
can be defined
as
T.Y.
170
Chen and P.F. LuckhamlColloids
Therefore the apparent viscosity ye of the ER fluid could be calculated from the relationship of shear stress vs. shear rate.
Surfaces A: Physicochem.
electric field [lo-131.
Initially measurements were carried out to select the linear viscoelastic region by sweeping the strain from 0 to 20 mrad. The linear viscoelastic regions for the ER fluid at different a.c. frequencies were hence obtained in this measurement. In this study, most measurements were performed below an amplitude of 1 mrad. Oscillatory
shear measurements
Measurements were performed to investigate the structure of ER fluids at small deformation by means of oscillatory shear. The structure of ER fluids can be determined from their viscoelastic properties. In this measurement, the viscoelastic properties of ER fluids can be observed because their structure is not disrupted by these small applied deformations. In this study, most measurements were performed at an amplitude of between 0.1 and 1 mrad over the oscillatory frequency range O.Ol- 10 Hz. The response (stress, z,,) of the ER fluid to a sinusoidally varying strain of amplitude y0 and phase shift 0 can be monitored by the rheometer. Hence the moduli may be determined as [21]
78 (1993)
167-175
Thus
r = r,j + qj
(3)
where rB is the so-called Strain sweep measurements
Eng. Aspects
Bingham
yield stress. Both
fluid and solid behaviour can be seen in a Bingham fluid. For t < zg, it behaves as a Hookean solid while Newtonian behaviour is exhibited for z > rB. Figure 2 demonstrates Bingham flow model
a good agreement with the in a.c. electric fields. The
relationship
stress
of shear
and
shear
rate
at
different a.c. frequencies over the range lo- 1500 Hz is shown for corn oil suspensions of silica gel at 300 V mm - ‘. Moreover, the yield or shear stress can be seen to decrease as the a.c. frequency increases. This decrease in yield stress, as illustrated further in Fig. 3, where the extrapolated yield stress is plotted as a function of a.c. frequency, may be explained in terms of the change in the strength of the structure present in the ER fluid, as will be discussed further below. Also shown in Fig. 2 is the shear stress behaviour for the dispersion in the absence of an electric field. In this case, the flow behaviour is similar to the behaviour of the system in a.c. fields of high frequencies. In Fig. 4, a plot of viscosity vs. shear rate at
30 g
25
4
20
c
‘5
IG*l = r,ly, G’ = ]G*l cos 0 G” = IG*( sin 0 G* = G’ + iG”
10
(2)
where G* is the complex modulus, G’ is the storage or elastic modulus, G” is the loss or viscous modulus and i is J-1, Results The Bingham model describes well the behaviour of the ER fluids in the presence of an external
5
00 0
10 20
30 40
50 60
70 60
90 100
Shear Rate (s-‘) Fig. 2. The shear stress plotted as a function of shear rate at different a.c. frequencies, and also in the absence of any a.c. electric field, for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength, 300Vmm-I): W, 10 Hz; 0, 30 Hz; A, 100 Hz; +, 300 Hz; 0, 500 Hz; 0, 1500 Hz; A, 0 kV.
T. Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993) 167-175
Orn
10000
Frequency (HZ) Fig. 3. The yield stress plotted as a function of a.c. frequency for silica particles suspended in corn oil. The particle volume fraction is 0.1111 and the water content is 0.0265. The applied field strength is 300 V mm-‘.
O’ 0
171
is tending towards a constant value, i.e. is becoming independent of the a.c. frequency. Figure 5 shows the viscosity of the ER suspension as a function of a.c. frequency at three different shear rates for corn oil suspensions at 300 V mm - ‘. Once again the viscosity is independent of the a.c. frequency at high shear rates. However, at lower shear rates there is an obvious increase in viscosity below an a.c. frequency of 500 Hz. These effects are similar to those reported by Klass and Martinek [19]. In Fig. 6, the storage modulus is plotted as a function of applied strain for corn oil suspensions of silica gel at 300 V mm-i and a.c. frequency of 10 Hz. A linear viscoelastic region can be found between 0.1 and 1 m rad; this implies that the structure is destroyed by applied strain above 1 mrad. All subsequent viscoelastic measurements were taken at strains well within the linear viscoelastic region. Figure 7 shows the results of the oscillatory shear measurements. The storage modulus and loss modulus are plotted as a function of the oscillatory frequency at different a.c. frequencies for corn oil suspensions of silica gel at 300 V mm-‘. It is clear from the data that G’ is some two orders of
160 Shear rate (s-‘)
Fig. 4. The viscosity plotted as a function of shear rate at different a.c. frequencies for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength, 300 Vmm-‘): A, 10 Hz; n , 30 Hz; A, 100 Hz; 0, 300 Hz; 0, 500 Hz; +, 1500 Hz.
different a.c. frequencies is presented for a corn oil suspension at 300 V mm- ‘. Typical shear thinning behaviour of the ER fluid can be observed in these viscometric measurements. The decrease in viscosity as the a.c. frequency increases is also detected. It can be seen that at high shear rate the viscosity
10
1000 100 Frequef~cy (HZ)
IC
Fig. 5. The viscosity plotted as a function of a.c. frequency at different shear rates for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength, 300Vmm-‘): W, 1.467~~‘; 0, 14.65 s-r; A, 146.7 s-‘.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
172 100
Fig. 7, are the elastic moduli
167-175
for the dispersion
in
the absence of an electric field. The data are some two orders of magnitude lower, implying that little or no structure is present so that the fluid in the absence of an electric field has liquid-like E
istics. According
10
to this graph,
character-
there is no signifi-
cant effect of the ax. frequency on the elastic modulus G’. There also appears to be no dependence of G” on the a.c. frequency; however, it should be noted that G” is small and at the 1 0.1
1 Strain (m.rad)
10
Fig. 6. The storage modulus plotted as a function of applied strain for silica particles suspended in corn oil suspension. The particle volume fraction is 0.1111 and the water content is 0.0265. The applied field strength is 300 V mm-’ and the a.c. frequency is 10 Hz.
detection limit of the modified rheometer, so the error is fairly high. It is believed that the static strength of the chain-like structure was not changed by the fast turnover of dipoles in particles. Figure 8 shows the effect of electric field strength on the yield stress for the corn oil suspensions of silica gel. The yield stress is plotted as a function of the a.c. frequency at 180 V mm-’ and 300 V mm 1 respectively. Discussion One initially surprising feature of these results is the different trends in G’ and TV with a.c. frequency: G’ is independent of the frequency whilst zB falls by a factor of 4 between 10 and 500 Hz
“~“bbl Oscillatory
1 10 frequency(Hz)
Fig. 7. The storage modulus (open symbols) and loss modulus (filled symbols) plotted as a function of the oscillatory frequency at various a.c. frequencies, and also in the absence of any a.c. electric field, for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength 300Vmm~‘): 0, 10 Hz; W, 10 Hz; 0, 100 Hz; 0, 100 Hz; A, 500 Hz; A, 500 Hz; ‘J, 1500 Hz; v’, 1500 Hz; +, 0 kV; x , 0 kV. Since G’ data for different a.c. frequencies are almost the same, the superimposition of symbols for indicating G’ data is seen in this graph.
magnitude of the very the electric as a solid.
greater than G”. This is a consequence strong structure which is built up by field, causing the fluid to behave more To illustrate this point, also shown in
“b
1600 FWJ=Y
(Hz)
Fig. 8. The shear stress plotted as a function of a.c. frequency at different strengths of the applied a.c. electric field for corn oil suspensions of silica particles with volume fraction of 0.1111 and water content of 0.0265: n , 300 V mm-‘; 0, 180 V mm-‘.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
and is constant thereafter. Both indirect measures of the structure and
thus
one
would
intuitively
show similar trends. However, both measures of the structure
rg and G’ are of the system expect
them
to
although they are of the system, they
probe different properties of the structure. The yield value is related to the energy required to break the structure (ultimately into individual particles) whilst in the elastic modulus
measurements,
operating in the linear viscoelastic region ensures that the structure is not broken. (We recall that in these experiments the electric field was applied for 5 min to enable the structure to build up before the rheological measurements were made.) Thus G’ is more a measure of the morphology of the structure rather than a measure of its strength. Thus clearly the morphology of the structure is not significantly affected by the frequency of the a.c. field. Presumably all the particles had formed chains [ 121 before the rheological measurements were performed. Preliminary microscopic studies have also shown this to be the case in our work. Let us now turn our attention to the zg data, which are related to the strength of the structure. Since at high shear the viscosity is constant, it means that the structure has been broken down to primary flow units. Thus zg is related to the energy required to separate these particle chains [22], such that zB =
N-L,
(4)
where N is the total number of contacts in the system. The total number of contacts is related to the particle volume fraction 4 and particle radius a, and Eq. (4) can be rewritten as
zB =
36
-$&n 8na
where n is the number of contacts per particle. Since ER fluids form chains, n will be approximately two. Thus we can estimate the energy required to separate particles from the chains. These data are given in Table 1. We are not aware of anyone estimating the energy needed to separate
167-175
173
Table 1 The separation energies of corn oil suspensions of silica with a volume fraction of 0.11 II and water content of 0.0265 at different frequencies of a.c. electric field of strength 300 V mm- 1 A.c. frequency
Bingham
(Hz)
(pa)
yield stress
Separation energy per particle (xIO-‘~J)
10 30 50 70 too 200 300 500 1000 1500
16.17 13.21 9.251 8.787 7.814 6.828 5.681 3.201 3.357 3.241
6.097 4.981 3.488 3.313 2.946 2.574 2.142 1.207 1.266 1.222
particles in an ER fluid previously; however, Sprecher et al. [23] have determined that the force required to separate two particles was about 1.0 uN. Since the energy required to separate two particles is given by E=FD
(6)
we may estimate the energy if we have a reasonable estimate for D, the separation of two adjacent particles. If we assume D is of the order of the dimensions of the particle diameter (which is actually likely to be an overestimate) then we would estimate E ~10~ I2 J. Thus the estimated particle separation energy from our rheological experiments seems reasonable. We now turn our attention to the effect of a.c. frequency in these data. In an a.c. field both the magnitude and sign of the potential are varying (the potential varies sinusoidally). We observe that both the viscosity and yield values decrease as the a.c. frequency is increased, until above a frequency of 500 Hz these parameters are constant. These data give insights into the response time of the ER fluid. Recently Jones [20] has shown that in an a.c. electric field, isolated particles actually oscillate. At low frequencies the particles have sufficient time to restructure and form the well-known chain structure; as the frequency is increased the degree
T.Y. Chen and P.F. LuckhamjColloids
174
of structuring
is reduced
as fewer particles
are able
to respond in the time available. At 500 Hz the change in field direction is too fast to enable any structuring
to occur
in the fluid.
Thus
we may
expect that at high frequencies the yield value will tend to the yield value in the absence of an electric field, as indeed we observe. Therefore we propose that the response time of this ER fluid is of the order of 2 ms. Similar data have also been obtained by Klass and Martinek [19] where the viscosity was constant above 500 Hz. At different strengths of the electric field, 300 the yield stress is shown as a and 180 V mm-‘, function of the a.c. frequency in Fig. 8. Since the dipolar force is proportional to the strength of the electric field squared [ 10,ll ,16- 181, the fibrous structure in the strong electric field is stronger than in a weak electric field at lower frequencies. Again at higher frequencies the yield value is approximately independent of field strength, once more revealing that at high frequencies the particles do not have time to restructure. Hence the yield value in a strong field is higher than that in a weak electric field, particularly at low frequencies. This trend will be reported more fully in a later publication.
Surfaces
shift of induced dipoles of dispersed particles in an ac. field brings about the change of the strength of fibrous structure of ER fluids because of regularly reversing the direction of induced dipoles. Therefore the rheological properties of ER fluids may be affected by varying the frequency of the a.c. electric field. In this case, the frequency of the a.c. electric field becomes an important factor affecting the ER performance in an a.c. electric field. In this study, experimental results are presented on the measurements of a water-activated ER suspension under continuous and oscillatory shear. In an external ac. electric field, the behaviour of an ER fluid is dependent on the a.c. frequency at
Eng. Aspects 78 (1993)
167-175
large deformations, but independent of the a.c. frequency at small deformations. This is a consequence
of the type of experiment
performed.
At
large deformations the structure is broken such that the yield value reflects changes in the particle-particle ations, however,
interaction, the structure
At small deformof the ER fluid is
maintained, so that the elastic modulus is a measure of the morphology. Furthermore, the data are in agreement
with the recently
model of induced
dipoles
postulated
turnover
[20].
Acknowledgements We would like to thank Professor B.J. Briscoe for many useful discussions. We also thank Dr. S.R. Ren and Dr. I.T. Kim for their helpful discussions and encouragement. A grateful acknowledgement is also due to Mr. D.M. Kiminta for his kindly assistance with setting up safety devices.
References 1 2
Conclusions The induced dipole is primarily responsible for the ER effect in the a.c. electric field. The directional
A: Phgsicochem.
7 8 9 IO II 12 13 14 15 16 17 18
W.M. Winslow, J. Appl. Phys., 20 (1949) 1137. D.A. Brooks, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1989. F.E. Filisko, Chem. Ind., 10 (1992) 370. W.A. Bullough, Endeavour, 15 (4) (1991) 165. G. Goldstein, Mech. Eng., October, (1990) 48. Z.P. Shulman, R.G. Gorodkin, E.V. Korobko and V.K. Gleb, J. Non-Newtonian Fluid Mech., 8 (1981) 29. M. Whittle, J. Non-Newtonian Fluid Mech., 37 (1990) 233. M.E. Green, J. Theor. Biol., 138 (1989) 413. M. Whittle and W.A. Bullough, Nature, 358 (1992) 373. D.J. Klingenberg, F.V. Swol and C.F. Zukoski, J. Chem. Phys., 94 (9) (1991) 6170. H. Block and J.P. Kelly, J. Phys. D, 21 (1988) 1661. H. Conrad and A.F. Sprecher, J. Stat. Phys., 64 (5) (1991) 1073. A. Cast and CF. Zukoski, Adv. Colloid Interface Sci., 30 (1989) 153. J.C. Hill and T.H.V. Steenkiste, J. Appl. Phys., 70 (3) (1991) 1207. C.J. Cow and CF. Zukoski J. Colloid Interface Sci., 136 (1) (1990) 175. R.T. Bonnecaze and J.F. Brady, J. Chem. Phys., 96 (3) (1992) 2183. Y. Chen, A.F. Sprecher and H. Conrad, J. Appl. Phys., 70 (I I) (1991) 6796. D.J. Klingenberg, F.V. Swol and CF. Zukoski, J. Chem. Phys., 94 (9) (1991) 6160.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993) 19 20 21
D.L. Klass and T.W. Martinek, J. Appl. Phys., 38 (1) (1967) 67. T.B. Jones, Proc. 2nd Int. Conf. on Electrorheological Fluids, Technomics Publishing Co., Lancaster, 1990, p.14. LT. Kim, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1992.
22 23
167-175
175
P.F. Luckham, B. Vincent and Th.F. Tadros, Colloids Surfaces, 6(2) (1983) 101. A.F. Sprecher, Y. Chen and H. Conrad, Proc. 2nd Int. Conf. on Electrorheological Fluids, Technomics Publishing Co., Lancaster, 1990 p. 82.
167
Effect of frequency on a water-activated electrorheological fluid in an a.c. electric field T.Y. Chen, P.F. Luckham* Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, Prince Consort Road, London S W7 2BY, UK
(Received 10 August 1992; accepted 18 March 1993) Abstract The electrorheological (ER) behaviour of particulates in an external a.c. electric field can be explained by the structuring of dispersed particles caused by the oscillations of induced dipoles in the particles. In this work, the effect of an a.c. electric field on a water-activated ER fluid was investigated under both continuous and oscillatory shear. An a.c. frequency-dependent behaviour of a model ER fluid was found at large deformations (continuous shear). Specifically, it was observed that the Bingham yield value decreased as the a.c. frequency increased and above 500 Hz was independent of frequency, implying that the fluid has a response time of 2 ms. However, there was no significant dependence on the a.c. frequency at small deformations (oscillatory shear); the elastic modulus was found to be constant over the range lo-1500 Hz. This dichotomy has been resolved by recalling that the Bingham yield value is a measure of the energy needed to break the structure, whilst the elastic modulus is more a measure of the extent of structure. The data suggest that in the oscillatory experiments, which were obtained in the linear viscoelastic region, the structure is not destroyed, whilst in the continuous shear experiments the structure is broken and at high frequencies, above 500 Hz, the structure does not have time to reform. Key words: A.c. electric field; Continuous
shear; Oscillatory
shear; Water-activated
Introduction
Since Winslow [l] discovered the electrorheological (ER) phenomenon just before the Second World War, ER fluids have attracted increasing attention from scientists and engineers to this fascinating area, owing to their potential engineering applications in such diverse fields as torque transmission, braking systems, hydraulic valves, vibration absorbers, robotics joints, actuators [2-71 and gating of membrane channels [S] etc. For the past 50 years, many studies have been performed on these so-called “smart” fluids and the current state of the art of the properties of these materials has been outlined recently by *Corresponding
author.
electrorheological
fluid
Whittle and Bullough [9]. In general, the ER phenomenon is a fast and reversible phase change, from a viscous liquid to an elastic solid, as a consequence of an imposed electric field. In addition, this drastic change in the flow behaviour on the application of an external electric field is accompanied with the formation of chain-like aggregates, sometimes termed fibrinated structures, in the ER fluids. The viscosity can vary by several orders of magnitude [lo-131 and the change usually takes place in milliseconds [14]. This instantaneous phase shift, and hence the conversion of physical properties, provides simpler and more flexible options for the control of mechanical devices. However, many of the characteristics of ER fluids are still not clear. Further research is required for understanding their properties.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
168
Essentially,
ER
fluids
are
composed
of tiny
dielectric particles suspended in a non-conductive oil [lo-l 33. Despite the recent discovery of anhy-
167-175
attributed to the dipolar turnover of particles. He also indicated that particles may align perpendicu-
drous ER fluids [ 11,151, traditional water-activated ER fluids are by far the commonest; furthermore,
lar to the applied electric field at frequencies in the intermediate range while the particles always align parallel to the applied electric field to form a long
by changing the water content, the magnitude of the ER response may be varied. Absorbed water
chain across the electrodes at low and high frequencies. However, experimentally the a.c. frequency-
in dispersed
particles
increases
the dielectric
mis-
match between the disperse phase and the medium [ 133. This dielectric mismatch consequently causes the polarisation of dispersed particles in ER fluids when suspensions are subject to an external electric field. The polarisation induces interactions between particles and results in the formation of chains of particles between electrodes. This induced-dipolar force is well recognised by many researchers as the dominant force in the ER response of suspensions [lo-13,16-181. It is the presence of these structures which contributes to the enhancement of rheological properties of ER fluids. Despite the intensive study of the ER response of dispersions to an external electric field, the behaviour of ER fluids in an alternating current (ac.) electric field is still poorly understood. In early research on the frequency dependence of the ER effect, Klass and Martinek [19] measured the frequency dependence of the apparent viscosity of an insulating oil suspension of silica gel and calcium titanate by using a rotating viscometer cell. They reported a rapid drop in the electromechanical coupling above 1000 Hz and a 20% drop in the viscosity over a narrow a.c. frequency band around 500 Hz. This was attributed to the change in double-layer polarisation in an a.c. electric field. Furthermore, by examining the frequency response of ER fluids at different polarising voltages, Brooks [2] pointed out that the electrical permittivity of ER fluids decreases as the frequency increases. In other words, the dielectric mismatch may decrease as a.c. frequency increases. This effect was found to be most significant at ac. frequencies below 100 Hz. Recently, Jones [20] described the phenomenon in an a.c. electric field by using a frequency-dependent alignment model. In his mathematical model, this phenomenon could be
dependent
behaviour
of ER fluids in an external
a.c. electric field has not been well investigated. For example, the a.c. frequency dependences of apparent viscosity, yield stress and viscoelastic moduli of ER fluids are poorly understood. In this study, the ER behaviour in an external a.c. electric field was investigated for silica suspensions under both continuous and oscillatory shear. The frequency dependences of apparent viscosity, shear stress, yield stress, complex modulus, storage (elastic) modulus and loss (viscous) modulus are presented.
Experimental Rheological experiments were carried out to study the response of a model ER fluid under both continuous and oscillatory shear. This section describes the experimental system, apparatus and methods.
System The model ER suspensions used in the rheological measurements were made up of porous silica particles (standard TLC grade without binder) (Aldrich) and pure corn oil. The average diametric range and average pore diameter of the particles are 2-25 urn and 6 nm respectively. The pure corn oil is a Newtonian fluid with shear viscosity of 0.049 Pa s. Furthermore, an evaporation method was used to moisten the surface of the silica particles and the water content of the dispersed particles was determined gravimetrically. In all the experiments reported here, the water fraction in the silica particles was 0.0265 and the volume fraction of the silica particles was 0.1111.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
Apparatus All the modified
167-175
and procedure
i Computer Shows : i 1ShearStress. G’ . G” j Shear Rate ,‘Str& ,
measurements were performed on a Bohlin VOR rheometer (Bohlin
Viscosities (Tcmper;_fure, etcl.
Rheologie, Lund, Sweden) with a set of concentric cylinders. This is a fully computer-controlled rheological outer velocity selected
instrument. cup
rotates
During either
for steady shear angular frequency
measurements, at
a selected
169
_)
~
H--L-.
/Torque\
the angular
measurements or at a o for oscillatory shear
measurements. Under these conditions the sample, contained in the gap, induces a torque which is detected by the inner bob and measured by a torque bar. In addition, a temperature-controlling unit was used to provide constant temperature during measurement. The concentric cylinder set-up consists of a bob (25 mm outside diameter and 37.4 mm high) and a cup (27 mm inside diameter and 62 mm high). Consequently, the 1 mm annular gap was utilised to exert a high potential difference. The above setup is the standard concentric cylinder geometry for the Bohlin rheometer. In order to convert the instrument to an electrorheometer it was necessary to isolate the bob and cup from the rest of the rheometer (see Fig. 1). Thus an electrically insulated part made in Delrin (Du Pont) was designed for each cylinder to protect the rest of the rheometer from the high voltage. An electrical brush contact was used to supply the large a.c. potential difference to the cup and an electrical lead was applied to ground the bob. The whole apparatus was placed inside an isolating cabinet (see Fig. 1) containing a microswitch which interrupts the high voltage when the door of the cabinet is open. To produce the high ac. voltage the following set-up was assembled. A function generator (Thandar TG501 RS Components Ltd) supplied the wave form (5 V) which was amplified 10 times by an amplifier (model 762-1, Weir). This output was fed into a 10 kV EHT electrical modulator powered by a 30 kV high voltage power supply (Alpha Series II, Brandenburg). This assembly enabled the frequency to be varied from 0.005 Hz to 5 MHz at a maximum voltage of 10 kV.
Control Clutch Fig. 1. A schematic representation of the Bohlin VOR rheometer with a modified concentric cylinder assembly, revealing the insulation necessary to adapt the instrument to allow the application of high potentials.
In all the current experiments the electric field at the desired frequency was applied for 5 min before any rheological measurement was performed. Viscometric
measurements
Measurements were performed to study the structure of ER fluids at large deformation by means of continuous shear. In these measurements the flow behaviour of ER fluids can be examined because their structure is broken under this considerable deformation. A shear rate range of 1.4677146.7 s ’ was applied by increasing or decreasing the shear rate at a constant temperature of 25°C. The shear stress of the ER fluid can be obtained as a function of shear rate. Thus the apparent
v(P)= di)
viscosity
can be defined
as
T.Y.
170
Chen and P.F. LuckhamlColloids
Therefore the apparent viscosity ye of the ER fluid could be calculated from the relationship of shear stress vs. shear rate.
Surfaces A: Physicochem.
electric field [lo-131.
Initially measurements were carried out to select the linear viscoelastic region by sweeping the strain from 0 to 20 mrad. The linear viscoelastic regions for the ER fluid at different a.c. frequencies were hence obtained in this measurement. In this study, most measurements were performed below an amplitude of 1 mrad. Oscillatory
shear measurements
Measurements were performed to investigate the structure of ER fluids at small deformation by means of oscillatory shear. The structure of ER fluids can be determined from their viscoelastic properties. In this measurement, the viscoelastic properties of ER fluids can be observed because their structure is not disrupted by these small applied deformations. In this study, most measurements were performed at an amplitude of between 0.1 and 1 mrad over the oscillatory frequency range O.Ol- 10 Hz. The response (stress, z,,) of the ER fluid to a sinusoidally varying strain of amplitude y0 and phase shift 0 can be monitored by the rheometer. Hence the moduli may be determined as [21]
78 (1993)
167-175
Thus
r = r,j + qj
(3)
where rB is the so-called Strain sweep measurements
Eng. Aspects
Bingham
yield stress. Both
fluid and solid behaviour can be seen in a Bingham fluid. For t < zg, it behaves as a Hookean solid while Newtonian behaviour is exhibited for z > rB. Figure 2 demonstrates Bingham flow model
a good agreement with the in a.c. electric fields. The
relationship
stress
of shear
and
shear
rate
at
different a.c. frequencies over the range lo- 1500 Hz is shown for corn oil suspensions of silica gel at 300 V mm - ‘. Moreover, the yield or shear stress can be seen to decrease as the a.c. frequency increases. This decrease in yield stress, as illustrated further in Fig. 3, where the extrapolated yield stress is plotted as a function of a.c. frequency, may be explained in terms of the change in the strength of the structure present in the ER fluid, as will be discussed further below. Also shown in Fig. 2 is the shear stress behaviour for the dispersion in the absence of an electric field. In this case, the flow behaviour is similar to the behaviour of the system in a.c. fields of high frequencies. In Fig. 4, a plot of viscosity vs. shear rate at
30 g
25
4
20
c
‘5
IG*l = r,ly, G’ = ]G*l cos 0 G” = IG*( sin 0 G* = G’ + iG”
10
(2)
where G* is the complex modulus, G’ is the storage or elastic modulus, G” is the loss or viscous modulus and i is J-1, Results The Bingham model describes well the behaviour of the ER fluids in the presence of an external
5
00 0
10 20
30 40
50 60
70 60
90 100
Shear Rate (s-‘) Fig. 2. The shear stress plotted as a function of shear rate at different a.c. frequencies, and also in the absence of any a.c. electric field, for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength, 300Vmm-I): W, 10 Hz; 0, 30 Hz; A, 100 Hz; +, 300 Hz; 0, 500 Hz; 0, 1500 Hz; A, 0 kV.
T. Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993) 167-175
Orn
10000
Frequency (HZ) Fig. 3. The yield stress plotted as a function of a.c. frequency for silica particles suspended in corn oil. The particle volume fraction is 0.1111 and the water content is 0.0265. The applied field strength is 300 V mm-‘.
O’ 0
171
is tending towards a constant value, i.e. is becoming independent of the a.c. frequency. Figure 5 shows the viscosity of the ER suspension as a function of a.c. frequency at three different shear rates for corn oil suspensions at 300 V mm - ‘. Once again the viscosity is independent of the a.c. frequency at high shear rates. However, at lower shear rates there is an obvious increase in viscosity below an a.c. frequency of 500 Hz. These effects are similar to those reported by Klass and Martinek [19]. In Fig. 6, the storage modulus is plotted as a function of applied strain for corn oil suspensions of silica gel at 300 V mm-i and a.c. frequency of 10 Hz. A linear viscoelastic region can be found between 0.1 and 1 m rad; this implies that the structure is destroyed by applied strain above 1 mrad. All subsequent viscoelastic measurements were taken at strains well within the linear viscoelastic region. Figure 7 shows the results of the oscillatory shear measurements. The storage modulus and loss modulus are plotted as a function of the oscillatory frequency at different a.c. frequencies for corn oil suspensions of silica gel at 300 V mm-‘. It is clear from the data that G’ is some two orders of
160 Shear rate (s-‘)
Fig. 4. The viscosity plotted as a function of shear rate at different a.c. frequencies for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength, 300 Vmm-‘): A, 10 Hz; n , 30 Hz; A, 100 Hz; 0, 300 Hz; 0, 500 Hz; +, 1500 Hz.
different a.c. frequencies is presented for a corn oil suspension at 300 V mm- ‘. Typical shear thinning behaviour of the ER fluid can be observed in these viscometric measurements. The decrease in viscosity as the a.c. frequency increases is also detected. It can be seen that at high shear rate the viscosity
10
1000 100 Frequef~cy (HZ)
IC
Fig. 5. The viscosity plotted as a function of a.c. frequency at different shear rates for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength, 300Vmm-‘): W, 1.467~~‘; 0, 14.65 s-r; A, 146.7 s-‘.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
172 100
Fig. 7, are the elastic moduli
167-175
for the dispersion
in
the absence of an electric field. The data are some two orders of magnitude lower, implying that little or no structure is present so that the fluid in the absence of an electric field has liquid-like E
istics. According
10
to this graph,
character-
there is no signifi-
cant effect of the ax. frequency on the elastic modulus G’. There also appears to be no dependence of G” on the a.c. frequency; however, it should be noted that G” is small and at the 1 0.1
1 Strain (m.rad)
10
Fig. 6. The storage modulus plotted as a function of applied strain for silica particles suspended in corn oil suspension. The particle volume fraction is 0.1111 and the water content is 0.0265. The applied field strength is 300 V mm-’ and the a.c. frequency is 10 Hz.
detection limit of the modified rheometer, so the error is fairly high. It is believed that the static strength of the chain-like structure was not changed by the fast turnover of dipoles in particles. Figure 8 shows the effect of electric field strength on the yield stress for the corn oil suspensions of silica gel. The yield stress is plotted as a function of the a.c. frequency at 180 V mm-’ and 300 V mm 1 respectively. Discussion One initially surprising feature of these results is the different trends in G’ and TV with a.c. frequency: G’ is independent of the frequency whilst zB falls by a factor of 4 between 10 and 500 Hz
“~“bbl Oscillatory
1 10 frequency(Hz)
Fig. 7. The storage modulus (open symbols) and loss modulus (filled symbols) plotted as a function of the oscillatory frequency at various a.c. frequencies, and also in the absence of any a.c. electric field, for silica particles suspended in corn oil (particle volume fraction, 0.1111; water content, 0.0265; applied field strength 300Vmm~‘): 0, 10 Hz; W, 10 Hz; 0, 100 Hz; 0, 100 Hz; A, 500 Hz; A, 500 Hz; ‘J, 1500 Hz; v’, 1500 Hz; +, 0 kV; x , 0 kV. Since G’ data for different a.c. frequencies are almost the same, the superimposition of symbols for indicating G’ data is seen in this graph.
magnitude of the very the electric as a solid.
greater than G”. This is a consequence strong structure which is built up by field, causing the fluid to behave more To illustrate this point, also shown in
“b
1600 FWJ=Y
(Hz)
Fig. 8. The shear stress plotted as a function of a.c. frequency at different strengths of the applied a.c. electric field for corn oil suspensions of silica particles with volume fraction of 0.1111 and water content of 0.0265: n , 300 V mm-‘; 0, 180 V mm-‘.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993)
and is constant thereafter. Both indirect measures of the structure and
thus
one
would
intuitively
show similar trends. However, both measures of the structure
rg and G’ are of the system expect
them
to
although they are of the system, they
probe different properties of the structure. The yield value is related to the energy required to break the structure (ultimately into individual particles) whilst in the elastic modulus
measurements,
operating in the linear viscoelastic region ensures that the structure is not broken. (We recall that in these experiments the electric field was applied for 5 min to enable the structure to build up before the rheological measurements were made.) Thus G’ is more a measure of the morphology of the structure rather than a measure of its strength. Thus clearly the morphology of the structure is not significantly affected by the frequency of the a.c. field. Presumably all the particles had formed chains [ 121 before the rheological measurements were performed. Preliminary microscopic studies have also shown this to be the case in our work. Let us now turn our attention to the zg data, which are related to the strength of the structure. Since at high shear the viscosity is constant, it means that the structure has been broken down to primary flow units. Thus zg is related to the energy required to separate these particle chains [22], such that zB =
N-L,
(4)
where N is the total number of contacts in the system. The total number of contacts is related to the particle volume fraction 4 and particle radius a, and Eq. (4) can be rewritten as
zB =
36
-$&n 8na
where n is the number of contacts per particle. Since ER fluids form chains, n will be approximately two. Thus we can estimate the energy required to separate particles from the chains. These data are given in Table 1. We are not aware of anyone estimating the energy needed to separate
167-175
173
Table 1 The separation energies of corn oil suspensions of silica with a volume fraction of 0.11 II and water content of 0.0265 at different frequencies of a.c. electric field of strength 300 V mm- 1 A.c. frequency
Bingham
(Hz)
(pa)
yield stress
Separation energy per particle (xIO-‘~J)
10 30 50 70 too 200 300 500 1000 1500
16.17 13.21 9.251 8.787 7.814 6.828 5.681 3.201 3.357 3.241
6.097 4.981 3.488 3.313 2.946 2.574 2.142 1.207 1.266 1.222
particles in an ER fluid previously; however, Sprecher et al. [23] have determined that the force required to separate two particles was about 1.0 uN. Since the energy required to separate two particles is given by E=FD
(6)
we may estimate the energy if we have a reasonable estimate for D, the separation of two adjacent particles. If we assume D is of the order of the dimensions of the particle diameter (which is actually likely to be an overestimate) then we would estimate E ~10~ I2 J. Thus the estimated particle separation energy from our rheological experiments seems reasonable. We now turn our attention to the effect of a.c. frequency in these data. In an a.c. field both the magnitude and sign of the potential are varying (the potential varies sinusoidally). We observe that both the viscosity and yield values decrease as the a.c. frequency is increased, until above a frequency of 500 Hz these parameters are constant. These data give insights into the response time of the ER fluid. Recently Jones [20] has shown that in an a.c. electric field, isolated particles actually oscillate. At low frequencies the particles have sufficient time to restructure and form the well-known chain structure; as the frequency is increased the degree
T.Y. Chen and P.F. LuckhamjColloids
174
of structuring
is reduced
as fewer particles
are able
to respond in the time available. At 500 Hz the change in field direction is too fast to enable any structuring
to occur
in the fluid.
Thus
we may
expect that at high frequencies the yield value will tend to the yield value in the absence of an electric field, as indeed we observe. Therefore we propose that the response time of this ER fluid is of the order of 2 ms. Similar data have also been obtained by Klass and Martinek [19] where the viscosity was constant above 500 Hz. At different strengths of the electric field, 300 the yield stress is shown as a and 180 V mm-‘, function of the a.c. frequency in Fig. 8. Since the dipolar force is proportional to the strength of the electric field squared [ 10,ll ,16- 181, the fibrous structure in the strong electric field is stronger than in a weak electric field at lower frequencies. Again at higher frequencies the yield value is approximately independent of field strength, once more revealing that at high frequencies the particles do not have time to restructure. Hence the yield value in a strong field is higher than that in a weak electric field, particularly at low frequencies. This trend will be reported more fully in a later publication.
Surfaces
shift of induced dipoles of dispersed particles in an ac. field brings about the change of the strength of fibrous structure of ER fluids because of regularly reversing the direction of induced dipoles. Therefore the rheological properties of ER fluids may be affected by varying the frequency of the a.c. electric field. In this case, the frequency of the a.c. electric field becomes an important factor affecting the ER performance in an a.c. electric field. In this study, experimental results are presented on the measurements of a water-activated ER suspension under continuous and oscillatory shear. In an external ac. electric field, the behaviour of an ER fluid is dependent on the a.c. frequency at
Eng. Aspects 78 (1993)
167-175
large deformations, but independent of the a.c. frequency at small deformations. This is a consequence
of the type of experiment
performed.
At
large deformations the structure is broken such that the yield value reflects changes in the particle-particle ations, however,
interaction, the structure
At small deformof the ER fluid is
maintained, so that the elastic modulus is a measure of the morphology. Furthermore, the data are in agreement
with the recently
model of induced
dipoles
postulated
turnover
[20].
Acknowledgements We would like to thank Professor B.J. Briscoe for many useful discussions. We also thank Dr. S.R. Ren and Dr. I.T. Kim for their helpful discussions and encouragement. A grateful acknowledgement is also due to Mr. D.M. Kiminta for his kindly assistance with setting up safety devices.
References 1 2
Conclusions The induced dipole is primarily responsible for the ER effect in the a.c. electric field. The directional
A: Phgsicochem.
7 8 9 IO II 12 13 14 15 16 17 18
W.M. Winslow, J. Appl. Phys., 20 (1949) 1137. D.A. Brooks, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1989. F.E. Filisko, Chem. Ind., 10 (1992) 370. W.A. Bullough, Endeavour, 15 (4) (1991) 165. G. Goldstein, Mech. Eng., October, (1990) 48. Z.P. Shulman, R.G. Gorodkin, E.V. Korobko and V.K. Gleb, J. Non-Newtonian Fluid Mech., 8 (1981) 29. M. Whittle, J. Non-Newtonian Fluid Mech., 37 (1990) 233. M.E. Green, J. Theor. Biol., 138 (1989) 413. M. Whittle and W.A. Bullough, Nature, 358 (1992) 373. D.J. Klingenberg, F.V. Swol and C.F. Zukoski, J. Chem. Phys., 94 (9) (1991) 6170. H. Block and J.P. Kelly, J. Phys. D, 21 (1988) 1661. H. Conrad and A.F. Sprecher, J. Stat. Phys., 64 (5) (1991) 1073. A. Cast and CF. Zukoski, Adv. Colloid Interface Sci., 30 (1989) 153. J.C. Hill and T.H.V. Steenkiste, J. Appl. Phys., 70 (3) (1991) 1207. C.J. Cow and CF. Zukoski J. Colloid Interface Sci., 136 (1) (1990) 175. R.T. Bonnecaze and J.F. Brady, J. Chem. Phys., 96 (3) (1992) 2183. Y. Chen, A.F. Sprecher and H. Conrad, J. Appl. Phys., 70 (I I) (1991) 6796. D.J. Klingenberg, F.V. Swol and CF. Zukoski, J. Chem. Phys., 94 (9) (1991) 6160.
T.Y. Chen and P.F. LuckhamlColloids Surfaces A: Physicochem. Eng. Aspects 78 (1993) 19 20 21
D.L. Klass and T.W. Martinek, J. Appl. Phys., 38 (1) (1967) 67. T.B. Jones, Proc. 2nd Int. Conf. on Electrorheological Fluids, Technomics Publishing Co., Lancaster, 1990, p.14. LT. Kim, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1992.
22 23
167-175
175
P.F. Luckham, B. Vincent and Th.F. Tadros, Colloids Surfaces, 6(2) (1983) 101. A.F. Sprecher, Y. Chen and H. Conrad, Proc. 2nd Int. Conf. on Electrorheological Fluids, Technomics Publishing Co., Lancaster, 1990 p. 82.