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Stability of magnetizable colloidal suspensions by addition of oleic acid and silica nanoparticles
Colloids and Surfaces A: Physicochem. Eng. Aspects 264 (2005) 75–81
Stability of magnetizable colloidal suspensions by addition of oleic acid and silica nanoparticles M.T. L´opez-L´opez ∗ , J. de Vicente, F. Gonz´alez-Caballero, J.D.G. Dur´an Departamento de F´ısica Aplicada, Facultad de Ciencias, Universidad de Granada, Av. Fuentenueva s/n, 18071 Granada, Spain Received 4 October 2004; received in revised form 9 May 2005; accepted 11 May 2005 Available online 20 July 2005
Abstract An experimental investigation is described on the stability of suspensions of micron-sized iron particles by (1) using oleic acid–mineral oil mixtures as a continuous phase and (2) adding silica nanoparticles to the continuous phase (silicone oil). The time evolution of the optical absorbance of the suspensions as a function of oleic acid (OA) concentration, silica nanoparticles concentration and magnetic field strength and direction has been analyzed. Adsorption isotherm demonstrated that OA adsorbs onto iron particles. However, only after the addition of very large amounts of OA (i.e. much more than the amount needed to form a monolayer coating) it is possible to design stable suspensions. The application of an external magnetic field provokes a faster sedimentation due to the formation of field-induced aggregates. When silica nanoparticles are used as stabilizer, a threshold value has been found in the silica concentration. Above this value iron suspensions are stable. The application of a magnetic field decreases this threshold concentration value due to the combined effect of the induced iron chains aggregation and the silica gel network. © 2005 Elsevier B.V. All rights reserved. Keywords: Magnetic suspensions; Magnetic field; Adsorption isotherm; Stability; Silica gel
1. Introduction Magnetic control of the flow of liquids is a challenging field for both basic research and applications. Two kinds of materials are especially interesting for this purpose, suspensions of ferromagnetic nanoparticles (ferrofluids) and micron-sized particles (metals or ferrites), commonly called magnetorheological fluids (MRF) [1]. In the absence of a magnetic field, MRF typically behave as nearly ideal Newtonian liquids. However, the application of a magnetic field induces magnetic dipole and multipole moments on each particle which interact leading to the formation of columnar structures parallel to the field [2]. The stability of magnetic colloids constitutes one of the problems of largest interest from the point of view of the technological applications of these systems. Due to the high density of the magnetic particles, MRF usually suffer from ∗
Corresponding author. Tel.: +34 958249099; fax: +34 958243214. E-mail address: [email protected] (M.T. L´opez-L´opez).
0927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2005.05.026
excessive gravitational settling and, as a result, it can interfere with the magnetorheological response because of the non-uniform distribution of particles [3,4]. Small magnetic particles, high loadings, and high viscosities of the base oil are usually recommended for reducing the sedimentation rate, although the requirement of multidomain particles and low enough viscosity in the absence of field make the problem difficult to be solved. Approaches to improve the stability include: (1) adding thixotropic agents (e.g. carbon fibers, silica nanoparticles) [5–7]; (2) adding surfactants (e.g. oleic, stearic acid) [5,8,9]; (3) adding magnetic nanoparticles [10,11]; (4) the use of viscoplastic media as continuous phase [12]; (5) water-in-oil emulsions as continuous phase [13]. In this paper, the stability properties of micron-sized ironbased MRF in mineral and silicone oil are studied. The additions of oleic acid (OA) and silica nanoparticles are investigated and their anti-settling efficiency reported. Oleic acid is a classical surfactant used in the preparation of ferrofluids, and silica nanoparticles form gel networks that prevent particles from settling in classical MRF.
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Also, the adsorption isotherm of oleic acid on iron particles has been studied. The stability of these MRF has been investigated performing optical absorbance versus time experiments, for different OA and silica concentrations, both in the presence and absence of low applied magnetic fields (up to 2 mT). In the case of iron–silica suspensions, the effects of both gel network formation and adhesion between iron and silica nanoparticles on the sedimentation velocity have been studied as well.
Table 1 Viscosity of oleic acid–mineral oil homogeneous mixtures Continuous medium
Viscosity (mPa s)
Mineral oil (MO) Oleic acid (OA) 1% OA + 99% MO 7.5% OA + 92.5% MO 20% OA + 80% MO 30% OA + 70% MO 50% OA + 50% MO
39.58 ± 0.16 43.8 ± 0.4 40.0 ± 0.4 38.9 ± 0.3 37.62 ± 0.21 36.0 ± 0.2 39.1 ± 0.3
Concentrations in vol.%.
2. Experimental
tinuous media were measured using a Bohlin CS 10 rheometer in cup-and-bob configuration.
2.1. Materials 2.2. Preparation of suspensions Iron powder, originally obtained from carbonyl iron precursors, was a HQ quality powder from BASF (Germany) of micrometer size, was used without ulterior treatment. Scanning electron microscope (SEM) pictures (Fig. 1) were taken to analyze the size and shape of the particles, showing that they are spherical and polydisperse, with average diameter 930 ± 330 nm. The specific surface area of the iron powder, determined by means of N2 adsorption using the BET multipoint method (Quantasorb Jr., Quantachrome, USA), was 0.98 m2 /g. Silicone oil (polydimethylsiloxane) (Fluka, Germany) with viscosity 35.1 ± 0.3 mPa s and density 954 kg m−3 was used as a continuous medium in the iron-silica suspensions whereas mineral oil (MO) with viscosity 39.58 ± 0.16 mPa s and density 854 kg m−3 (Fluka, Germany) was used as a continuous medium in the iron–OA suspensions. Fine spherical particles of silica (∼7 nm diameter) with commercial name Aerosil-300 were from Deggusa-H¨uls (Germany). Oleic acid (purity > 90%) with viscosity 43.8 ± 0.4 mPa s and density 887 kg m−3 was from Sigma–Aldrich. The viscosities of con-
The preparation of iron-silica suspensions is relatively simple. It involves the following steps: (1) iron, silica, and silicone oil (in this order) were mixed in a polyethylene container; (2) the mixture was stirred first by hand, and then put in an ultrasonic bath; (3) step (2) was repeated several times and finally the sample was immersed in a Branson homogenizer (model 450) to ensure the required final homogeneity. Also several silica-silicone oil mixtures were prepared and their viscosities were measured. No relevant change of the viscosity of these mixtures with silica concentration was observed. The formulation of iron–OA suspensions is a bit more complicated: (1) different oleic acid–mineral oil homogeneous mixtures were prepared. Their viscosities were measured and some of the obtained data are shown in Table 1; (2) iron was mixed with the appropriate oleic acid–mineral oil mixture in a polyethylene container; (3) this mixture was stirred first by hand and then put in an ultrasonic bath; (4) step (3) was repeated several times and then the sample was immersed in a Branson homogenizer (model 450) to ensure the required homogeneity; (5) finally the sample was kept at 25 ◦ C and shaken at 50 rpm during 24 h to allow the complete adsorption of oleic acid on the iron particles. 2.3. Adsorption isotherm of oleic acid on iron particles
Fig. 1. Scanning electron microscope (SEM) picture of iron particles. Bar length 2 m.
In order to investigate the oleic acid adsorption capacity on the iron particles, the optical absorbance was measured versus oleic acid concentration for different oleic acid–mineral oil mixtures and the data fitted to Beer law by the method of least squares. For this purpose, a Dinko Instruments spectrophotometer (model UV–vis 8500 double-beam, Spain) was used at a wavelength λ = 244 nm. Then we took 10 vol.% iron suspensions, prepared as described in paragraph 2.2, and induced the phase separation with the help of a magnet. Finally, the optical absorbance of the supernatants was measured and we calculated their respective OA concentrations by using the previous fitting to the Beer law. The adsorbed amount follows from subtracting the OA amount in the supernatant from the initial total amount. The adsorption density, Γ , was calculated as the ratio between the adsorbed amount and the total solid
M.T. L´opez-L´opez et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 264 (2005) 75–81
Fig. 2. Schematic drawing of the device used in absorbance measurements in presence of magnetic field. Coil diameter D = 39.5 cm; distance between coils h = 21.5 cm.
surface area in the suspension, taking into account the BET specific surface area of the iron powder. The corresponding errors in the equilibrium OA concentration and in adsorption density were calculated considering the standard deviation in the fitting parameters in the above-mentioned calibration of absorbance versus OA concentration. 2.4. Stability The stability of both iron–silica and iron–OA suspensions was investigated by means of optical absorbance versus time experiments, using a Milton Roy spectrophotometer (model Spectronic 601, USA) at a wavelength λ = 590 nm. In all studied suspensions the iron content was fixed to 1.25 g/L. Square cuvettes with 1 cm light path were used; the center of the light beam strikes the cuvette 1.5 cm above its bottom. A pair of coils (Phywe, Germany) was used to generate the magnetic field. In the experiments under vertical field, the coils were placed so that their axes coincided with that of the sample cuvette (see the scheme shown in Fig. 2), and in the experiments under horizontal field the coils were placed in perpendicular position to the cuvette axis. The magnetic flux density, B, inside the sample varied between 0 and 2.0 mT and was measured with a Hall-effect teslameter (Phywe, Germany). Variations of the magnetic field inside the sample were always below 10%.
3. Results and discussion 3.1. Iron suspensions in the presence of oleic acid 3.1.1. Adsorption isotherm of oleic acid on iron particles and stability of the suspensions Fig. 3 shows the adsorption density of oleic acid on iron particles, as a function of the OA equilibrium concentration at 25 ◦ C in the range 0–13 mM. The adsorption curve has the typical S-shape where the initial slope is very large until an equilibrium concentration of approximately 1 mM is reached. Considering, as proposed by Rosenweig
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Fig. 3. Adsorption isotherm of oleic acid on iron particles.
[14], that an adsorption density of 2 × 1018 mol/m2 (equivalent in Fig. 3 to Γ = 3.32 mol/m2 , and OA equilibrium concentration ≈ 1 mM) corresponds to a 100% coverage by oleic acid molecules, the initial sharp adsorption rise in Fig. 3 can be ascribed to the deposition of a first monolayer of fatty acid molecules. To calculate the above-mentioned monolayer coverage, Rosensweig [14] assumed that one adsorbed OA molecule occupies a surface area of 0.5 nm2 (i.e. 0.5 nm2 /mol). This value is similar to that reported by McMahon [15] (0.65 nm2 /mol) for the adsorption of oleic imidazoline (a corrosion inhibitor) on wet iron in oil media. Therefore, the surface coverage proposed by Rosensweig [14], and assumed by us in the present work, seems to be a reasonable estimation. For oleic acid concentration larger than 1 mM, the adsorption becomes intense by a precipitation mechanism and the number of statistical OA monolayers covering the surface increases rapidly. However, saturation of the adsorption is not reached in the range of concentrations studied. All our inferences on the stability of iron suspensions were based on the characteristics of the evolution with time of the optical absorbance (A) of the suspensions under the different conditions studied. Fig. 4 shows the normalized optical absorbance, An (=A/A0 ), versus time for six different OA–MO mixtures in the absence of an external magnetic field. Because of the large density and diameter of the particles, there is an overall trend of An to decrease with time, due to the disappearance of the solids from the illuminated region as settling proceeds. Absorbance versus time experiments for suspensions containing OA in the range from 0.01 to 0.5 vol.% (up to 15 mM) (high enough to cover the particles surface, see Fig. 3), show that there is no significant effect of the oleic acid in this range of concentrations, on the stability properties of the suspensions (see inset in Fig. 4). Thus, although the affinity of OA molecules by the iron surface is quite evident from the results shown in Fig. 3, it seems that steric repulsion is not relevant for the stability of the suspensions in the lower range of OA concentrations, since no improvement on the stability properties of iron suspensions was reached in this range. However, higher OA concentrations (≥1 vol.%, i.e. ≥30 mM) involve an improvement of the stability properties
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Fig. 4. Normalized absorbance An (=A/A0 ) vs. time in the absence of applied magnetic field. All suspensions contain 1.25 g/L Fe. The continuous media are the oleic acid–mineral oil mixtures indicated in the figure.
because the absorbance decreases at a slower rate. Larger OA concentrations than 50 vol.% do not provoke further noticeable increase in the stability. The improvement of the stability properties as OA concentration is raised is simultaneous to the increasing coverage of iron by the OA molecules. Thus, the mechanism of particles repulsion and thus stabilization of the system must have its origin in the progressive structuring of the adsorbed (in fact precipitated) OA, which causes a steric hindrance for approaching particles and hence minimizes particles sedimentation. By separate experiments, we performed surface tension measurements of OA–mineral oil dispersions in a wide range of OA concentrations and found that no micellization of oleic acid takes place. Thus, any possible effect of the presence of micelles on the stability of the suspensions must be excluded. Finally, if the sedimentation velocity (v) of individual iron spheres is calculated by means of the Stokes’s law, considering the different viscosities and densities of the liquid carriers (see Table 1 and Section 2.1), the result is practically the same in all cases: v ranges between 3.1 × 10−4 mm/s (in pure mineral oil) and 3.5 × 10−4 mm/s (in silicone oil). Therefore, the different slopes in the absorbance versus time curves in Fig. 4 can only be attributed to the presence of iron aggregates at low OA concentrations. 3.1.2. Effect of applied magnetic field Due to the magnetic character of the particles, a significant effect of a uniformly applied magnetic field on the sedimentation rate of the particles is expected. The first experiment was performed allowing the particles to settle in the presence of a constant magnetic flux density, B = 2 mT (parallel to the gravitational field). Fig. 5 shows the absorbance versus time
curves measured in this experiment for different OA content. Two important differences are observed with respect to the same experiment but in the absence of applied magnetic field (Fig. 4). First, no effect of OA concentration on the stability was obtained for oleic acid concentration below 7.5 vol.%. This is due to the effect of the magnetostatic interactions, which are the dominant in suspensions with OA concentrations below this value. Second, it is observed in Fig. 5 that even for the highest OA concentration in the suspensions (50 vol.%), the absorbance decreases at a faster rate than for the same suspensions, but in the absence of magnetic field. Hence, the application of a magnetic field involves a worsening on the stability properties. The field magnetizes the particles and the subsequent attraction between them brings about the formation of aggregates that settle quickly. de Vicente et al. [4] found a similar behavior for cobalt ferrite suspensions in water in the presence of applied magnetic field.
Fig. 5. Same as in Fig. 4 but in the presence of a magnetic flux density, B = 2 mT.
M.T. L´opez-L´opez et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 264 (2005) 75–81
Fig. 6. Initial slope (of the absorbance–time curves) vs. magnetic flux density for 1.25 g/L iron suspensions. The continuous media are the oleic acid–mineral oil mixtures indicated in the figure.
The effect of magnetic field strength in vertical direction was also studied. It is known, that for magnetorheological fluids in the presence of low external magnetic fields, the magnetic field interaction and hence the induced aggregation is proportional to the magnetic flux density squared [16]. Experiments similar to those shown in Fig. 5 were performed but for magnetic flux densities ranging from 0 to 2 mT. The effect of three OA concentrations (0, 5 and 20 vol.%) was studied. For each curve, the initial slope was determined and represented as a function of the magnetic flux density. Fig. 6 shows these results. As can be seen there, the curve for the suspension without OA is a parabolic-shaped curve; therefore, it could be concluded, according to Rankin et al. [16], that in this suspension the magnetostatic interaction is the only important one. On the contrary, the quadratic dependence is lost as soon as there is OA in solution. In these cases, colloidal interactions between OA molecules and particles could be comparable or even larger than magnetostatic forces. In order to check the behavior of the suspensions under horizontal magnetic fields we performed absorbance versus time experiments for various OA concentrations and magnetic flux density, B = 2.00 ± 0.05 mT fixed in horizontal direction. As an example, Fig. 7 shows the results for 20 vol.% OA suspension in the absence of magnetic field, and in the presence of a magnetic field perpendicular or parallel to gravity. It is observed that there is a significant effect of the magnetic field strength on the stability properties of the suspension, but there is no effect of the direction of application of the magnetic field (similar induced particle aggregation). These results are in agreement with those obtained earlier by de Vicente et al. [4].
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Fig. 7. Normalized absorbance vs. time for 1.25 g/L iron suspension in 20 vol.% OA–80 vol.% MO mixture; (): in the absence of magnetic field; (䊉): in the presence of horizontal magnetic field (B = 2 mT); ( ): in the presence of vertical magnetic field (B = 2 mT).
from 0 to 2.92 g/L). Fig. 8 shows the results. As observed, suspensions with silica concentration below 0.5 g/L are rather unstable. This behavior is a consequence of iron–silica adhesion that causes a growing of the particles diameter and so a faster sedimentation rate than bare iron particles. The existence of iron–silica adhesion in similar systems was demonstrated earlier by de Vicente et al. [6]. Above 0.5 g/L silica concentration, the formation of a silica network that imparts a gel-like structure to the suspensions could be the dominant phenomenon [5]. For 0.58, 0.88 and 1.46 g/L silica contents it can be observed that the absorbance increases with time at the beginning of the experiment and after some time it falls down. This is due to the fact that the silica gel network induces the formation of big flocculi, which provoke a loss of light intensity in the direction of the detector as a result of light scattering. The silica gel network is not strong enough to hold up the iron particles and the structure breaks and falls down and so the absorbance. Larger silica particle concentrations involve larger gel network formation times (there is a displacement of the peaks to the right in Fig. 8) and stronger
3.2. Iron suspensions in the presence of silica nanoparticles 3.2.1. Stability of the suspensions Optical absorbance versus time experiments were performed for suspensions of iron (constant concentration, 1.25 g/L) and silica nanoparticles (concentration ranging
Fig. 8. Normalized absorbance vs. time in the absence of applied magnetic field. All suspensions contain 1.25 g/L iron and the silica concentrations shown in the figure.
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Fig. 9. Absorbance vs. time for both 1.25 g/L iron-0.88 g/L silica suspension and 0.88 g/L silica suspension.
networks (absorbance decreases at a smaller rate as silica concentration increases). Finally, at 2.92 g/L silica concentration the gel network is stiff enough to hold up the whole concentration of iron particles (we performed these last measurements during a period of 72 h and no change in the absorbance was obtained). Finally, to demonstrate that the absorption in the iron–silica suspensions due to silica nanoparticles is negligible in the above experiments, we performed absorbance versus time experiments for pure silica suspensions. As an example, Fig. 9 shows the result for 1.25 g/L iron + 0.88 g/L silica suspension and 0.88 g/L silica suspension. As can be seen, both curves show a similar trend, but the absorbance of the iron suspension is approximately two orders of magnitude higher. 3.2.2. Effect of applied magnetic field Experiments similar to those described in Section 3.2.1 were carried out in the presence of a constant magnetic flux density, B = 2 mT (parallel to the gravitational field). Fig. 10 shows the obtained results. Similar qualitative trends to those in the absence of applied magnetic field were found. Nevertheless, the threshold silica concentration, above which the silica gel network is stiff enough to hold up the iron particles,
Fig. 10. Same as in Fig. 8 but in the presence of a magnetic flux density, B = 2 mT.
Fig. 11. Slope (of the absorbance–time curves) vs. silica concentration; (): in the absence of applied magnetic field; ( ): in the presence of vertical applied magnetic field (B = 2.00 mT).
is now 1.17 g/L (again, the measurements were performed during 10 h and no change in the absorbance was found). This value is considerably smaller than that in the absence of magnetic field. The magnetic induced attraction among iron particles, and the subsequent formation of chain structures of iron parallel to the field, is the mechanism that makes stiffer the iron–silica structures, thus being necessary a lower silica concentration to hold up the iron particles. In order to better investigate the effect of the magnetic field on the iron–silica structures, we calculated the slope of the fall in the curves of Figs. 8 and 10 (absorbance versus time in the absence and in the presence of magnetic field). As can be observed in Fig. 11, the slope is higher in the presence of magnetic field than in its absence, for silica concentrations lower than 0.6 g/L. This behavior is consistent with the fact that magnetostatic interactions are the main important ones; the presence of a magnetic field induces aggregation and as a consequence the absorbance decreases at a faster rate. However, for concentrations of silica higher than 0.8 g/L, the reverse effect takes place, and the slope is higher in the absence of magnetic field. This means that magnetostatic interactions do not play the main role, but other colloidal interactions become as important as the magnetostatic ones. So, as we discussed above, for high silica nanoparticles concentration the application of a magnetic field involves a hardening in the iron–silica structure and hence a slower sedimentation rate. In order to investigate the behavior of the suspensions under horizontally applied magnetic field we performed absorbance versus time experiments for various silica concentrations and fixed magnetic flux density, B = 2.00 ± 0.05 mT in horizontal direction. The result is that there is not any important difference between the curves obtained either in the presence of a vertical applied field or a horizontal applied field. As an example, Fig. 12 shows the absorbance versus time curves for suspensions of 0.58 g/L silica concentration in the absence of magnetic field, and in the presence of both horizontal and vertical magnetic fields. The curves obtained in the presence of either horizontal or vertical magnetic field are nearly coincident and the net effect
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to the continuous phase. The mechanism is the formation of a silica gel network that prevents iron settling for high enough concentration of these nanoparticles. There is a threshold of silica concentration above which the system is fully stable. (4) The application of an external magnetic field to iron–silica suspensions provokes the decrease of the threshold of silica needed to stabilize them. This is due to the combined effect of the induced iron chains aggregation and the silica gel network.
Acknowledgements Fig. 12. Normalized absorbance vs. time for 1.25 g/L iron–0.58 g/L silica suspension; (): in the absence of magnetic field; (): in the presence of horizontal magnetic field (B = 2 mT); ( ): in the presence of vertical magnetic field (B = 2 mT).
Financial support by Ministerio de Ciencia y Tecnolog´ıa (Spain) and FEDER (EU) under Project No. MAT200400866 is gratefully acknowledged.
of the magnetic field is again destabilizing the suspension for silica concentration below 0.6 g/L.
References
4. Conclusions (1) It is possible to stabilize non-aqueous suspensions of micron-sized iron particles by using oleic acid–mineral oil mixtures as a continuous phase. The stabilizing effect of oleic acid comes from the progressive coverage of the iron particles. The affinity of OA molecules by the iron surface has been demonstrated through adsorption isotherm. It is necessary the presence of OA in moderate amounts to observe a significant effect on the stability of the suspensions. In the systems studied in this work, OA concentrations higher than 1 vol.% (≥30 mM) provoke a noticeable improvement on the stability properties of the suspensions. OA concentrations larger than 50 vol.% do not involve further increase in the stability. (2) The effect of a magnetic field applied either horizontally or vertically to iron–oleic acid suspensions is a worsening on their stability properties. It is the consequence of the induced iron aggregation in the presence of the field. Besides magnetostatic interactions, colloidal interactions are not negligible in the presence of magnetic field for high enough oleic acid concentration (in our systems, ≥5 vol.%). (3) It is possible to stabilize non-aqueous suspensions of micron-sized iron particles by adding silica nanoparticles
[1] P.P. Phul´e, J.M. Ginder, MRS Bull. 23 (1998) 19. [2] J.M. Ginder, MRS Bull. 23 (1998) 26. [3] S.W. Charles, in: S. Odenbach (Ed.), Ferrofluids, Springer, Berlin, 2002 (Chapter 1). [4] J. de Vicente, A.V. Delgado, J.D.G. Dur´an, F. Gonz´alez-Caballero, Langmuir 16 (2000) 7954. [5] G. Bossis, O. Volkova, S. Lacis, A. Meunier, in: S. Odenbach (Ed.), Ferrofluids, Springer, Berlin, 2002 (Chapter 11). [6] J. de Vicente, M.T. L´opez-L´opez, F. Gonz´alez-Caballero, J.D.G. Dur´an, J. Rheol. 47 (2003) 1093. [7] O. Volkova, G. Bossis, M. Guyot, V. Bashtovoi, A. Reks, J. Rheol. 44 (2000) 91. [8] A. Dang, L. Ooi, J. Fales, P. Strove, Ind. Eng. Chem. Res. 39 (2000) 2269. [9] G.A. van Ewijk, J. Vroege, A.P. Philipse, J. Magn. Magn. Mater. 201 (1999) 31. [10] Z.Y. Chen, X. Tang, G.C. Zhang, Y. Jin, W. Ni, Y.R. Zhu, in: M. Nakano, K. Koyama (Eds.), Proceedings of the Sixth International Conference on Electro-Rheological Fluids, Magneto-Rheological Suspensions and their Applications, Yonezawa, July 22–25, 1997, World Scientific Publishing, Singapore, 1998, p. 486. [11] B.D. Chin, J.H. Park, M.H. Kwon, O.O. Park, Rheol. Acta 40 (2001) 211. [12] P.J. Rankin, A.T. Horvath, D.J. Klingenberg, Rheol. Acta 38 (1999) 471. [13] J.H. Park, B.D. Chin, O.O. Park, J. Colloid Interface Sci. 240 (2001) 349. [14] R.E. Rosensweig, Ferrohydrodynamic, Cambridge University Press, Cambridge, 1985, p. 48. [15] A.J. McMahon, Colloids Surf. 59 (1991) 187–208. [16] P.J. Rankin, J.M. Ginder, D.J. Klingenberg, Curr. Opin. Colloid Interface Sci. 3 (1998) 373.
Stability of magnetizable colloidal suspensions by addition of oleic acid and silica nanoparticles M.T. L´opez-L´opez ∗ , J. de Vicente, F. Gonz´alez-Caballero, J.D.G. Dur´an Departamento de F´ısica Aplicada, Facultad de Ciencias, Universidad de Granada, Av. Fuentenueva s/n, 18071 Granada, Spain Received 4 October 2004; received in revised form 9 May 2005; accepted 11 May 2005 Available online 20 July 2005
Abstract An experimental investigation is described on the stability of suspensions of micron-sized iron particles by (1) using oleic acid–mineral oil mixtures as a continuous phase and (2) adding silica nanoparticles to the continuous phase (silicone oil). The time evolution of the optical absorbance of the suspensions as a function of oleic acid (OA) concentration, silica nanoparticles concentration and magnetic field strength and direction has been analyzed. Adsorption isotherm demonstrated that OA adsorbs onto iron particles. However, only after the addition of very large amounts of OA (i.e. much more than the amount needed to form a monolayer coating) it is possible to design stable suspensions. The application of an external magnetic field provokes a faster sedimentation due to the formation of field-induced aggregates. When silica nanoparticles are used as stabilizer, a threshold value has been found in the silica concentration. Above this value iron suspensions are stable. The application of a magnetic field decreases this threshold concentration value due to the combined effect of the induced iron chains aggregation and the silica gel network. © 2005 Elsevier B.V. All rights reserved. Keywords: Magnetic suspensions; Magnetic field; Adsorption isotherm; Stability; Silica gel
1. Introduction Magnetic control of the flow of liquids is a challenging field for both basic research and applications. Two kinds of materials are especially interesting for this purpose, suspensions of ferromagnetic nanoparticles (ferrofluids) and micron-sized particles (metals or ferrites), commonly called magnetorheological fluids (MRF) [1]. In the absence of a magnetic field, MRF typically behave as nearly ideal Newtonian liquids. However, the application of a magnetic field induces magnetic dipole and multipole moments on each particle which interact leading to the formation of columnar structures parallel to the field [2]. The stability of magnetic colloids constitutes one of the problems of largest interest from the point of view of the technological applications of these systems. Due to the high density of the magnetic particles, MRF usually suffer from ∗
Corresponding author. Tel.: +34 958249099; fax: +34 958243214. E-mail address: [email protected] (M.T. L´opez-L´opez).
0927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2005.05.026
excessive gravitational settling and, as a result, it can interfere with the magnetorheological response because of the non-uniform distribution of particles [3,4]. Small magnetic particles, high loadings, and high viscosities of the base oil are usually recommended for reducing the sedimentation rate, although the requirement of multidomain particles and low enough viscosity in the absence of field make the problem difficult to be solved. Approaches to improve the stability include: (1) adding thixotropic agents (e.g. carbon fibers, silica nanoparticles) [5–7]; (2) adding surfactants (e.g. oleic, stearic acid) [5,8,9]; (3) adding magnetic nanoparticles [10,11]; (4) the use of viscoplastic media as continuous phase [12]; (5) water-in-oil emulsions as continuous phase [13]. In this paper, the stability properties of micron-sized ironbased MRF in mineral and silicone oil are studied. The additions of oleic acid (OA) and silica nanoparticles are investigated and their anti-settling efficiency reported. Oleic acid is a classical surfactant used in the preparation of ferrofluids, and silica nanoparticles form gel networks that prevent particles from settling in classical MRF.
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Also, the adsorption isotherm of oleic acid on iron particles has been studied. The stability of these MRF has been investigated performing optical absorbance versus time experiments, for different OA and silica concentrations, both in the presence and absence of low applied magnetic fields (up to 2 mT). In the case of iron–silica suspensions, the effects of both gel network formation and adhesion between iron and silica nanoparticles on the sedimentation velocity have been studied as well.
Table 1 Viscosity of oleic acid–mineral oil homogeneous mixtures Continuous medium
Viscosity (mPa s)
Mineral oil (MO) Oleic acid (OA) 1% OA + 99% MO 7.5% OA + 92.5% MO 20% OA + 80% MO 30% OA + 70% MO 50% OA + 50% MO
39.58 ± 0.16 43.8 ± 0.4 40.0 ± 0.4 38.9 ± 0.3 37.62 ± 0.21 36.0 ± 0.2 39.1 ± 0.3
Concentrations in vol.%.
2. Experimental
tinuous media were measured using a Bohlin CS 10 rheometer in cup-and-bob configuration.
2.1. Materials 2.2. Preparation of suspensions Iron powder, originally obtained from carbonyl iron precursors, was a HQ quality powder from BASF (Germany) of micrometer size, was used without ulterior treatment. Scanning electron microscope (SEM) pictures (Fig. 1) were taken to analyze the size and shape of the particles, showing that they are spherical and polydisperse, with average diameter 930 ± 330 nm. The specific surface area of the iron powder, determined by means of N2 adsorption using the BET multipoint method (Quantasorb Jr., Quantachrome, USA), was 0.98 m2 /g. Silicone oil (polydimethylsiloxane) (Fluka, Germany) with viscosity 35.1 ± 0.3 mPa s and density 954 kg m−3 was used as a continuous medium in the iron-silica suspensions whereas mineral oil (MO) with viscosity 39.58 ± 0.16 mPa s and density 854 kg m−3 (Fluka, Germany) was used as a continuous medium in the iron–OA suspensions. Fine spherical particles of silica (∼7 nm diameter) with commercial name Aerosil-300 were from Deggusa-H¨uls (Germany). Oleic acid (purity > 90%) with viscosity 43.8 ± 0.4 mPa s and density 887 kg m−3 was from Sigma–Aldrich. The viscosities of con-
The preparation of iron-silica suspensions is relatively simple. It involves the following steps: (1) iron, silica, and silicone oil (in this order) were mixed in a polyethylene container; (2) the mixture was stirred first by hand, and then put in an ultrasonic bath; (3) step (2) was repeated several times and finally the sample was immersed in a Branson homogenizer (model 450) to ensure the required final homogeneity. Also several silica-silicone oil mixtures were prepared and their viscosities were measured. No relevant change of the viscosity of these mixtures with silica concentration was observed. The formulation of iron–OA suspensions is a bit more complicated: (1) different oleic acid–mineral oil homogeneous mixtures were prepared. Their viscosities were measured and some of the obtained data are shown in Table 1; (2) iron was mixed with the appropriate oleic acid–mineral oil mixture in a polyethylene container; (3) this mixture was stirred first by hand and then put in an ultrasonic bath; (4) step (3) was repeated several times and then the sample was immersed in a Branson homogenizer (model 450) to ensure the required homogeneity; (5) finally the sample was kept at 25 ◦ C and shaken at 50 rpm during 24 h to allow the complete adsorption of oleic acid on the iron particles. 2.3. Adsorption isotherm of oleic acid on iron particles
Fig. 1. Scanning electron microscope (SEM) picture of iron particles. Bar length 2 m.
In order to investigate the oleic acid adsorption capacity on the iron particles, the optical absorbance was measured versus oleic acid concentration for different oleic acid–mineral oil mixtures and the data fitted to Beer law by the method of least squares. For this purpose, a Dinko Instruments spectrophotometer (model UV–vis 8500 double-beam, Spain) was used at a wavelength λ = 244 nm. Then we took 10 vol.% iron suspensions, prepared as described in paragraph 2.2, and induced the phase separation with the help of a magnet. Finally, the optical absorbance of the supernatants was measured and we calculated their respective OA concentrations by using the previous fitting to the Beer law. The adsorbed amount follows from subtracting the OA amount in the supernatant from the initial total amount. The adsorption density, Γ , was calculated as the ratio between the adsorbed amount and the total solid
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Fig. 2. Schematic drawing of the device used in absorbance measurements in presence of magnetic field. Coil diameter D = 39.5 cm; distance between coils h = 21.5 cm.
surface area in the suspension, taking into account the BET specific surface area of the iron powder. The corresponding errors in the equilibrium OA concentration and in adsorption density were calculated considering the standard deviation in the fitting parameters in the above-mentioned calibration of absorbance versus OA concentration. 2.4. Stability The stability of both iron–silica and iron–OA suspensions was investigated by means of optical absorbance versus time experiments, using a Milton Roy spectrophotometer (model Spectronic 601, USA) at a wavelength λ = 590 nm. In all studied suspensions the iron content was fixed to 1.25 g/L. Square cuvettes with 1 cm light path were used; the center of the light beam strikes the cuvette 1.5 cm above its bottom. A pair of coils (Phywe, Germany) was used to generate the magnetic field. In the experiments under vertical field, the coils were placed so that their axes coincided with that of the sample cuvette (see the scheme shown in Fig. 2), and in the experiments under horizontal field the coils were placed in perpendicular position to the cuvette axis. The magnetic flux density, B, inside the sample varied between 0 and 2.0 mT and was measured with a Hall-effect teslameter (Phywe, Germany). Variations of the magnetic field inside the sample were always below 10%.
3. Results and discussion 3.1. Iron suspensions in the presence of oleic acid 3.1.1. Adsorption isotherm of oleic acid on iron particles and stability of the suspensions Fig. 3 shows the adsorption density of oleic acid on iron particles, as a function of the OA equilibrium concentration at 25 ◦ C in the range 0–13 mM. The adsorption curve has the typical S-shape where the initial slope is very large until an equilibrium concentration of approximately 1 mM is reached. Considering, as proposed by Rosenweig
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Fig. 3. Adsorption isotherm of oleic acid on iron particles.
[14], that an adsorption density of 2 × 1018 mol/m2 (equivalent in Fig. 3 to Γ = 3.32 mol/m2 , and OA equilibrium concentration ≈ 1 mM) corresponds to a 100% coverage by oleic acid molecules, the initial sharp adsorption rise in Fig. 3 can be ascribed to the deposition of a first monolayer of fatty acid molecules. To calculate the above-mentioned monolayer coverage, Rosensweig [14] assumed that one adsorbed OA molecule occupies a surface area of 0.5 nm2 (i.e. 0.5 nm2 /mol). This value is similar to that reported by McMahon [15] (0.65 nm2 /mol) for the adsorption of oleic imidazoline (a corrosion inhibitor) on wet iron in oil media. Therefore, the surface coverage proposed by Rosensweig [14], and assumed by us in the present work, seems to be a reasonable estimation. For oleic acid concentration larger than 1 mM, the adsorption becomes intense by a precipitation mechanism and the number of statistical OA monolayers covering the surface increases rapidly. However, saturation of the adsorption is not reached in the range of concentrations studied. All our inferences on the stability of iron suspensions were based on the characteristics of the evolution with time of the optical absorbance (A) of the suspensions under the different conditions studied. Fig. 4 shows the normalized optical absorbance, An (=A/A0 ), versus time for six different OA–MO mixtures in the absence of an external magnetic field. Because of the large density and diameter of the particles, there is an overall trend of An to decrease with time, due to the disappearance of the solids from the illuminated region as settling proceeds. Absorbance versus time experiments for suspensions containing OA in the range from 0.01 to 0.5 vol.% (up to 15 mM) (high enough to cover the particles surface, see Fig. 3), show that there is no significant effect of the oleic acid in this range of concentrations, on the stability properties of the suspensions (see inset in Fig. 4). Thus, although the affinity of OA molecules by the iron surface is quite evident from the results shown in Fig. 3, it seems that steric repulsion is not relevant for the stability of the suspensions in the lower range of OA concentrations, since no improvement on the stability properties of iron suspensions was reached in this range. However, higher OA concentrations (≥1 vol.%, i.e. ≥30 mM) involve an improvement of the stability properties
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Fig. 4. Normalized absorbance An (=A/A0 ) vs. time in the absence of applied magnetic field. All suspensions contain 1.25 g/L Fe. The continuous media are the oleic acid–mineral oil mixtures indicated in the figure.
because the absorbance decreases at a slower rate. Larger OA concentrations than 50 vol.% do not provoke further noticeable increase in the stability. The improvement of the stability properties as OA concentration is raised is simultaneous to the increasing coverage of iron by the OA molecules. Thus, the mechanism of particles repulsion and thus stabilization of the system must have its origin in the progressive structuring of the adsorbed (in fact precipitated) OA, which causes a steric hindrance for approaching particles and hence minimizes particles sedimentation. By separate experiments, we performed surface tension measurements of OA–mineral oil dispersions in a wide range of OA concentrations and found that no micellization of oleic acid takes place. Thus, any possible effect of the presence of micelles on the stability of the suspensions must be excluded. Finally, if the sedimentation velocity (v) of individual iron spheres is calculated by means of the Stokes’s law, considering the different viscosities and densities of the liquid carriers (see Table 1 and Section 2.1), the result is practically the same in all cases: v ranges between 3.1 × 10−4 mm/s (in pure mineral oil) and 3.5 × 10−4 mm/s (in silicone oil). Therefore, the different slopes in the absorbance versus time curves in Fig. 4 can only be attributed to the presence of iron aggregates at low OA concentrations. 3.1.2. Effect of applied magnetic field Due to the magnetic character of the particles, a significant effect of a uniformly applied magnetic field on the sedimentation rate of the particles is expected. The first experiment was performed allowing the particles to settle in the presence of a constant magnetic flux density, B = 2 mT (parallel to the gravitational field). Fig. 5 shows the absorbance versus time
curves measured in this experiment for different OA content. Two important differences are observed with respect to the same experiment but in the absence of applied magnetic field (Fig. 4). First, no effect of OA concentration on the stability was obtained for oleic acid concentration below 7.5 vol.%. This is due to the effect of the magnetostatic interactions, which are the dominant in suspensions with OA concentrations below this value. Second, it is observed in Fig. 5 that even for the highest OA concentration in the suspensions (50 vol.%), the absorbance decreases at a faster rate than for the same suspensions, but in the absence of magnetic field. Hence, the application of a magnetic field involves a worsening on the stability properties. The field magnetizes the particles and the subsequent attraction between them brings about the formation of aggregates that settle quickly. de Vicente et al. [4] found a similar behavior for cobalt ferrite suspensions in water in the presence of applied magnetic field.
Fig. 5. Same as in Fig. 4 but in the presence of a magnetic flux density, B = 2 mT.
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Fig. 6. Initial slope (of the absorbance–time curves) vs. magnetic flux density for 1.25 g/L iron suspensions. The continuous media are the oleic acid–mineral oil mixtures indicated in the figure.
The effect of magnetic field strength in vertical direction was also studied. It is known, that for magnetorheological fluids in the presence of low external magnetic fields, the magnetic field interaction and hence the induced aggregation is proportional to the magnetic flux density squared [16]. Experiments similar to those shown in Fig. 5 were performed but for magnetic flux densities ranging from 0 to 2 mT. The effect of three OA concentrations (0, 5 and 20 vol.%) was studied. For each curve, the initial slope was determined and represented as a function of the magnetic flux density. Fig. 6 shows these results. As can be seen there, the curve for the suspension without OA is a parabolic-shaped curve; therefore, it could be concluded, according to Rankin et al. [16], that in this suspension the magnetostatic interaction is the only important one. On the contrary, the quadratic dependence is lost as soon as there is OA in solution. In these cases, colloidal interactions between OA molecules and particles could be comparable or even larger than magnetostatic forces. In order to check the behavior of the suspensions under horizontal magnetic fields we performed absorbance versus time experiments for various OA concentrations and magnetic flux density, B = 2.00 ± 0.05 mT fixed in horizontal direction. As an example, Fig. 7 shows the results for 20 vol.% OA suspension in the absence of magnetic field, and in the presence of a magnetic field perpendicular or parallel to gravity. It is observed that there is a significant effect of the magnetic field strength on the stability properties of the suspension, but there is no effect of the direction of application of the magnetic field (similar induced particle aggregation). These results are in agreement with those obtained earlier by de Vicente et al. [4].
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Fig. 7. Normalized absorbance vs. time for 1.25 g/L iron suspension in 20 vol.% OA–80 vol.% MO mixture; (): in the absence of magnetic field; (䊉): in the presence of horizontal magnetic field (B = 2 mT); ( ): in the presence of vertical magnetic field (B = 2 mT).
from 0 to 2.92 g/L). Fig. 8 shows the results. As observed, suspensions with silica concentration below 0.5 g/L are rather unstable. This behavior is a consequence of iron–silica adhesion that causes a growing of the particles diameter and so a faster sedimentation rate than bare iron particles. The existence of iron–silica adhesion in similar systems was demonstrated earlier by de Vicente et al. [6]. Above 0.5 g/L silica concentration, the formation of a silica network that imparts a gel-like structure to the suspensions could be the dominant phenomenon [5]. For 0.58, 0.88 and 1.46 g/L silica contents it can be observed that the absorbance increases with time at the beginning of the experiment and after some time it falls down. This is due to the fact that the silica gel network induces the formation of big flocculi, which provoke a loss of light intensity in the direction of the detector as a result of light scattering. The silica gel network is not strong enough to hold up the iron particles and the structure breaks and falls down and so the absorbance. Larger silica particle concentrations involve larger gel network formation times (there is a displacement of the peaks to the right in Fig. 8) and stronger
3.2. Iron suspensions in the presence of silica nanoparticles 3.2.1. Stability of the suspensions Optical absorbance versus time experiments were performed for suspensions of iron (constant concentration, 1.25 g/L) and silica nanoparticles (concentration ranging
Fig. 8. Normalized absorbance vs. time in the absence of applied magnetic field. All suspensions contain 1.25 g/L iron and the silica concentrations shown in the figure.
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Fig. 9. Absorbance vs. time for both 1.25 g/L iron-0.88 g/L silica suspension and 0.88 g/L silica suspension.
networks (absorbance decreases at a smaller rate as silica concentration increases). Finally, at 2.92 g/L silica concentration the gel network is stiff enough to hold up the whole concentration of iron particles (we performed these last measurements during a period of 72 h and no change in the absorbance was obtained). Finally, to demonstrate that the absorption in the iron–silica suspensions due to silica nanoparticles is negligible in the above experiments, we performed absorbance versus time experiments for pure silica suspensions. As an example, Fig. 9 shows the result for 1.25 g/L iron + 0.88 g/L silica suspension and 0.88 g/L silica suspension. As can be seen, both curves show a similar trend, but the absorbance of the iron suspension is approximately two orders of magnitude higher. 3.2.2. Effect of applied magnetic field Experiments similar to those described in Section 3.2.1 were carried out in the presence of a constant magnetic flux density, B = 2 mT (parallel to the gravitational field). Fig. 10 shows the obtained results. Similar qualitative trends to those in the absence of applied magnetic field were found. Nevertheless, the threshold silica concentration, above which the silica gel network is stiff enough to hold up the iron particles,
Fig. 10. Same as in Fig. 8 but in the presence of a magnetic flux density, B = 2 mT.
Fig. 11. Slope (of the absorbance–time curves) vs. silica concentration; (): in the absence of applied magnetic field; ( ): in the presence of vertical applied magnetic field (B = 2.00 mT).
is now 1.17 g/L (again, the measurements were performed during 10 h and no change in the absorbance was found). This value is considerably smaller than that in the absence of magnetic field. The magnetic induced attraction among iron particles, and the subsequent formation of chain structures of iron parallel to the field, is the mechanism that makes stiffer the iron–silica structures, thus being necessary a lower silica concentration to hold up the iron particles. In order to better investigate the effect of the magnetic field on the iron–silica structures, we calculated the slope of the fall in the curves of Figs. 8 and 10 (absorbance versus time in the absence and in the presence of magnetic field). As can be observed in Fig. 11, the slope is higher in the presence of magnetic field than in its absence, for silica concentrations lower than 0.6 g/L. This behavior is consistent with the fact that magnetostatic interactions are the main important ones; the presence of a magnetic field induces aggregation and as a consequence the absorbance decreases at a faster rate. However, for concentrations of silica higher than 0.8 g/L, the reverse effect takes place, and the slope is higher in the absence of magnetic field. This means that magnetostatic interactions do not play the main role, but other colloidal interactions become as important as the magnetostatic ones. So, as we discussed above, for high silica nanoparticles concentration the application of a magnetic field involves a hardening in the iron–silica structure and hence a slower sedimentation rate. In order to investigate the behavior of the suspensions under horizontally applied magnetic field we performed absorbance versus time experiments for various silica concentrations and fixed magnetic flux density, B = 2.00 ± 0.05 mT in horizontal direction. The result is that there is not any important difference between the curves obtained either in the presence of a vertical applied field or a horizontal applied field. As an example, Fig. 12 shows the absorbance versus time curves for suspensions of 0.58 g/L silica concentration in the absence of magnetic field, and in the presence of both horizontal and vertical magnetic fields. The curves obtained in the presence of either horizontal or vertical magnetic field are nearly coincident and the net effect
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to the continuous phase. The mechanism is the formation of a silica gel network that prevents iron settling for high enough concentration of these nanoparticles. There is a threshold of silica concentration above which the system is fully stable. (4) The application of an external magnetic field to iron–silica suspensions provokes the decrease of the threshold of silica needed to stabilize them. This is due to the combined effect of the induced iron chains aggregation and the silica gel network.
Acknowledgements Fig. 12. Normalized absorbance vs. time for 1.25 g/L iron–0.58 g/L silica suspension; (): in the absence of magnetic field; (): in the presence of horizontal magnetic field (B = 2 mT); ( ): in the presence of vertical magnetic field (B = 2 mT).
Financial support by Ministerio de Ciencia y Tecnolog´ıa (Spain) and FEDER (EU) under Project No. MAT200400866 is gratefully acknowledged.
of the magnetic field is again destabilizing the suspension for silica concentration below 0.6 g/L.
References
4. Conclusions (1) It is possible to stabilize non-aqueous suspensions of micron-sized iron particles by using oleic acid–mineral oil mixtures as a continuous phase. The stabilizing effect of oleic acid comes from the progressive coverage of the iron particles. The affinity of OA molecules by the iron surface has been demonstrated through adsorption isotherm. It is necessary the presence of OA in moderate amounts to observe a significant effect on the stability of the suspensions. In the systems studied in this work, OA concentrations higher than 1 vol.% (≥30 mM) provoke a noticeable improvement on the stability properties of the suspensions. OA concentrations larger than 50 vol.% do not involve further increase in the stability. (2) The effect of a magnetic field applied either horizontally or vertically to iron–oleic acid suspensions is a worsening on their stability properties. It is the consequence of the induced iron aggregation in the presence of the field. Besides magnetostatic interactions, colloidal interactions are not negligible in the presence of magnetic field for high enough oleic acid concentration (in our systems, ≥5 vol.%). (3) It is possible to stabilize non-aqueous suspensions of micron-sized iron particles by adding silica nanoparticles
[1] P.P. Phul´e, J.M. Ginder, MRS Bull. 23 (1998) 19. [2] J.M. Ginder, MRS Bull. 23 (1998) 26. [3] S.W. Charles, in: S. Odenbach (Ed.), Ferrofluids, Springer, Berlin, 2002 (Chapter 1). [4] J. de Vicente, A.V. Delgado, J.D.G. Dur´an, F. Gonz´alez-Caballero, Langmuir 16 (2000) 7954. [5] G. Bossis, O. Volkova, S. Lacis, A. Meunier, in: S. Odenbach (Ed.), Ferrofluids, Springer, Berlin, 2002 (Chapter 11). [6] J. de Vicente, M.T. L´opez-L´opez, F. Gonz´alez-Caballero, J.D.G. Dur´an, J. Rheol. 47 (2003) 1093. [7] O. Volkova, G. Bossis, M. Guyot, V. Bashtovoi, A. Reks, J. Rheol. 44 (2000) 91. [8] A. Dang, L. Ooi, J. Fales, P. Strove, Ind. Eng. Chem. Res. 39 (2000) 2269. [9] G.A. van Ewijk, J. Vroege, A.P. Philipse, J. Magn. Magn. Mater. 201 (1999) 31. [10] Z.Y. Chen, X. Tang, G.C. Zhang, Y. Jin, W. Ni, Y.R. Zhu, in: M. Nakano, K. Koyama (Eds.), Proceedings of the Sixth International Conference on Electro-Rheological Fluids, Magneto-Rheological Suspensions and their Applications, Yonezawa, July 22–25, 1997, World Scientific Publishing, Singapore, 1998, p. 486. [11] B.D. Chin, J.H. Park, M.H. Kwon, O.O. Park, Rheol. Acta 40 (2001) 211. [12] P.J. Rankin, A.T. Horvath, D.J. Klingenberg, Rheol. Acta 38 (1999) 471. [13] J.H. Park, B.D. Chin, O.O. Park, J. Colloid Interface Sci. 240 (2001) 349. [14] R.E. Rosensweig, Ferrohydrodynamic, Cambridge University Press, Cambridge, 1985, p. 48. [15] A.J. McMahon, Colloids Surf. 59 (1991) 187–208. [16] P.J. Rankin, J.M. Ginder, D.J. Klingenberg, Curr. Opin. Colloid Interface Sci. 3 (1998) 373.