Experimental investigation of dipole-dipole interaction in a water-free glass particle/oil electrorheological fluid Weijia Wena) Department of Physics, Hong Kong University of Science and Technology, Hong Kong and Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Kunquan Lu Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
~Received 13 February 1996; accepted for publication 24 April 1996! An experimental investigation of the dipole interaction in a water-free glass/oil electrorheological fluid under an alternating electric field is presented in this letter. The values of the dielectric constant e and conductivity s of glass and oil with respect to the frequency of the external electric field are measured, respectively. Corresponding to the changes in e and s, the square of the absolute dielectric mismatch parameter ubu { b 5(˜ e p ( v )2˜ e f ( v ) # / @˜ e p ( v )12˜ e f ( v ) # , where ˜ e5e 1 s /i e 0 v , and subscripts p and f indicate the glass and oil% decreases as the frequency is increased. After comparing the variation tendency of the ubu2 with the yield stress of the electrorheological ~ER! fluid in a measured frequency range we found that they coincide very well. This result confirms that the polarization theory can explain the mechanism of the ER effect not only in a dc electric field but also in that with a wide frequency range. However, the interaction within the multipoles should be considered in an exact calculation. © 1996 American Institute of Physics. @S0003-6951~96!02825-2#
Electrorheological ~ER! fluids, which consist of microscopic particles suspended in an insulating liquid, show a large increase in the apparent viscosity when an external electric field is applied and it returns to its original state if the electric field is cut off. These phenomena have attracted considerable attention for their possible applications in industry and engineering. The polarization model is usually applied to explain the nature and strength of the particleparticle force which gives rise to the increase in the shear yield strength of the electrorheological fluids.1–5 According to the conventional expression of dipole approximation, the force between the dipoles under an alternating electric field is given by6,7 f d}u pu2}ubu2,
~1!
where p is the dipole moment and b is a factor expressed below:
b5
˜ e p ~ v ! 2˜ e f~v! . ˜ e p ~ v ! 12˜ e f~v!
~2!
The complex dielectric constant is ˜ e (v )5e (v )2 @s (v )/ i e 0 v ], where e~v! and s~v! are the dielectric constant and conductivity. The angular frequency v52pf. The subscripts p and f indicate the particle and fluid respectively. Then, ubu25
@ s p ~ v ! 2 s f ~ v !# 2 1 v 2 e 20 @ e p ~ v ! 2 e f ~ v !# 2 @ s p ~ v ! 12 s f ~ v !# 2 1 v 2 e 20 @ e p ~ v ! 12 e f ~ v !# 2
. ~3!
It is obvious that the frequency dependence of u b u 2 can be obtained if the values of the s p ( v ), e p ( v ), e f ( v ), and s f ( v ), with respect to the frequency are given. Most previous experiments were performed under dc and 50 Hz ac electric fields, and few of them examined the a!
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ER effect in a wide frequency range. An early work by Klass8 showed that the shear stress of ER fluids would decrease when the frequency is increased and the same tendency has also been observed in most commercial ER fluids, however, no explanation for the mechanism was given. The opposite phenomena have been observed by Lu et al. which revealed that the shear stress of ER fluids composed of ferroelectric material increases linearly as the frequency rises from 10 Hz to about 3 kHz.7 The reason for this may be that not only the dipole induced by the external electric field but also the turning of the permanent dipole contained in ferroelectric material contributes to the ER effect.9 Another investigation for the metal/oil ER fluid showed that the shear stress would increase in low frequency range and then tend to be saturate, a result consistent with Davis’ prediction.6 Unfortunately, the dielectric loss of the metal/oil ER fluid was so great that the large electrical current would break down the ER fluid if the frequency surpassed 2 kHz or if it was exposed to the high strength of electric field. The frequency dependence in a higher range could not be observed.10 In this letter, the experimental measurements for the dielectric constant e and conductivity s of the glass and insulating oil has been carried out under the different frequency of the electric field. Corresponding to the changes in e and s, the dielectric mismatch parameter u b u 2 would decrease as the frequency is increased. After comparing it with the yield stress of the ER fluid in a wide frequency range from 30 Hz to 7 kHz we found that they coincide very well. This result confirms that the polarization theory can explain the mechanism of the ER effect in a wide frequency range, however, it is not valid if the ER fluid contained the hydrous particles. Our ER fluid consists of vacuum pump oil containing glass particles which were ground from microscope slides. The particles selected were 4565 mm in size and the volume
Appl. Phys. Lett. 68 (25), 17 June 1996 0003-6951/96/68(25)/3659/3/$10.00 © 1996 American Institute of Physics 3659 Downloaded¬01¬Jun¬2003¬to¬202.40.139.162.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/aplo/aplcr.jsp
FIG. 1. Dielectric constants of the glass and oil as a function of the frequency.
fraction f was 0.24. The glass particles as well as oil was heated in an oven at 130 °C for 4 h to remove any surface water. On the both sides of a piece of glass slide two gold electrodes were evaporated for the dielectric measurements. The dielectric measurement for the oil was performed in a cell with two parallel plate electrodes. The frequency dependence of capacitance and conductance of the glass and oil were measured by an HP 4284A LCR meter in a frequency range from 20 Hz–100 kHz, from which the relationships of e –f and s –f were obtained. The rheological measurements were performed on a rotating cylinder rheometer. The power supply used in our experiments was specially designed with a sinusoidal voltage output ranging from 0 to 5000 V and a frequency ranging from 30 to 8000 Hz. Due to the effect of inductance of transformer, the output voltage was continuously adjusted to keep it stable over the whole measuring period. The impedance of the high voltage probe ~HP 1137 A! was greater than 500 MV and the frequency response width was about 1 MHz. The measured results of the dielectric constants of glass e glass and oil e oil with respect to frequency are shown in Fig. 1, from which we can see that the variation of e glass is obvious in a lower frequency range while e oil remains almost unchanged over the whole frequency range. Moreover, the e glass measured here is larger than that for the usual glass material. Corresponding to Fig. 1, the conductivity of the
FIG. 2. Conductivity of glass and oil as a function of the frequency. The unit of the conductivity is S/m.
FIG. 3. The variations of u b u 2 with respect to the frequency.
glass s glass and oil s oil are presented in Fig. 2. From this figure, we can observe that the s glass and s oil change rapidly with values of one more order of magnitude when the frequency varies from 20 Hz to 5 kHz and then they would keep almost unchanged when the frequency is over 10 kHz. Submitting the experimental dates of the e glass, e oil , s glass , and s oil to Eq. ~3!, the frequency dependence of the u b u 2 can be calculated and that is shown in Fig. 3, where the u b u 2 decreases as the frequency is increased. The measured dynamic yield stress ~here the shear rate was fixed at 15.50 s21 ) of the ER fluid at the different frequencies under an electric field strength of 1550 V/mm is plotted in Fig. 4. As can be seen from the plot the yield stress decreases rapidly when the frequency rises from 30 Hz to 1 kHz and then remains almost unchanged. In order to fit the experimental result, we have multiplied the scaling factor k @here k also represents a proportional constant which appeared in Eq. ~1! and the values is about 14.5# to the dates of Fig. 3, which is plotted as solid line curve in Fig. 4. As can be seen from Fig. 4, the experimental dates are in agreement with that of the theoretical prediction @i.e, Eq. ~3!#. This result confirms that the polarization model can be used to explain the ER effect in a wide frequency range. It should be pointed out that the most important point presented here is the variation tendency of the frequency dependence of yield stress which resulted only from the dipole-dipole interaction and not the absolute
FIG. 4. Values of the yield stress at different frequencies, where the solid line represents k u b u 2 ~k is a proportional constant!. The shear rate is 15.50 s21 and applied electric field is fixed at 1550 V/mm.
3660 Appl. Phys. Lett., Vol. 68, No. 25, 17 June 1996 W. Wen and K. Lu Downloaded¬01¬Jun¬2003¬to¬202.40.139.162.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/aplo/aplcr.jsp
values. However, the exact calculation of the particle-particle interaction is complex and not only the multipole interaction but also some other parameters should be considered. Moreover, our previous experimental result shows that the dipoledipole force cannot be applied to explain the frequency dependence of the hydrous glass particle ER fluids. We would like to thank Dr. W. Y. Tam and Dr. Hongru Ma for helpful discussions and much thanks to Raymond A. Dragan for his editorial suggestions.
T. C. Halsey, Science 258, 373 ~1992!. R. Tao and J. M. Sun, Phys. Rev. Lett. 67, 398 ~1991!. 3 L. C. Davis, Appl. Phys. Lett. 60, 319 ~1992!. 4 H. Conrad, in Particulate Two-Phase Flow, edited by M. C. Roco ~Butterworth, Boston, MA, 1992!, p. 355. 5 Y. Chen, A. F. Sprecher, and H Conrad, J. Appl. Phys. 70, 6796 ~1991!. 6 L. C. Davis, J. Appl. Phys. 73, 680 ~1993!. 7 K. Lu, W. Wen, C. X. Li, and S. S. Xie, Phys. Rev. E 52, 6329 ~1995!. 8 D. L. Klass and T. W. Martinek, J. Appl. Phys. 38, 67 ~1967!. 9 W. Wen and K. Lu, Appl. Phys. Lett. 68, 1046 ~1996!. 10 W. Wen and K. Lu, Appl. Phys. Lett. 67, 2147 ~1995!. 1 2
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