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Quasi-Static Electrorheological Properties of Hematite/ Silicone Oil Suspensions under DC Electric Fields M. J. Espin,† A. V. Delgado,*,† and J. Płocharski‡ Group of Physics of Interfaces and Colloidal Systems, Department of Applied Physics, Faculty of Science, University of Granada, 18071-Granada, Spain, and Faculty of Chemistry, Warsaw University of Technology, 00-664 Warszawa, Poland Received January 20, 2005. In Final Form: March 17, 2005 In this work, a modified rheometer has been used to gain information on the “start-up” of the shear flow of an electrorheological (ER) fluid consisting of hematite particles dispersed in silicone oil. The results show that unelectrified suspensions behave essentially as fluids, continuously deforming upon application of shear. However, this behavior changes in the presence of an electric field. For low fields and low volume fractions of solids, a solidlike (drastic increase in shear stress after the strain is applied) behavior is observed for small deformations. If the strain is increased, the yield starts and a transition to a viscoelasticplastic nature is observed. Finally, a plastic behavior is characteristic of the post-yield regime. If the field strength and solids content are high, a discontinuous flow profile develops. These results, together with direct structural observations, suggest that the observed behavior is compatible with the formation of layers of particles electrophoretically deposited on the electrodes; the layers turn into rings when the shear field is applied. It is the slip of the fluid between these rings that can be considered responsible for the ER effect in these suspensions.
Introduction Field-responsive materials belong to a group of engineering systems, smart materials, whose physical properties strongly depend on the application of an external field upon them. Particularly, electro-active systems, when subjected to high electric fields (of the order of kV/mm), show different behaviors1 associated to the alteration of their optical (electro-optical effect), electrical, and mechanical properties (electrorheological effect). In this paper we focus on electrorheological (ER) fluids, i.e., suspensions of micrometer-sized solid particles dispersed in nonconducting oil,2,3 which show a dramatic change in their rheological properties (including high shear viscosity, yield stress, and viscoelasticity) when an electric field is imposed to them. This modification is related to a phase transition from a liquid to a quasi-solid state induced by the application of the external field. Although the ER effect was observed as early as 1949 by Winslow,4 it is only in the past two decades that the controllable, reversible, and rapid change in the mechanical behavior of ER fluids has made these materials an attractive choice in a wide range of active devices2,3,5-7 such as clutches, brakes, valves, etc. However, an efficient application of these fluids still encounters a number of technological problems mainly associated to the lack of systematic studies in a wide range of working conditions and a conclusive model that includes all their rheological properties. * Author to whom correspondence should be addressed. Fax: +34-958243214. E-mail:
[email protected]. † University of Granada. ‡ Warsaw University of Technology. (1) Deinega, Y. F.; Vinogradov, G. V. Rheol. Acta 1984, 23, 636-651. (2) Block, H.; Kelley J. P. J. Phys. D: Appl. Phys. 1988, 21, 16611677. (3) Hao, T. Adv. Colloid Interface Sci. 2002, 97, 1-35. (4) Winslow, W. M. J. Appl. Phys. 1949, 20, 1137-1140. (5) Coulter, J. P.; Weiss, K. D.; Carlson, J. D. J. Intell. Mater. Syst. Struct. 1993, 4, 248-259. (6) Duclos, T. G. SAE 1988, Paper No. 881134, 2532-2536. (7) Stanway, R.; Sproston, J. L.; El-Wahed, A. K. Smart Mater. Struct. 1996, 5, 464-482.
Regarding this point, the mechanical behavior of these systems is typically evaluated in the shearing mode, with an external electric field applied normally to the shearing planes. At steady state, ER materials are typically described like plastic materials, i.e., fluids that exhibit Newtonian behavior above a certain stress known as the yield stress. This is the Bingham fluid model:8-11
τ ) τy + ηplγ˘ (for τ > τy)
(1)
γ ) 0 (for τ > τy)
(2)
and
where τ is the shear stress, γ˘ the shear rate, τy the yield stress, and ηpl the plastic viscosity. τy is strongly dependent on a number of factors including system composition, field strength, and particle concentration.12-14 In contrast, the plastic viscosity is essentially independent of the field strength15 and is very close to the high shear rate viscosity of the unelectrified suspensions. According to ideal Bingham behavior, the ER materials, under a nonzero field, are solids up to a certain critical shear stress, the yield stress, τy, and liquids above it. However, the behavior of ER systems is likely to be more complex than that described by this ideal plastic model; although adequate in steady flow situations (post-yield) where transient or “start-up” effects are neglected or (8) Bloodworth, R., Wendt, E. In Progress in Electrorheology; Havelka K. O., Filisko, F. E., Eds.; Plenum: New York, 1995; pp 185-193. (9) Goodwin, J. W.; Markhan, G. M.; Vincent, B. J. Phys. Chem. B. 1997, 101, 1961-1967. (10) Klingenberg, D. J.; Zukoski, C. F. Langmuir 1990, 6, 15-24. (11) Marshall, L.; Zukoski, C. F.; Goodwin, J. W. J. Chem. Soc., Faraday Trans. 1989, 85, 2785-2795. (12) Chen, Y.; Sprecher, A. F.; Conrad, H. J. Appl. Phys. 1991, 70, 6796-6803. (13) Davis, L. C. J. Appl. Phys. 1992, 72, 1334-1340. (14) Klingenberg, D. J.; Van Swol, F.; Zukoski C. F. J. Chem. Phys. 1991, 94, 6160-6169. (15) Parthasarathy, M.; Klingenberg, D. J. Mater. Sci. Eng. R 1996, 17, 57-103.
10.1021/la0501583 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/20/2005
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unimportant, it is not applicable in situations where the transient behavior is important or under dynamic loading.16,17 In these situations, the Bingham model completely overlooks the properties of the materials at small strain below the yield point (pre-yield stage) because of the assumption that the system does not deform at all. In comparison to the post-yield behavior, the controllable viscoelastic characteristics of ER materials in the preyield phase (under very small deformations) remain virtually uninvestigated, although they may provide valuable information both from the scientific (better theoretical understanding of ER mechanisms) and technological (improvement of working conditions) viewpoints. In this work, we report on the response, at the “startup” of shear flow, of an ER fluid consisting of hematite/ silicone oil suspensions since we have previously studied their electro-optical properties in a quiescent state18 and mechanical characteristics in steady state under DC electric fields.19 This paper is organized as follows. In the next section, we describe materials, experimental setup, and measurement conditions. Following that, we present and discuss the results of the shear “start-up” tests. Finally, we summarize the most relevant concluding remarks. Experimental Section Materials. The iron oxide (R-Fe2O3 or hematite, density 5.24 g/cm3) powder was purchased from Aldrich, USA, and was used as received. It consisted of irregular polyhedra, with an average size of 105 ( 25 nm, which was determined by fitting a lognormal distribution to the size of about 200 particles on TEM micrographs. Prior to any measurement, we performed a thermogravimetric analysis (Shimadzu TGA-50H, Japan) of the hematite powder in the 20-300 °C temperature interval, and the maximum weight loss detected was 0.022%, just about the instrument sensitivity. Hence, we concluded that the moisture content in the particles was negligible. The conductivity20 of the particles is σp ) (2.6 ( 0.2) × 10-7 S/m, and their relative permittivity21 is p ) 12. In all cases, the continuous phase consisted of poly(dimethylsiloxane)/silicone oil with nominal viscosity ηc ) 1 Pa‚s, delivered by Fluka (USA). The conductivity of the oil is σc ) 10-14 S/m, and its relative electric permittivity22 is c ) 2.6. The manufacturers do not report any water content in the oil. Methods. Preparation of the Suspensions. Different volume fractions (15, 17.5, 20, 22.5, and 25%) were prepared by gentle blending of a stock sample with silicone oil in a Pyrex container and applying vigorous stirring. To ensure the required final homogeneity of the samples, this was verified by disappearing of the initially observed aggregates at the container bottom before pouring more powder. After about 30 min, the suspensions obtained looked completely uniform and no additives appeared to be necessary. Rheological Measurements. Viscoelastic measurements on ER fluids have been mostly performed using rotational geometries such as Couette cells or parallel plate shearing devices which are suitable for high shear strains and shear rates. However, conventional rheometers generally do not have enough resolution to provide sufficiently reliable data of “start-up” effects and small strains. (16) See, H.; Chen, R. Rheol. Acta 2004, 43, 175-179. (17) Tang, X. L.; Conrad, H. J. Rheol. 1996, 40, 1167-1178. (18) Espin, M. J.; Delgado, A. V.; Dura´n J. D. G. J. Colloid Interface Sci. 2005, in press. (19) Espin, M. J.; Delgado, A. V.; Rejon, L. J. Non-Newtonian Fluid Mech. 2005, 125, 1-10. (20) Espin, M. J.; Delgado, A. V.; Martin, J. E. Rheol. Acta 2004, 44, 71-79. (21) Young, K. F.; Frederikse, H. P. R. J. Phys. Chem. Ref. Data 1973, 2, 313-409. (22) Conrad, H.; Chen, Y. In Progress in Electrorheology Havelka K. O., Filisko, F. E., Eds., Plenum: New York, 1995; pp 55-85.
Langmuir, Vol. 21, No. 11, 2005 4897 Indeed, to obtain precise enough data, we have built a shearing apparatus23-27 (a coaxial arrangement, in our case) designed for low strains. The device consists of a metal cup 2.2 cm in diameter with a fixed 2 cm bob (height 2.5 cm). The cup can be rotated by means of a couple of springs connected to electric transducers which transferred data to an acquisition unit and a PC. Both the shear stress applied by the cup and the shear strain of the material could be determined from the signals of the force and displacement transducers. The detailed description of the static rheometer will be published elsewhere.28 The device was always calibrated prior to any measurement. A dc voltage was applied between the grounded cup and the insulated bob by a power source. The electric field strength ranged from 1 to 4 kV/mm. Rheological tests were conducted at ambient temperature (about 20 °C) and consisted of the three following steps: (i) Prior to each measurement, the cup was filled with a new sample, and to ensure good dispersion, the suspension was energetically sheared for 60 s at approximately 100 s-1 rate in absence of the electric field. In that way, all curves were well reproducible, as we always started with a homogeneous sample and the same initial conditions. (ii) The suspension was left to equilibrate, with the electric field applied in order to eventually allow particle structures to form. It is well known that the time required for ER fluids to respond to a step change of electric fields is reported to be of the order of 1 ms. However, a fully stable structure in a static suspension is found through microscopic observation and rheological techniques to form on a time scale of seconds or even minutes.25,29-32 For hematite/silicone oil suspensions19 the response time under very small shear rate was below 40 s, so we decided to choose 60 s as the structure time prior to each experiment. (iii) Finally, with the electric field still applied, shear “start-up” tests under various electric fields were performed by applying shear to the sample and values of shear strain up to 1.5 were monitored. Each experiment at the same field was repeated three times to verify reproducibility of the results. Structural Observations. Because of the high turbidity of the suspensions, their optical observation is not possible for high concentrations of particles and a gap between electrodes as small as 1 mm. For these reasons, we performed some experiments on semidiluted dispersions, φ ) 1.5%, which were electrified with a pair of parallel stainless steel electrodes separated 3.2 mm. Photos of the suspensions were taken with a digital camera (1 megapixel resolution) controlled by a commercial image acquisition software.
Results and Discussion Overview of Experimental Results. Figure 1a-e shows the shear stress curves for hematite/silicone oil suspensions as a function of electric field strength, E, volume fraction, φ, and shear strain, γ. A first preliminary analysis of these graphs reflects the dramatic changes that high external fields provoke on the mechanical behavior of these systems. Thus, unelectrified suspensions exhibit the typical flow properties of liquids, namely, a continuous (23) Conrad, H.; Shamala, A. R.; Sprecher, A. F. Proceedings of the 1st International Symposium on ER Fluids; NCSU Engineering Publishers: Raleigh, 1989. (24) Conrad, H.; Chen, Y.; Sprecher, A. F. Proceedings of the 2nd International Conference on Electrorheological Fluids; Technomics: Lancaster, 1990. (25) Sprecher, A. F.; Carlson, J. D.; Conrad, H. Mater. Sci. Eng. 1987, 95, 187-197. (26) Stevens, N. G.; Sproston, J. L.; Stanway, R. Trans. ASME 1987, 54, 456-458. (27) Koyama, K.; Minagawa, K.; Yoshida, T.; Kuramoto, N. Proceedigns of the 4th Int. Conference on Electrorheological Fluids; World Scientific Publishing: Singapore, 1994. (28) Płocharski, J.; Harasimowicz, J.; Jabłon´ski, Z.; Osuchowski, M.; De¸ bska, D., in preparation. (29) Martin, J. E.; Odinek, J.; Halsey, T C.; Kamien, R. Phys. Rev. E 1998, 57, 756-774. (30) Otsubo, Y.; Edamura, K. Colloids Surf., A 1996, 109, 63-69. (31) Otsubo Y.; Edamura, K. J. Non-Newtonian Fluid Mech. 1997, 71, 183-195. (32) Otsubo, Y.; Sekine, M.; Katayama S. J. Colloid Interface Sci. 1991, 146, 395-404.
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Figure 1. Shear stress as a function of shear strain and electric field strength (1.0-4.0 kV/mm) for suspensions of different volume fractions: 15.0% (a), 17.5% (b), 20.0% (c), 22.5% (d), and 25.0% (e).
deformation upon the application of a shear stress. However, dispersions behave very differently under the action of the field: at low and moderate field strengths and low concentration of particles, a drastic increase in the shear stress is observed immediately after the shear strain was applied and, finally, slowly reached a saturation value. On the other hand, an unexpected discontinuous flow regime appears in conditions where a more pronounced ER effect is expected (i.e., increase of either the intensity of the field or volume fraction of solids). This consists of a series of abrupt jumps in deformation when a certain stress is exceeded; below such stress the system does not increase its deformation. This flow regime will be discussed later. Solidlike Behavior. Let us first focus on the first kind of flow regime. The observed profile of curves is the typical response of solidlike materials33 at small strains: the shear stress rapidly increases from zero as the strain is applied (pre-yield stage), and finally, after a small transition region, a plateau value is reached at large strains where (33) Makosko, C. Rheology. Principles, measurements and applications; VCH Publishers: New York, 1994; p 92.
a complete steady flow is formed. This is the post-yield region usually studied in steady-state rheological experiments. The previous mechanical behavior is closely related to the changes in the structure of the systems induced by a shear field. At small deformations, solidlike bodies exhibit a certain elasticity, but when the strain and/or stress exceed some critical values, a transition region is reached where the curves of the shear stress bend over and reach a plateausat this stage, it is thought that the microstructure is undergoing significant break-up and a transition to steady flow is occurring. Thus, the shear “startup” tests show that there is a transition from the solidtype response at small strains to steady flowing behavior for larger deformations. In the case of ER materials, the origin of this solidlike behavior lies on the modifications that electric fields induce in their structures. This causes some differences in their mechanical properties with respect to those of materials whose internal configuration is originated by physicochemical factors. For instance, once electro-active materials reach the post-yield region, the shear stress is not completely constant since the permanent application of
Properties of Suspensions under DC Electric Fields
Figure 2. Shear stress at very small shear strain for a suspension of 17.5% volume fraction and an applied field strength of 3.0 kV/mm. Schematic description of the three rheological stages and their characteristic parameters (τy, yield stress, γy, yield strain; G, storage modulus).
the electric field originates a continuous rebuilding of the field-induced structures and, thus, suspensions do not behave as perfect liquids (which permanently deform at a constant shear stress). A more careful observation of these curves indicates other important characteristics of the hematite/silicone oil system under “start-up” conditions. For example, Figure 2 shows the low-strain shear stress vs shear strain curve for a suspension of 17.5% volume fraction and an applied electric field of 3.0 kV/mm. First of all, it is worth mentioning that the transition from a solidlike behavior at low shear strains to the steady-state type corresponding to large strains is not as smooth as we have simply described. At very small deformations (pre-yield region), the shear stress increases linearly until a yield point (γ < γy) is reached; beyond this, the stress first goes through a maximum (yield stage) and then decreases before reaching the steady-state condition (post-yield regime19), the extrapolation of which is one definition of the exhibited yield stress, τy. According to this, the rheological changes that electric fields induce on ER systems cannot be just described as the commonly admitted transition from a linear viscous to a plastic body but, more properly, to a nonlinear or viscoelastic-plastic behavior which exhibits different mechanical properties depending on the measuring range:34-36 (i) Pre-yield. The linear dependence between shear stress and strain suggests that ER fluids show Hookean elasticity, that is to say, deformation is recoverable (elastic) providing that the yield strain, γy, is not exceeded. In this manner, a linear viscoelastic description is suitable for these systems under these deformation conditions. (ii) Yield. As the strain increases above γy, the deformation starts to distort the structure and finally the elasticity of the ER fluid cannot be dominant any more. In this measuring range, materials are nonlinearly elastic and can be described as viscoelastic-plastic. (iii) Postyield. Systems are permanently deformed or flow. This is the region which is usually characterized in steady-state conditions and where a plastic model, yield stress,τy, and plastic viscosity, ηpl, are typically reported. To assess in a more quantitative way these three different regions, we determined the effect of electric field strength and concentration of particles on the parameters (34) Filisko, F. E. In Progress in Electrorheology; Havelka K. O., Filisko, F. E., Eds.; Plenum: New York, 1995; pp 3-18. (35) Gamota, D. R.; Filisko, F. E. J. Rheol. 1991, 35, 399-424. (36) Kamath, G. M.; Wereley, N. M. Smart Mater. Struct. 1997, 6, 351-359.
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Figure 3. Yield stress, τy, as a function of the electric field strength at different volume fractions. Lines correspond to linear fits of the data τy ) a + bE (Table 1).
Figure 4. Volume fraction dependence of the yield stress, τy, of hematite suspensions for the field strengths indicated. Lines are the best fit to a power law τy ) cφd (Table 2). Table 1. Dependence of the Yield Stress on the Electric Field Strength at Different Volume Fractions (Figure 3)a φ
a
b
F
0.150 0.175 0.200 0.225
-6 ( 3 (-5.7 ( 0.6) × 101 (-6.6 ( 0.3) × 101 (-9.0 ( 0.9) × 101
(5.74 ( 0.13) × 101 (1.12 ( 0.03) × 102 (1.484 ( 0.018) × 102 (1.84 ( 0.06) × 102
0.99877 0.99914 0.99993 0.99949
a Parameters of the linear fit, τ ) a + bE (τ in Pa, E in kV/mm). y y F: correlation coefficient.
characteristic of each of them: yield stress, τy, which describes the modification on plastic flow (since plastic viscosity is almost field-independent), yield strain, γy, which indicates the transition between solid- and liquidlike behaviors, and storage modulus, G, which reflects the linear and recoverable elasticity of the suspensions. G corresponds to the slope of the linear part of the stressstrain dependence below γy. Figures 3 and 4 show the dependence of the yield stress (which was determined by extrapolation of the post-yield region of shear stress-strain curves to zero deformation, γ ) 0) on field strength and volume fraction, respectively. First, it is interesting to underline that the increase of these parameters provokes an enhancement of the plasticity of the suspensions under large strains. These data also demonstrate that yield stress in an increasing linear function of electric field and depends on volume fraction in a parabolic-like fashion. Tables 1 and 2 correspondingly include the best-fit parameters (and their correlation coefficients) to linear, τy ) a + bE, and power-law, τy ) cφd, functions. These two tendencies also agree with the previously reported results of steady-state sweeps for DC electrified hematite/silicone oil suspensions performed
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Table 2. Dependence of Yield Stress, τy, on Volume Fraction, O, for Different Field Strengths, E (Figure 4)a E (kV/mm)
c (Pa)
d
1.0 1.5 2.0
(1.6 ( 0.4) × (3 ( 1.5) × 103 (6.5 ( 1.9) × 103 103
1.88 ( 0.17 1.9 ( 0.3 2.10 ( 0.18
F2 0.97907 0.95526 0.98791
a Best-fit parameters to a power law fit, τ ) cφd. F2: coefficient y of determination.
Figure 5. Yield strain, γy, as a function of the electric field strength at different volume fractions. Lines are the best fit to a power law γy ) fEg (Table 3).
Figure 6. Volume fraction dependence of the yield stress, γy, of hematite suspensions for the field strengths indicated. Lines are the best fit to a power law γy ) hφi (Table 4). Table 3. Dependence of the Yield Strain on the Electric Field Strength at Different Volume Fractions (Figure 5)a φ
f
0.150 0.175 0.200 0.225
(2.94 ( 0.07) × (2.4 ( 0.1) × 102 (1.71 ( 0.08) × 102 (1.39 ( 0.11) × 102 102
g
F2
-1.08 ( 0.04 -1.13 ( 0.09 -1.02 ( 0.13 -1.02 ( 0.24
0.99376 0.98205 0.98542 0.95287
a Best-fit parameters to a power law, τ ) fEg (E in kV/mm). F2: y coefficient of determination.
with a conventional rheometer,19 showing that the Bingham model is a suitable description only for flowing ER fluids at large and permanent deformations. Concerning the yield stage, which separates the elastic and plastic regions, it is also influenced by the intensity of the electric field and the concentration of iron oxide powder as Figures 5 and 6 show. The yield strain (defined as the deformation where the relationship between shear stress and strain deviates from linearity) decreases substantially with increasing field, while at low field strengths, it follows an approximately linear trend; the strain tends to saturate for high fields so that the global behavior can be described in a hyperbolic fashion (Table 3), γy ∝ E-1. The effect of volume fraction consists of a similar decrease and saturating trends, although the yield strain follows a quadratic law, γy ∝ φ-2 (Table 4). These
Table 4. Dependence of Yield Strain, τy, on Volume Fraction, O, for Different Field Strengths, E (Figure 6)a E (kV/mm) 1.0 1.5 2.0
h 10-4
(6.9 ( 1.6) × (1.03 ( 0.45) × 10-3 (3.2 ( 0.4) × 10-4
i
F2
-1.98 ( 0.13 -1.5 ( 0.3 -1.98 ( 0.06
0.98875 0.95495 0.99818
a Best-fit parameters to a power law, τ ) hφi. F2: coefficient of y determination.
Figure 7. Storage modulus, G, as a function of the electric field strength at different volume fractions. Lines are the best fit to a power law G ) jEk (Table 5).
Figure 8. Volume fraction dependence of the storage modulus, G, of hematite suspensions for the field strengths indicated. Lines are the best fit to a power law G ) lφm (Table 6).
tendencies and data also agree with those previously reported by these and other authors.15,19,35-37 According to these results, as the field and concentration increase, the pre-yield region is shortened so that, for high strengths and volume fractions, the ER fluids tend to behave as perfect solids since they can withstand only small deformations before structure breakdown. Finally, we have studied the usually forgotten pre-yield region, where, as we have previously mentioned, the shear stress increases linearly with shear strain for very low deformations. ER materials behave as solidlike bodies in this stage since the deformation of the system is proportional to the applied shear stress. This relationship is typically described by the expression τ ) Gγ, where G is the elastic or storage modulus which reflects the elastic energy stored by the system. Therefore, G indicates to what extent an ER fluid is solidified because of the application of an electric field. Figures 7 and 8 show the storage modulus as a function of field strength and volume fraction, respectively. According to these data, the magnitude of G increases in a parabolic fashion with the field strength (see best-fit parameters in Table 5), a result also (37) Pan, X. D.; McKinley, G. H. Appl. Phys. Lett. 1997, 71, 333-335.
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Table 5. Dependence of the Storage Modulus on the Electric Field Strength at Different Volume Fractions (Figure 7)a φ
j
k
F2
0.150 0.175 0.200 0.225
(9 ( 1.5) × 102 (1.6 ( 0.25) × 103 (2.6 ( 0.5) × 103 (3.6 ( 2.3) × 102
2.33 ( 0.13 2.19 ( 0.15 2.02 ( 0.28 2.26 ( 0.10
0.9931 0.98892 0.98892 0.99887
a Best-fit parameters to a power law, G ) jEk (G in Pa, E in KV/mm). F2: coefficient of determination.
Table 6. Dependence of Storage Modulus, G, on Volume Fraction, O, for Different Field Strengths, E (Figure 8)a E (kV/mm)
l (Pa)
10 15 20
(1.34 ( 0.05) × (1.6 ( 0.5) × 106 (4.17 ( 0.11) × 106 106
m
F2
4.0 ( 0.3 3.45 ( 0.18 3.69 ( 0.17
0.99133 0.99615 0.99713
Figure 9. Maximum shear stress, τyn, for each n as a function of shear strain and electric field strength (1.0-4.0 kV/mm) for a suspension of 20% volume fraction.
a Best-fit parameters to a power law, G ) lφm. F2: coefficient of determination.
reported experimentally and theoretically by other authors,15,35,38 and approximately depends on concentration of particles in a power law, G ∝ φm, with m ≈ 4 (Table 6). These tendencies agree with the above-mentioned behaviors of yield stress and strain, an expected result, since elastic modulus can be approximately defined as G ≈ τy/ γy. However, what is more important, these experiments demonstrate that an increase both of electric field and volume fraction not only affects the fluidlike behavior (plastic) at large deformation but also affects the viscoelastic behavior at the transition region between solid and liquid and the solidlike behavior (elastic) at very low shear strains. Discontinuous Flow Behavior. Let us now concentrate on the second kind of flow regime exhibited by the suspensions. As we have previously pointed out, when the ER effect is much more pronounced (that is, at high field strengths and concentrations of particles), the ER response involves the unexpected development of a discontinuous flow profile (Figure 1b-e): shear stress begins to increase at a given shear strain until a certain critical value is reached; above this, there is an abrupt deformation and the monitored shear stress dramatically decreases. This behavior repeats again and again in all the shear strain range investigated. In that way, the flow of the suspensions can be described as a finite number of steps or jumps. The first thing to mention is that it is not possible to properly describe and analyze this regime in terms of the three stages observed at moderate ER activity: pre-yield, yield, and post-yield (for this reason, we have considered them separately). For example, since there is no continuous flow, it makes no sense to define a yield stress or strain. However, it is still possible to study the changes that increasing electric fields and volume fraction provoke. To achieve this, we have defined a pseudo-yield stress, τyn, as the maximum stress reached in each jump/step (where n indicates its number). Figures 9 and 10, respectively, show the pseudo-yield stress and strain for all the field strengths evaluated and two different volume fractions, 20 and 25%. It is interesting to note that, although, as we have just pointed out, it is not possible to define this discontinuous regime in the same mechanical terms as the previous one, there are some similarities. For example, at a given E and φ, τyn (as shear stress, τ, in the flow regime) increases at low shear
strain and, finally, reaches a saturation value for large deformations. Moreover, the value of τyn increases with both the field strength and volume fraction, confirming the growing solidification of the system. This manifests also in the decrease of the number of shear jumps observed in Figure 1b-e when the field or the solids concentration are raised. Structure of Electrified Suspensions. Finally, let us briefly focus on the structural features of the electrified suspensions. Theoretical and experimental studies generally indicate that, for usual ER fluids (such as silica, glass beads, etc. dispersed in an insulator host), the application of electric fields gives rise to the formation of fibrils of particles between electrodes. Particles polarize under the applied external fields, and anisotropic polarization forces (Felec ∼ E2) between these dipoles cause the formation of chains of particles.4 To confirm the appearance or not of this structure in hematite/silicone oil suspensions, there is some information that can be extracted from the previous results before performing any experiments. For instance, the yield stress reported by different authors for common ER systems is typically of the order of ∼kPa for the volume fractions considered in this work. In contrast, for hematite/silicone oil suspensions, this critical stress is much lower (0.3 kPa, at most). On the other hand, since the yield stress is related to electrostatic polarization forces, several experimental and theoretical studies support E2 and φ dependences of yield stress.39,40 However, we have observed that this parameter follows well-defined linear and quadratic tendencies with field strength and volume fraction, respectively. In addition, polarization12,13,15 and conduc-
(38) McLeish, T. C. B.; Jordan, T.; Shaw, M. T. J. Rheol. 1991, 35, 427-448.
(39) Bonnecaze, R. T.; Brady, J. F. J. Rheol. 1992, 36, 73-115. (40) Otsubo, Y. J. Rheol. 1992, 36, 479-496.
Figure 10. Same as Figure 9 for φ ) 25%.
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Figure 11. Photographs of an iron oxide/silicone oil suspension of 1.5% volume fraction for a field strength of 2.5 kV/mm at different times: (a) suspension in quiescent state, (b) electrohydrodynamic convection and electrophoretic deposition of solids, and (c) layers of particles.
tion41,42 (that consider τy ∝ E∆, with 1 < ∆ < 2) theories clearly state that an increase of E and φ only originate a stronger columnar structure and, hence, an increase in ER activity (with yield stress or storage modulus depending on the test and measurement range) but do not explain the existence of the discontinuous flow. All these facts suggest that the observed rheological behavior cannot be simply explained by a chain description of the electrified iron oxide/silicone oil suspensions and the random breakage of these individual fibers. Indeed, our structural studies18,19 indicate that for sufficiently high electric fields (>0.5 kV/mm) no columns are formed between electrodes. Parts a-c of Figure 11 confirm this point. They show a suspension of hematite powder subjected to 2500 V. When the electric field is switched on, the solid phase starts to move from the electrodes to the center of the suspension which gives rise to the formation of convection cells and to a progressive migration of particles toward the electrodes. Finally, this situation collapses in the formation of layers or deposits of hematite solids on the surface of the electrodes that, for sufficiently high volume fractions, could be effectively in touch forming a structure of aggregates spanning the region between the electrodes. The origin of this phenomenon is the injection of charge from the electrodes to the bulk of the suspension that happens at high field strengths. The charge acquired by the solvent and the particles provokes the observed electrohydrodynamic cells31,43,44 and, eventually, the electrophoretic deposition1 since monopolar electric forces become predominant over polarization interactions (which require longer time18,25,29,31stens of seconds or even minutessto develop a pattern of columns). Other authors (41) Chin, B. D.; Lee, Y. S.; Park, O. O. J. Colloid Interface Sci. 1998, 201, 172-179. (42) Tang, X.; Wu, C.; Conrad, H., J. Rheol. 1995, 39, 1059-1073. (43) Bezryadin, A.; Westervelt, R. M.; Tinkham, M. Phys. Rev. E 1999, 59, 6896-6902. (44) Castellanos, A. IEEE. Trans. Electron. Insul. 1991, 26, 12011215.
Espin et al.
Figure 12. Photograph of rings (R) and slip regions (SR) in a bob geometry observed after a simultaneous application of a DC electric field and a shear rate field.
have reported on the possibility of gap-spanning chain formation depending on the solid conductivity,45 and they have shown that chains can only form if the conductivity of the solid is not excessively large (σp e 10-7 S/m). When shear is applied in addition to the electric field, we observe the formation of rings or lamellas distributed along the measuring cell both in “start-up” and steadystate tests.19 Figure 12 is a photo of this pattern of rings that has also been reported by other authors with different materials. Although some of them observed that these rings have formed from structures such as chains or columns,46-49 and others simply from layers of aggregates of particles,31 all authors agree that the observed ER response (i.e., appearance of yield stress and high viscosities) is due to the formation of the periodical annular structures. The number of rings formed is a complex function of the field strength, volume fraction, and maximum shear rate applied.31,47,48 According to this, since the yield stress is related to the breakdown and restructuring of layers of particles into rings and the appearance of slip regions between adjacent lamellas,47,48 their measured values are much lower than those originated by the breakdown of chains between electrodes. For this reason, hematite/silicone oil suspensions do not exhibit a critical stress as high as other suspensions of the same volume fraction. In addition, there is a linear increase of yield stress with field strength (Figure 4) since it reflects the shear force required to balance and overcome the tendency of these rings to maintain their integrity, which is due to the electrostatic attraction force between the charged particles and the electrodes.19 What is more, a simple columnar structure cannot justify the observed discontinuous regime: once chains are formed and the shear stress exceeds the yield point, (45) Boissy, C.; Atten, P.; Foulc, J. N. J. Intell. Mater. Syst. Struct. 1996, 7, 599-603. (46) Cutillas, S.; Bossis, G.; Lemaire, E.; Meunier, A. Int. J. Mod. Phys. B 1999, 13, 1791-1797. (47) Filisko, F. E.; Henley, S.; Quist, G. J. Intell. Mater. Sys. Str. 1999, 10, 476-480. (48) Henley, S.; Filisko, F. E. J. Rheol. 1999, 43, 1323-1336. (49) Lemaire, E.; Bossis, G.; Grasselli, Y.; Meunier, A. Proceedigns of the 4th International Conference on Electrorheological Fluids; World Scientific Publishing: Singapore, 1994.
Properties of Suspensions under DC Electric Fields
chains break down and suspensions start to flow. Although there is some rebuilding, this is not strong enough to give rise to a new yield process (the rebuilt structure, yet at very small shear rates, will never be as strong as one formed without shear). In contrast, when a pattern of annular structures is formed, the flow consists of slip between neighbor rings. If the field strength and/or volume fraction are high enough, restructuring forces become increasingly predominant in all slip regions (particularly at small deformations). Hence, the shear stress must overcome the newly built deposits or layers between rings; when this happens, the flow starts abruptly again. Conclusions We have employed a modified rheometer in order to achieve high-resolution and more-reliable results for shear stress-strain measurements and, thus, more-reliable results. These show the existence of two flow regimes: a continuous one at low field strength and volume fraction and an abrupt one for higher ER activity. The usual flow reflects that electrified ER materials can be described in terms of a field-induced transition from an elastically dominated behavior (pre-yield), via an intermediate yield region (viscoelastic) to a fluidlike, Bingham-plastic behavior (post-yield), depending on the measurement range. In other words, the electric field not
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only affects the apparent viscosity, as is the most common description of the rheological properties of these materials but also alters the rheological mechanism by which the materials can be modeled. The three previous rheological behaviors were analyzed by means of storage modulus, G, yield stress, τy, and strain, γy, and their dependences on field strength and volume fraction. Similarly, pseudo-yield stress, γyn was defined to study the effect of electric field and concentration of particles on the second flow regime observed. Finally, an analysis was performed to elucidate the field-induced structure of the suspensions. It was observed that not chains but layers of particles are on the surfaces of the electrodes which, together with the action of shear fields, give rise to the formation of rings. The slip between adjacent particles is proposed as an explanation to the two different flows observed. Acknowledgment. Financial support from the Spanish Ministry of Science and Technology and Feder Funds (EU) (Project No. MAT2004-0866) is acknowledged. M.J.E. thanks the Spanish Ministry of Education for the Grant covering his stay at the Faculty of Chemistry, Warsaw University of Technology (Poland), and the research group led by Prof. J. Płocharski for assistance and support during this work. LA0501583
