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Effect of medium viscosity on rheological characteristics of magnetite-based magnetorheological fluids
Journal of Industrial and Engineering Chemistry 80 (2019) 197–204
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Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
Effect of medium viscosity on rheological characteristics of magnetite-based magnetorheological fluids Ehsan Esmaeilnezhada,* , Seyed Hasan Hajiabadia , Hyoung Jin Choib,* a b
Department of Petroleum Engineering, Hakim Sabzevari University, Sabzevar, Iran Department of Polymer Science and Engineering, Inha University, Incheon 22212, South Korea
A R T I C L E I N F O
A B S T R A C T
Article history: Received 3 June 2019 Received in revised form 5 July 2019 Accepted 27 July 2019 Available online 4 August 2019
This study examined the magnetorheological (MR) behavior of magnetite-based MR fluids according to the magnetite concentration, magnetic field strength, and different viscosity of silicone oil as the carrier fluid. To this end, an experimental design was chosen to decrease the experimental error and provide a better rheological interpretation. The flow behavior parameters increased remarkably with increasing medium viscosity and nanoparticles (NPs) concentration, whereas the magnetic field strength had a milder effect, exhibiting a saturation value above which its effect became almost negligible. Moreover, both the Bingham plastic and power law models were found to fit their flow behaviors well. Almost all the critical rheological parameters of the aforementioned models experienced remarkable improvement after increasing the magnetic field strength, NPs concentration and carried fluid viscosity. In addition, mathematical correlations were derived to model each of the rheological parameters such as plastic viscosity and yield stress (for Bingham fluid model) and the consistency and power-law indices (for power-law model). © 2019 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
Keywords: Magnetite Magnetorheological fluid Carrier fluid viscosity Experimental design
Introduction Since the introduction of smart magnetorheological (MR) fluids, scientists have assessed various applications based on their revolutionary features [1–3]. Smart MR fluids exhibit a rapid, tunable, and reversible transition from a fluid-like to a solid-like phase upon exposure to different magnetic fields [4–6]. Compared to MR elastomers, which are regarded as smart materials whose dynamic viscoelasticity is controllable by tuning an external magnetic field [7–11], these fluids are considered as one of the most prominent MR materials with potential industrial applications, such as polishing devices, sensors, clutches, and dampers [12–14]. MR fluids can be applied in a range of industries owing to their phenomenal rheological characteristics. MR fluids are generally a mixture of silicone oil (or mineral oil) and magnetic particles, ranging in size from the micro- to nano-scale [15–18]. In the course of developing MR fluids, a considerable number of magnetic particles have been introduced, such as carbonyl iron (CI), alloys [19] and iron oxides, including the maghemite [20] and magnetite [21]. Magnetite-based MR fluids are believed to be
* Corresponding authors. E-mail addresses: [email protected] (E. Esmaeilnezhad), [email protected] (H.J. Choi).
one of the most profitable systems to be utilized in industry owing to the easier and cheaper synthesis procedures of magnetite compared to other particles. A range of structures can be produced, such as nanocrystals [22], cubes [23], spindle [24], wire [25], sandwich-like sheets [26], chestnut-like [27], flower-like [28], and others [29–31]. Similar to all other magnetic materials, however, the stability of a particle within a carrier fluid is a major consideration regarding their applications [32]. Several methods have recently been suggested, where at least in the case of magnetite, a silica coating has been introduced [33,34]. On the other hand, a silica coating is believed to reduce the magnetic properties of magnetite, which places some limitations on their applications [35,36]. Along with main characteristics of magnetic particles, MR suspensions are strongly affected by the medium fluids and magnetic field strength applied. Indeed, the viscosity of the carrier fluid is a key parameter to control the fluid capacity when suspending the particles [37]. The viscosity of the medium can affect the dispersion stability of solid particles. A low carrier fluid viscosity results in a lower dispersion stability of particles and a higher likelihood of particle settlement, whereas a high mediumviscosity may adversely affect the quality of the particle dispersion, which inhibits the effects of magnetic field strength [38]. Many methods have been proposed to increase the magnetite suspension within a smart fluid. Of these, coating the particles with citric acid can enhance the dispersion stability of magnetite significantly [39].
https://doi.org/10.1016/j.jiec.2019.07.049 1226-086X/© 2019 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
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Temperature affects MR behavior and should be taken into account for application purposes. Indeed, although the critical rheological parameters, such as apparent viscosity and yield stress, decrease with increasing temperature, this effect can be reduced by increasing the magnetic field strength [40,41]. This study examined rheological characteristics of magnetitebased MR smart suspensions under a wide range of conditions involving different concentrations of citric acid-coated magnetite (CM) nanoparticles (NPs), a broad range of carrier fluid viscosity, and various magnetic field strengths. A designed experimental method was implemented to model the rheological behavior with reduced experimental error. Experimental Materials and method Fe3O4 (magnetite) nanoparticles were used as a dispersed phase, and were synthesized using a methodology reported elsewhere [42]. Briefly, 8 mmol of NaOH (Merck, Germany), 4 mmol of NaNO3 (Daejung Chem., Korea), and 2 mmol of citric acid trisodium salt dehydrate (C6H5Na3O72H2O, Sigma–Aldrich) were dissolved in 38 cc of distilled water and the solution temperature was increased to about 100 C. A 2 cc sample of a 2.0 M FeSO47H2O (Yukuri Pure Chem., Japan) solution was dropped and the temperature was kept constant for 1 h. The solution temperature was lowered down to room temperature and the CM NPs were separated by a magnet after washing more than three times with distilled water. In addition, silicone oils (ShinEtsu Co. Ltd., Korea) with various viscosities (100, 500, and 1000 cp) were used as the continuous phase throughout the experiments.
Results and discussion NPs properties Fig. 1a shows an SEM photo of the fabricated NPs in a spherical shape. TEM (Fig. 1b) revealed a quite regular spherical shape of CM NPs with a size of approximately 90 nm; the magnetite was well coated with citric acid. Fig. 2 presents an XRD pattern of CM NPs with peaks at 2u value of 30.2 , 35.7, 43.28 , 53.8 , 57.28 , and 62.85 , matching with (2 2 0), (3 11), (4 0 0), (4 2 2), (5 11), and (4 4 0) planes, respectively, which proved that the coating process had no effects on the crystal structure, as reported elsewhere [43]. The magnetic hysteresis loop of the CM NPs was measured at ambient temperature from 1000 to 1000 kA/m (Fig. 3), which revealed saturation magnetization at approximately 52 Am2/kg that is well accordance with literatures regard to coating process [44,45], size, and shape of magnetite NPs [46,47]. Experimental design Parameters, such as NPs concentration, carrier fluid viscosity, and magnetic field strength, affect MR responses considerably. On the other hand, owing to the huge number of experiments needed to analyze the effects of those parameters, a response surface methodology (RSM) was utilized to develop an optimized model to predict MR characteristics. The RSM is the approach through which experimental outcomes can be connected with independent variables through models, which can be expressed as Eqs. (1)
Characterization The morphology of the CM NPs was examined by scanning electron microscopy (SEM) (S-4300, Hitachi) and transmission electron microscopy (TEM) (Philips, CM200). The crystalline structure of the CM NPs and magnetic properties were tested by X-ray powder diffraction (XRD) (DMAX-2500, Rigaku) and vibrating sample magnetometer (VSM) 7407, Lake Shore, USA), respectively. Suspensions containing 2, 4, 6 and 8 vol% of synthesized CM NPs were fabricated in silicone oil (with different viscosity) using a vortex (IKA Genius 3) and sonicator (HSt-Power Sonic 401) and the MR characteristics of the MR suspensions were examined via a rotational rheometer (MCR 300, Anton Paar, Austria), equipped with a parallel-plate geometry (25-mm) and a magnetite field supplier. All the measurements were performed at approximately 25 C.
Fig. 2. XRD diffraction patterns of CM NPs.
Fig. 1. (a) SEM and (b) TEM images of the CM NPs.
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of the most well-known rheological models, namely Bingham and power law models, were used to evaluate MR properties, as shown in the following equations: Bingham plastic:
t ¼ t 0 þ mp g_
ð3Þ
Power law:
t ¼ K g_ n
Fig. 3. Magnetization curves of CM NPs as a function of magnetic field strength.
and (2) [48]: Y ¼ b0 þ
k X
b i xi
ð1Þ
i¼1
Y ¼ b0 þ
k X
b i xi þ
XX
i¼1
bi;j xi xj þ
i
k X
bi x2i
ð2Þ
i¼1
where Y and k are the response and rate of inputs, respectively; b0 , b1 , and bij are constant numbers, linear coefficient, and interaction coefficient, respectively. Moreover, xi and xi xj are single and interaction factors, respectively [49,50]. To model the rheological behavior of MR fluids, the following control factors were assessed: CM NPs concentration (vol%), magnetic field strength (kA/m), and carrier fluid viscosity (cp). Two
ð4Þ
where t , t 0 , mp , and g_ are representative of shear stress, yield stress, plastic viscosity, and shear rate, respectively. Plastic viscosity is estimated from the slope of flow curves and yield stress is estimated by extrapolating the shear stress at the very low shear rates (around 0.01/s) [51,52]. In addition, in terms of the power law equation, K and n are the consistency index and powerlaw index, respectively [53]. Table 1 lists the parameters for each model along with the figures estimated from the rheological tests. Having utilized the RSM model, some equations were derived based on the responses achieved. Fitting models for MR characteristics To achieve the most appropriate regression equations, some analytical models consisting of the linear, two-factor interaction, and quadratic model were used to examine the test results based on the model summary test, lack of fitting test, and sequential model sum of squares, which can be used to assess the acceptability of the predicted models. The results are shown in Table 2. Considering the P- and F-value, 2FI was opted as the model by which the Bingham fluid model parameters could be forecasted properly. On the other hand, although 2FI is accepted as an appropriate model to predict the behavior of consistency index, the quadratic equation was the best fitted model in terms of the power index. The R2 values were close to unity for both rheological models. Because the R2 values are dependent on adding a new
Table 1 Experimental design matrix along with the corresponding results. Std
14 9 2 3 13 4 15 17 16 12 5 11 18 1 7 10 8 6 19 20 21 22 23 24 25 26
Run
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Factors
Bingham responses
Power law responses
CM concentration (vol%)
Silicone oil viscosity (cp)
Magnetic field strength (kA/m)
Plastic viscosity (Pa s)
Yield stress (Pa)
Consistency index (Pa s)
Power index (–)
2 2 2 2 2 4 6 6 8 8 8 8 8 2 2 8 8 8 2 2 2 4 4 8 8 8
100 100 500 1000 1000 100 500 500 100 500 500 1000 1000 100 1000 500 1000 100 100 500 1000 100 100 100 100 500
68 137 68 34 137 34 68 137 102 34 102 34 137 0 137 68 102 137 0 0 102 68 137 68 0 0
0.24 0.26 1.05 1.34 1.70 0.43 3.37 4.41 1.707 2.71 4.99 4.48 9.52 0.15 1.70 4.68 7.91 2.04 0.15 0.68 1.69 0.6 0.7 1.27 0.88 1.95
7.96 9.04 18.58 7.07 11.68 21 123.59 198.35 174.51 62.44 228.53 94.77 368.1 1.39 11.68 149.58 292.65 201.54 1.39 4.90 11.66 38.24 48.69 135.06 21.96 32.84
9.1 10.41 19.48 5.28 2.17 23.52 141.66 226.2 190.83 72.19 262.48 104.21 419.64 1.17 2.17 175.15 419.64 220.40 1.16 3.61 9.64 43.02 54.47 147.89 23.51 32.82
0.21 0.19 0.35 0.69 0.94 0.15 0.19 0.16 0.07 0.25 0.14 0.31 0.18 0.54 0.94 0.18 0.18 0.08 0.53 0.63 0.61 0.12 0.11 0.06 0.264 0.371
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Table 2 Models’ summary statistics. Rheological model
Targeted parameters
Proposed model
df
Mean square
F-Value
P-value Prob > F
R square
Adjusted R square
Predicted R square
Bingham
Yield point Plastic viscosity Consistency index Power index
2FI 2FI 2FI Quadratic
6 6 6 9
41,630.4 22.91 61,094.8 0.18
78.05 72.35 51.12 29.97
<0.0001 <0.0001 <0.0001 <0.0001
0.961 0.958 0.942 0.944
0.949 0.945 0.923 0.913
0.919 0.903 0.867 0.818
Power law
predictor [54], the use of the adjusted R2 values can result in more reliable consequences [55]. Table 2 presents the adjusted R2 values; all R2 values were close to unity, confirming that the models can fit the flow behavior of suspensions well. Figs. 4 and 5 show the normal probability plots for the Bingham fluid and power law model, respectively. Both cases showed a linear relationship with data points revealing the appropriate fitness of the proposed model and the validity of the obtained equations. Eqs. (5)–(8) express the empirical models, where rewarding responses can be found using the input variables in terms of the coded factors, as listed in Table 3. In all the equations, A, B, and C denote the CM NPs concentration, silicone oil viscosity, and magnetic field strength, respectively. Some of the equations were modified by deleting less
important factors. The estimation of rheological behavior of the fluids based on these models was reasonable. This means that the amount of additives, magnetic field strength, and silicone oil viscosity to reach a desired rheological parameter can be determined easily using the above-mentioned equations. Furthermore, the equations can be performed in a straightforward manner whenever an optimization process is necessary. MR behavior Having obtained the predicted models, it is important to assess the rheological parameters and evaluate the shear stress–shear rate diagrams. Figs. 6 and 7 show the shear stress–shear rate alterations and shear viscosity vs. shear rate variations of MR fluids, respectively, at two constant additive concentrations of (2
Fig. 4. Normal plot of residuals for Bingham parameters: (a) plastic viscosity, and (b) yield stress.
Fig. 5. Normal plot of residuals for power law parameters: (a) consistency index, and (b) power index.
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Table 3 The regression models obtained for each rheological model. Models
Predicted equations
Bingham
Yield stress Plastic viscosity Consistency index Power index
Power law
Eq. =400.8 + 384.7*A + 114.5*B + 383.7*C + 20.8*A*B + 367.8*A*C + 111.6*B*C =7.2 + 5.4*A + 4.4*B + 5.75*C + A*B + 4.5*A*C + 3.4*B*C =467.7 + 457.5*A + 148*B + 448.4*C + 33.5*A*B + 435.6 *A*C + 141.4*B*C =3.360.28*A + 0.43*B + 8.1*C0.09*A*B0.14*A*C + 0.35*B*C + 0.1*A2 + 5.2*C2
and 8 volume percentage of CM NPs) over whole magnetic field strengths and three carrier fluid viscosities. To clarify the alterations and make a better judgment regarding the effects of miscellaneous parameters, a constant vertical offset, i.e. 15%, was placed on all figures, to help better interpret the diagrams [56]. Fig. 6a represents that an increase in shear rate resulted in a non-linear increase in shear stress, showing the pseudo-plastic characteristics of the fluids. An increase in the shear viscosity of the carrier fluid resulted in a sharp increase in shear stress within the
Fig. 6. Graphical illustrations of MR fluids’ rheological behavior at constant concentration of CM NPs (2 vol%): (a) shear stress–shear rate diagram, (b) viscosity– shear rate diagram.
(5) (6) (7) (8)
higher shear rate periods. In addition, the shear stress increased moderately with an input magnetic field strength. Meanwhile, after a certain magnetic field strength was reached, called the saturation value, the MR properties were relatively stable and further increases in magnetic field strength had a negligible effect [37]. The threshold for the present study was 68 kA/m, which is the magnetic field strength limitation. Higher shear rates resulted in shear viscosity decrease of the fluids depicting the shear thinning features of the MR fluids, which is of great significance in the majority of industrial applications and resulted from the reorientation of particles in the direction of shear
Fig. 7. Rheological behavior of MR fluids at constant concentration of CM NPs (8 vol %): (a) shear stress–shear rate diagram, (b) viscosity–shear rate diagram.
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flow as well as presence of inter particle interactions before shear [57–60] (Fig. 6b). High-viscosity carrier fluids increased the viscosity of the MR smart solutions. Furthermore, the viscosity increased slightly with increasing magnetic field strength. After reaching the foregoing threshold, the shear viscosity remains constant and is relatively unaffected by the magnetic field strength, which is of great importance in terms of real-scale applications [61]. Fig. 7a and b shows similar trends in that the viscosity decreased with a shear rate, whereas it increased with increasing the viscosity of carrier fluid and magnetic field strength. The impacts of CM NPs were examined further. Figs. 8 and 9 show the changes in the rheological properties of the fluids at two constant carrier fluid viscosities (100 and 1000 cp, respectively). As given in Fig. 8a, increasing the CM NPs concentration from 2 to 8 vol% resulted in an increase in shear stress, which reveals the effectiveness of the CM NPs on enhancing the flow behavior of the MR fluids. The same holds true for the shear viscosity–shear rate values shown in Fig. 8b, meaning an increase in shear rate with
increasing CM NPs concentration. The magnetic field strength had a similar effect reaching the threshold value of 68 kA/m. After reaching this saturation value, the shear viscosity stabilized, i.e., further increases in magnetic field strength had no additional effects on the rheological properties. This should be considered when developing applications of the MR suspensions, particularly when the distance from the magnetic field source is one of the key elements [62]. Fig. 9a and b demonstrates the rheological behavior of the fluids when the carrier fluid viscosity was 1000 cp. The trends of the shear stress–shear rate are comparable to those shown in Fig. 8a, meaning an increase in the shear stress with increasing viscosity of the silicone oil and shear-rate, but the viscosity had a greater effect. Overall, the viscosity of silicone oil, as the carrier fluid, has the main influence on the ultimate viscosity of the MR fluids, as shown in Fig. 9b. Fig. 10 shows the plastic viscosity and yield stress of the MR suspensions, as main parameters for assessing their rheological properties. These parameters are considered independent variables of the Bingham plastic model for modeling the rheological
Fig. 8. Flow behavior of MR fluids at constant viscosity of carrier fluids (100 cp) (a) shear stress–shear rate diagram, (b) viscosity–shear rate diagram.
Fig. 9. Flow behavior of MR fluids at constant viscosity of carrier fluids (1000 cp) (a) shear stress–shear rate diagram, (b) viscosity–shear rate diagram.
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Fig. 11. Changes in the power law's parameters of the MR fluids: (a) consistency index, (b) power law index.
Conclusion
Fig. 10. Changes in Bingham model's parameters of the MR fluids: (a) plastic viscosity, and (b) yield stress.
behavior of pseudo-plastic industrial fluids. In a plastic-viscosity angle of view, the magnetic field strength had a significant positive effect on the plastic viscosity and yield stress. In addition, an increase in the viscosity of the carrier fluid resulted in a tremendous effect on the yield stress. On the other hand, a higher concentration of CM NPs resulted in an increase in plastic viscosity and yield stress. For further rheological analysis, the power law [63] was assessed, as shown in Fig. 11. Fig. 11a shows the changes in consistency index which are similar to that of the plastic viscosity in the Bingham fluid model, suggesting that the addition of CM NPs results in an increase in plastic viscosity. Moreover, the magnetic field strength showed a similar trend to that of the CM NPs concentration. On the other hand, an increase in both the carrier fluid viscosity and magnetic field strength resulted in increase in power law index, while it is reduced with increasing the concentration of CM NPs as shown in Fig. 11(b). Non-laminar flow can stem from any decrease in power-law index, which means a flatter profile of flow and higher capacity of the fluid to carry solids [64]. It is worthy of note that, in order to show the changes clearly, a vertical offset is added to both the figures (11a and b) .
CM NPs were synthesized using a facile and inexpensive method and used as a dispersed phase in a carrier fluid to produce a suspension with MR properties. MR features of some solutions containing CM NPs with different concentrations suspended in silicone oils with a range of viscosities, as the carrier fluid, were assessed at various magnetic field strengths in a predesigned three-factor experimental program. Several equations were used to achieve appropriate equations fitting properly to predict the MR behavior of fluids. Of these, the 2FI method was found to be the best model for most of the parameters of the rheological models. Several equations were derived from statistical analyses, to model the flow behavior of CM NPs-based MR fluids under a range of conditions. The shear rate-associated alterations of the suspensions were improved by increased magnetic field strength. In contrast, a sharp increase in the MR properties was observed when the concentration of CM NPs was increased. Similarly, a similar trend to that of the CM NPs concentration was observed in the case of the viscosity of silicone oil, showing the optimal capacity of carrier fluids in enhancing the MR properties of CM-based smart fluids. The Bingham fluid model was found to be suitable for modeling the plastic viscosity and yield stress, which increased with a magnetite concentration, magnetic field strength, and viscosity of silicone oil as the carrier fluid. The power-law equation was effective in modeling the flow property of various nonNewtonian fluids, particularly the rheology of MR fluids, in which the consistency index and power law index increased significantly
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with increasing magnetite concentration, magnetic field strength, and different viscosity of silicone oil as the carrier fluid. Overall, the Bingham model showed a good fit to the rheological behaviors of the MR fluids examined. Acknowledgements One of authors (H.J.C.) was supported by National Research Foundation of Korea (2018R1A4A1025169). The authors are thankful to Stat-Ease, Minneapolis for the provision of the Design Expert package. References [1] Y.P. Seo, S. Han, J. Choi, A. Takahara, H.J. Choi, Y. Seo, Adv. Mater. 30 (2018) 1704769. [2] A.V. Anupama, V. Kumaran, B. Sahoo, Soft Matter. 14 (2018) 5407. [3] I. Bica, J. Magn. Magn. Mater. 283 (2004) 335. [4] F.H. Xu, Z.-D. Xu, X.-C. Zhang, Y.-Q. Guo, Y. Lu, J. Vib. Acoust. 138 (2016) 011017. [5] G. Wang, Y. Ma, Y. Tong, X. Dong, J. Ind. Eng. Chem. 48 (2017) 142. [6] D. Susan-Resiga, L. Vékás, Rheol. Acta 53 (2014) 645. [7] T. Hu, S. Xuan, L. Ding, X. Gong, Mater. Des. 156 (2018) 528. [8] T. Tian, M. Nakano, J. Intell. Mater. Syst. Struct. 29 (2018) 151. [9] Y. Tong, X. Dong, M. Qi, Soft Matter. 14 (2018) 3504. [10] A. Dargahi, R. Sedaghati, S. Rakheja, Compos. Part B-Eng. 159 (2019) 269. [11] K.J. Son, Korea-Austral. Rheo. J. 30 (2018) 29. [12] I. Bica, J. Magn. Magn. Mater. 270 (2004) 321. [13] P. Peer, M. Stenicka, P. Filip, N. Pizurova, V. Babayan, Colloid Polym. Sci. 296 (2018) 1849. [14] I. Bica, Y.D. Liu, H.J. Choi, J. Ind. Eng. Chem. 19 (2013) 394. [15] I.D.M. Kim, S.J. Park, J. Magn. Magn. Mater. 404 (2016) 40. [16] G.R. Iglesias, A. Roldán, L. Reyes, L. Rodriguez-Arco, J.D. Durán, J. Intell. Mater. Syst. Struct. 26 (2015) 1836. [17] G. Wang, Y. Ma, Y. Tong, X. Dong, Smart Mater. Struct. 25 (2016) 035028. [18] J. Yang, H. Yan, X. Wang, Z. Hu, Mater. Lett. 167 (2016) 27. [19] Z.D. Xu, B.B. Chen, J. Mater. Civil Eng. 28 (2015) 04015198. [20] I. Jonkkari, M. Sorvali, H. Huhtinen, E. Sarlin, T. Salminen, J. Haapanen, J.M. Makela, J. Vuorinen, Smart Mater. Struct. 26 (2017) 095004. [21] X. Ruan, L. Pei, S. Xuan, Q. Yan, X. Gong, J. Magn. Magn. Mater. 429 (2017) 1. [22] C.Y. Gao, M.W. Kim, D.H. Bae, Y.Z. Dong, S.H. Piao, H.J. Choi, Polymer 125 (2017) 21. [23] V.A. Bautin, A.G. Seferyan, M.S. Nesmeyanov, N.A. Usov, J. Magn. Magn. Mater. 460 (2018) 278. [24] S. Liu, L. Li, S. Zheng, S. Qi, J. Mater. Sci. Mater. Electron 29 (2018) 8978. [25] Q. Qu, S. Yang, X. Feng, Adv. Mater. 23 (2011) 5574. [26] F. Mou, J. Guan, Z. Xiao, Z. Sun, W. Shi, X. Fan, J. Mater. Chem. 21 (2011) 5414. [27] X. Tian, K. He, B. Wang, S. Yu, C. Hao, K. Chen, Q.J.C. Lei, Colloids Surf. A 498 (2016) 185.
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Contents lists available at ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
Effect of medium viscosity on rheological characteristics of magnetite-based magnetorheological fluids Ehsan Esmaeilnezhada,* , Seyed Hasan Hajiabadia , Hyoung Jin Choib,* a b
Department of Petroleum Engineering, Hakim Sabzevari University, Sabzevar, Iran Department of Polymer Science and Engineering, Inha University, Incheon 22212, South Korea
A R T I C L E I N F O
A B S T R A C T
Article history: Received 3 June 2019 Received in revised form 5 July 2019 Accepted 27 July 2019 Available online 4 August 2019
This study examined the magnetorheological (MR) behavior of magnetite-based MR fluids according to the magnetite concentration, magnetic field strength, and different viscosity of silicone oil as the carrier fluid. To this end, an experimental design was chosen to decrease the experimental error and provide a better rheological interpretation. The flow behavior parameters increased remarkably with increasing medium viscosity and nanoparticles (NPs) concentration, whereas the magnetic field strength had a milder effect, exhibiting a saturation value above which its effect became almost negligible. Moreover, both the Bingham plastic and power law models were found to fit their flow behaviors well. Almost all the critical rheological parameters of the aforementioned models experienced remarkable improvement after increasing the magnetic field strength, NPs concentration and carried fluid viscosity. In addition, mathematical correlations were derived to model each of the rheological parameters such as plastic viscosity and yield stress (for Bingham fluid model) and the consistency and power-law indices (for power-law model). © 2019 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
Keywords: Magnetite Magnetorheological fluid Carrier fluid viscosity Experimental design
Introduction Since the introduction of smart magnetorheological (MR) fluids, scientists have assessed various applications based on their revolutionary features [1–3]. Smart MR fluids exhibit a rapid, tunable, and reversible transition from a fluid-like to a solid-like phase upon exposure to different magnetic fields [4–6]. Compared to MR elastomers, which are regarded as smart materials whose dynamic viscoelasticity is controllable by tuning an external magnetic field [7–11], these fluids are considered as one of the most prominent MR materials with potential industrial applications, such as polishing devices, sensors, clutches, and dampers [12–14]. MR fluids can be applied in a range of industries owing to their phenomenal rheological characteristics. MR fluids are generally a mixture of silicone oil (or mineral oil) and magnetic particles, ranging in size from the micro- to nano-scale [15–18]. In the course of developing MR fluids, a considerable number of magnetic particles have been introduced, such as carbonyl iron (CI), alloys [19] and iron oxides, including the maghemite [20] and magnetite [21]. Magnetite-based MR fluids are believed to be
* Corresponding authors. E-mail addresses: [email protected] (E. Esmaeilnezhad), [email protected] (H.J. Choi).
one of the most profitable systems to be utilized in industry owing to the easier and cheaper synthesis procedures of magnetite compared to other particles. A range of structures can be produced, such as nanocrystals [22], cubes [23], spindle [24], wire [25], sandwich-like sheets [26], chestnut-like [27], flower-like [28], and others [29–31]. Similar to all other magnetic materials, however, the stability of a particle within a carrier fluid is a major consideration regarding their applications [32]. Several methods have recently been suggested, where at least in the case of magnetite, a silica coating has been introduced [33,34]. On the other hand, a silica coating is believed to reduce the magnetic properties of magnetite, which places some limitations on their applications [35,36]. Along with main characteristics of magnetic particles, MR suspensions are strongly affected by the medium fluids and magnetic field strength applied. Indeed, the viscosity of the carrier fluid is a key parameter to control the fluid capacity when suspending the particles [37]. The viscosity of the medium can affect the dispersion stability of solid particles. A low carrier fluid viscosity results in a lower dispersion stability of particles and a higher likelihood of particle settlement, whereas a high mediumviscosity may adversely affect the quality of the particle dispersion, which inhibits the effects of magnetic field strength [38]. Many methods have been proposed to increase the magnetite suspension within a smart fluid. Of these, coating the particles with citric acid can enhance the dispersion stability of magnetite significantly [39].
https://doi.org/10.1016/j.jiec.2019.07.049 1226-086X/© 2019 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
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Temperature affects MR behavior and should be taken into account for application purposes. Indeed, although the critical rheological parameters, such as apparent viscosity and yield stress, decrease with increasing temperature, this effect can be reduced by increasing the magnetic field strength [40,41]. This study examined rheological characteristics of magnetitebased MR smart suspensions under a wide range of conditions involving different concentrations of citric acid-coated magnetite (CM) nanoparticles (NPs), a broad range of carrier fluid viscosity, and various magnetic field strengths. A designed experimental method was implemented to model the rheological behavior with reduced experimental error. Experimental Materials and method Fe3O4 (magnetite) nanoparticles were used as a dispersed phase, and were synthesized using a methodology reported elsewhere [42]. Briefly, 8 mmol of NaOH (Merck, Germany), 4 mmol of NaNO3 (Daejung Chem., Korea), and 2 mmol of citric acid trisodium salt dehydrate (C6H5Na3O72H2O, Sigma–Aldrich) were dissolved in 38 cc of distilled water and the solution temperature was increased to about 100 C. A 2 cc sample of a 2.0 M FeSO47H2O (Yukuri Pure Chem., Japan) solution was dropped and the temperature was kept constant for 1 h. The solution temperature was lowered down to room temperature and the CM NPs were separated by a magnet after washing more than three times with distilled water. In addition, silicone oils (ShinEtsu Co. Ltd., Korea) with various viscosities (100, 500, and 1000 cp) were used as the continuous phase throughout the experiments.
Results and discussion NPs properties Fig. 1a shows an SEM photo of the fabricated NPs in a spherical shape. TEM (Fig. 1b) revealed a quite regular spherical shape of CM NPs with a size of approximately 90 nm; the magnetite was well coated with citric acid. Fig. 2 presents an XRD pattern of CM NPs with peaks at 2u value of 30.2 , 35.7, 43.28 , 53.8 , 57.28 , and 62.85 , matching with (2 2 0), (3 11), (4 0 0), (4 2 2), (5 11), and (4 4 0) planes, respectively, which proved that the coating process had no effects on the crystal structure, as reported elsewhere [43]. The magnetic hysteresis loop of the CM NPs was measured at ambient temperature from 1000 to 1000 kA/m (Fig. 3), which revealed saturation magnetization at approximately 52 Am2/kg that is well accordance with literatures regard to coating process [44,45], size, and shape of magnetite NPs [46,47]. Experimental design Parameters, such as NPs concentration, carrier fluid viscosity, and magnetic field strength, affect MR responses considerably. On the other hand, owing to the huge number of experiments needed to analyze the effects of those parameters, a response surface methodology (RSM) was utilized to develop an optimized model to predict MR characteristics. The RSM is the approach through which experimental outcomes can be connected with independent variables through models, which can be expressed as Eqs. (1)
Characterization The morphology of the CM NPs was examined by scanning electron microscopy (SEM) (S-4300, Hitachi) and transmission electron microscopy (TEM) (Philips, CM200). The crystalline structure of the CM NPs and magnetic properties were tested by X-ray powder diffraction (XRD) (DMAX-2500, Rigaku) and vibrating sample magnetometer (VSM) 7407, Lake Shore, USA), respectively. Suspensions containing 2, 4, 6 and 8 vol% of synthesized CM NPs were fabricated in silicone oil (with different viscosity) using a vortex (IKA Genius 3) and sonicator (HSt-Power Sonic 401) and the MR characteristics of the MR suspensions were examined via a rotational rheometer (MCR 300, Anton Paar, Austria), equipped with a parallel-plate geometry (25-mm) and a magnetite field supplier. All the measurements were performed at approximately 25 C.
Fig. 2. XRD diffraction patterns of CM NPs.
Fig. 1. (a) SEM and (b) TEM images of the CM NPs.
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of the most well-known rheological models, namely Bingham and power law models, were used to evaluate MR properties, as shown in the following equations: Bingham plastic:
t ¼ t 0 þ mp g_
ð3Þ
Power law:
t ¼ K g_ n
Fig. 3. Magnetization curves of CM NPs as a function of magnetic field strength.
and (2) [48]: Y ¼ b0 þ
k X
b i xi
ð1Þ
i¼1
Y ¼ b0 þ
k X
b i xi þ
XX
i¼1
bi;j xi xj þ
i
k X
bi x2i
ð2Þ
i¼1
where Y and k are the response and rate of inputs, respectively; b0 , b1 , and bij are constant numbers, linear coefficient, and interaction coefficient, respectively. Moreover, xi and xi xj are single and interaction factors, respectively [49,50]. To model the rheological behavior of MR fluids, the following control factors were assessed: CM NPs concentration (vol%), magnetic field strength (kA/m), and carrier fluid viscosity (cp). Two
ð4Þ
where t , t 0 , mp , and g_ are representative of shear stress, yield stress, plastic viscosity, and shear rate, respectively. Plastic viscosity is estimated from the slope of flow curves and yield stress is estimated by extrapolating the shear stress at the very low shear rates (around 0.01/s) [51,52]. In addition, in terms of the power law equation, K and n are the consistency index and powerlaw index, respectively [53]. Table 1 lists the parameters for each model along with the figures estimated from the rheological tests. Having utilized the RSM model, some equations were derived based on the responses achieved. Fitting models for MR characteristics To achieve the most appropriate regression equations, some analytical models consisting of the linear, two-factor interaction, and quadratic model were used to examine the test results based on the model summary test, lack of fitting test, and sequential model sum of squares, which can be used to assess the acceptability of the predicted models. The results are shown in Table 2. Considering the P- and F-value, 2FI was opted as the model by which the Bingham fluid model parameters could be forecasted properly. On the other hand, although 2FI is accepted as an appropriate model to predict the behavior of consistency index, the quadratic equation was the best fitted model in terms of the power index. The R2 values were close to unity for both rheological models. Because the R2 values are dependent on adding a new
Table 1 Experimental design matrix along with the corresponding results. Std
14 9 2 3 13 4 15 17 16 12 5 11 18 1 7 10 8 6 19 20 21 22 23 24 25 26
Run
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Factors
Bingham responses
Power law responses
CM concentration (vol%)
Silicone oil viscosity (cp)
Magnetic field strength (kA/m)
Plastic viscosity (Pa s)
Yield stress (Pa)
Consistency index (Pa s)
Power index (–)
2 2 2 2 2 4 6 6 8 8 8 8 8 2 2 8 8 8 2 2 2 4 4 8 8 8
100 100 500 1000 1000 100 500 500 100 500 500 1000 1000 100 1000 500 1000 100 100 500 1000 100 100 100 100 500
68 137 68 34 137 34 68 137 102 34 102 34 137 0 137 68 102 137 0 0 102 68 137 68 0 0
0.24 0.26 1.05 1.34 1.70 0.43 3.37 4.41 1.707 2.71 4.99 4.48 9.52 0.15 1.70 4.68 7.91 2.04 0.15 0.68 1.69 0.6 0.7 1.27 0.88 1.95
7.96 9.04 18.58 7.07 11.68 21 123.59 198.35 174.51 62.44 228.53 94.77 368.1 1.39 11.68 149.58 292.65 201.54 1.39 4.90 11.66 38.24 48.69 135.06 21.96 32.84
9.1 10.41 19.48 5.28 2.17 23.52 141.66 226.2 190.83 72.19 262.48 104.21 419.64 1.17 2.17 175.15 419.64 220.40 1.16 3.61 9.64 43.02 54.47 147.89 23.51 32.82
0.21 0.19 0.35 0.69 0.94 0.15 0.19 0.16 0.07 0.25 0.14 0.31 0.18 0.54 0.94 0.18 0.18 0.08 0.53 0.63 0.61 0.12 0.11 0.06 0.264 0.371
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Table 2 Models’ summary statistics. Rheological model
Targeted parameters
Proposed model
df
Mean square
F-Value
P-value Prob > F
R square
Adjusted R square
Predicted R square
Bingham
Yield point Plastic viscosity Consistency index Power index
2FI 2FI 2FI Quadratic
6 6 6 9
41,630.4 22.91 61,094.8 0.18
78.05 72.35 51.12 29.97
<0.0001 <0.0001 <0.0001 <0.0001
0.961 0.958 0.942 0.944
0.949 0.945 0.923 0.913
0.919 0.903 0.867 0.818
Power law
predictor [54], the use of the adjusted R2 values can result in more reliable consequences [55]. Table 2 presents the adjusted R2 values; all R2 values were close to unity, confirming that the models can fit the flow behavior of suspensions well. Figs. 4 and 5 show the normal probability plots for the Bingham fluid and power law model, respectively. Both cases showed a linear relationship with data points revealing the appropriate fitness of the proposed model and the validity of the obtained equations. Eqs. (5)–(8) express the empirical models, where rewarding responses can be found using the input variables in terms of the coded factors, as listed in Table 3. In all the equations, A, B, and C denote the CM NPs concentration, silicone oil viscosity, and magnetic field strength, respectively. Some of the equations were modified by deleting less
important factors. The estimation of rheological behavior of the fluids based on these models was reasonable. This means that the amount of additives, magnetic field strength, and silicone oil viscosity to reach a desired rheological parameter can be determined easily using the above-mentioned equations. Furthermore, the equations can be performed in a straightforward manner whenever an optimization process is necessary. MR behavior Having obtained the predicted models, it is important to assess the rheological parameters and evaluate the shear stress–shear rate diagrams. Figs. 6 and 7 show the shear stress–shear rate alterations and shear viscosity vs. shear rate variations of MR fluids, respectively, at two constant additive concentrations of (2
Fig. 4. Normal plot of residuals for Bingham parameters: (a) plastic viscosity, and (b) yield stress.
Fig. 5. Normal plot of residuals for power law parameters: (a) consistency index, and (b) power index.
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Table 3 The regression models obtained for each rheological model. Models
Predicted equations
Bingham
Yield stress Plastic viscosity Consistency index Power index
Power law
Eq. =400.8 + 384.7*A + 114.5*B + 383.7*C + 20.8*A*B + 367.8*A*C + 111.6*B*C =7.2 + 5.4*A + 4.4*B + 5.75*C + A*B + 4.5*A*C + 3.4*B*C =467.7 + 457.5*A + 148*B + 448.4*C + 33.5*A*B + 435.6 *A*C + 141.4*B*C =3.360.28*A + 0.43*B + 8.1*C0.09*A*B0.14*A*C + 0.35*B*C + 0.1*A2 + 5.2*C2
and 8 volume percentage of CM NPs) over whole magnetic field strengths and three carrier fluid viscosities. To clarify the alterations and make a better judgment regarding the effects of miscellaneous parameters, a constant vertical offset, i.e. 15%, was placed on all figures, to help better interpret the diagrams [56]. Fig. 6a represents that an increase in shear rate resulted in a non-linear increase in shear stress, showing the pseudo-plastic characteristics of the fluids. An increase in the shear viscosity of the carrier fluid resulted in a sharp increase in shear stress within the
Fig. 6. Graphical illustrations of MR fluids’ rheological behavior at constant concentration of CM NPs (2 vol%): (a) shear stress–shear rate diagram, (b) viscosity– shear rate diagram.
(5) (6) (7) (8)
higher shear rate periods. In addition, the shear stress increased moderately with an input magnetic field strength. Meanwhile, after a certain magnetic field strength was reached, called the saturation value, the MR properties were relatively stable and further increases in magnetic field strength had a negligible effect [37]. The threshold for the present study was 68 kA/m, which is the magnetic field strength limitation. Higher shear rates resulted in shear viscosity decrease of the fluids depicting the shear thinning features of the MR fluids, which is of great significance in the majority of industrial applications and resulted from the reorientation of particles in the direction of shear
Fig. 7. Rheological behavior of MR fluids at constant concentration of CM NPs (8 vol %): (a) shear stress–shear rate diagram, (b) viscosity–shear rate diagram.
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flow as well as presence of inter particle interactions before shear [57–60] (Fig. 6b). High-viscosity carrier fluids increased the viscosity of the MR smart solutions. Furthermore, the viscosity increased slightly with increasing magnetic field strength. After reaching the foregoing threshold, the shear viscosity remains constant and is relatively unaffected by the magnetic field strength, which is of great importance in terms of real-scale applications [61]. Fig. 7a and b shows similar trends in that the viscosity decreased with a shear rate, whereas it increased with increasing the viscosity of carrier fluid and magnetic field strength. The impacts of CM NPs were examined further. Figs. 8 and 9 show the changes in the rheological properties of the fluids at two constant carrier fluid viscosities (100 and 1000 cp, respectively). As given in Fig. 8a, increasing the CM NPs concentration from 2 to 8 vol% resulted in an increase in shear stress, which reveals the effectiveness of the CM NPs on enhancing the flow behavior of the MR fluids. The same holds true for the shear viscosity–shear rate values shown in Fig. 8b, meaning an increase in shear rate with
increasing CM NPs concentration. The magnetic field strength had a similar effect reaching the threshold value of 68 kA/m. After reaching this saturation value, the shear viscosity stabilized, i.e., further increases in magnetic field strength had no additional effects on the rheological properties. This should be considered when developing applications of the MR suspensions, particularly when the distance from the magnetic field source is one of the key elements [62]. Fig. 9a and b demonstrates the rheological behavior of the fluids when the carrier fluid viscosity was 1000 cp. The trends of the shear stress–shear rate are comparable to those shown in Fig. 8a, meaning an increase in the shear stress with increasing viscosity of the silicone oil and shear-rate, but the viscosity had a greater effect. Overall, the viscosity of silicone oil, as the carrier fluid, has the main influence on the ultimate viscosity of the MR fluids, as shown in Fig. 9b. Fig. 10 shows the plastic viscosity and yield stress of the MR suspensions, as main parameters for assessing their rheological properties. These parameters are considered independent variables of the Bingham plastic model for modeling the rheological
Fig. 8. Flow behavior of MR fluids at constant viscosity of carrier fluids (100 cp) (a) shear stress–shear rate diagram, (b) viscosity–shear rate diagram.
Fig. 9. Flow behavior of MR fluids at constant viscosity of carrier fluids (1000 cp) (a) shear stress–shear rate diagram, (b) viscosity–shear rate diagram.
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Fig. 11. Changes in the power law's parameters of the MR fluids: (a) consistency index, (b) power law index.
Conclusion
Fig. 10. Changes in Bingham model's parameters of the MR fluids: (a) plastic viscosity, and (b) yield stress.
behavior of pseudo-plastic industrial fluids. In a plastic-viscosity angle of view, the magnetic field strength had a significant positive effect on the plastic viscosity and yield stress. In addition, an increase in the viscosity of the carrier fluid resulted in a tremendous effect on the yield stress. On the other hand, a higher concentration of CM NPs resulted in an increase in plastic viscosity and yield stress. For further rheological analysis, the power law [63] was assessed, as shown in Fig. 11. Fig. 11a shows the changes in consistency index which are similar to that of the plastic viscosity in the Bingham fluid model, suggesting that the addition of CM NPs results in an increase in plastic viscosity. Moreover, the magnetic field strength showed a similar trend to that of the CM NPs concentration. On the other hand, an increase in both the carrier fluid viscosity and magnetic field strength resulted in increase in power law index, while it is reduced with increasing the concentration of CM NPs as shown in Fig. 11(b). Non-laminar flow can stem from any decrease in power-law index, which means a flatter profile of flow and higher capacity of the fluid to carry solids [64]. It is worthy of note that, in order to show the changes clearly, a vertical offset is added to both the figures (11a and b) .
CM NPs were synthesized using a facile and inexpensive method and used as a dispersed phase in a carrier fluid to produce a suspension with MR properties. MR features of some solutions containing CM NPs with different concentrations suspended in silicone oils with a range of viscosities, as the carrier fluid, were assessed at various magnetic field strengths in a predesigned three-factor experimental program. Several equations were used to achieve appropriate equations fitting properly to predict the MR behavior of fluids. Of these, the 2FI method was found to be the best model for most of the parameters of the rheological models. Several equations were derived from statistical analyses, to model the flow behavior of CM NPs-based MR fluids under a range of conditions. The shear rate-associated alterations of the suspensions were improved by increased magnetic field strength. In contrast, a sharp increase in the MR properties was observed when the concentration of CM NPs was increased. Similarly, a similar trend to that of the CM NPs concentration was observed in the case of the viscosity of silicone oil, showing the optimal capacity of carrier fluids in enhancing the MR properties of CM-based smart fluids. The Bingham fluid model was found to be suitable for modeling the plastic viscosity and yield stress, which increased with a magnetite concentration, magnetic field strength, and viscosity of silicone oil as the carrier fluid. The power-law equation was effective in modeling the flow property of various nonNewtonian fluids, particularly the rheology of MR fluids, in which the consistency index and power law index increased significantly
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