Investigation on relation of viscosity and inner structure of suspension under a magnetic field

Transcription

1 Investigation on relation of viscosity and inner structure of suspension under a magnetic field Yan Mi*,Peng Xiaoling,Shi Weitang State Key Laboratory of Silicon Materials,Zhejiang University,Hangzhou (310027) mse_yanmi@zju.edu.cn Abstract For preparing functionally graded materials (FGMs), an external magnetic field is applied on the suspension composed of ferromagnetic (FM) Ni and nonmagnetic (NM) ZrO 2 particles to control the motion of Ni particles. The variation in viscosity of suspensions under a series of static magnetic fields was investigated. The results show that the viscosity varies with the field strength and Ni content because of the influence of magnetic field on Ni particles. The increase of viscosity is beyond the range of validity of Shliomis s theory, which can be mainly attributed to the interaction between Ni particles and the resulting formation of chain-like Ni clusters. Keywords:Viscosity;Magnetic particle;chain-like cluster;magnetic field;fgm 1. Introduction The preparation of FGMs has attracted much interest because the continuous change of components in FGMs eliminates the macroscopic interface, and hence continuously changed mechanical, physical and chemical properties are achieved [1-5]. Recently, we proposed a new approach to prepare ZrO 2 -Ni FGM with a continuously changing composition via slip casting in a magnetic field based on their distinct difference in magnetic susceptibility [6]. The applied field is effective to control the movement of magnetic particles of the suspension for preparing FGMs. In general, viscosity describes the internal resistance to flow [7], which can also be considered as an important parameter to describe flowing property of the suspension composed of FM and NM particles. The viscosity of magnetic fluids always increases with increasing the applied field [8, 9]. However, the increase in viscosity of the suspension will hinder the movement of FM particles, which may be harmful for the preparation of FGMs. So, it is vitally essential to investigate the field dependence of viscosity of the suspension composed of FM and NM particles. In this work, Ni and ZrO 2 were respectively selected as FM and NM particles to prepare suspension for the fabrication of ZrO 2 -Ni FGMs, and viscosity of the suspension was investigated in a series of applied fields ranged up to 80 ka/m. 2. Experiments Ni with an average diameter of 1.2 µm and ZrO 2 with an average diameter of 0.75 µm were used as FM and NM particles, respectively. Polyvinylpyrrolidone (PVP) was selected as the deflocculant. ZrO 2 and Ni particles were ball milled with PVP for 6 h in distilled water, respectively. The content of PVP was fixed at 0.7 wt % in ZrO 2 suspension, and 1.2 wt % in Ni suspension, respectively. The two suspensions were then mixed together through mechanical stirring for 4 h to disperse the particles homogeneously. The solid content of the mixed suspension was 20 vol %

2 Fig. 1 Schematic illustration for the viscosity measurement under magnetic field generated by a Helmholtz coil system. The viscosities of the mixed suspensions were measured using a NDJ-1 rotational viscometer in a series of applied fields ranged up to 80 ka/m. A schematic illustration for the viscosity measurement is shown in Fig. 1.The magnetic field was generated by a Helmholtz coil system consisting of a pair of identical coils, each with an inner and outer diameter of 0.10 m and 0.23 m, respectively. The distance between the two coils is 0.11 m. This Helmholtz coil system was used to generate nearly uniform magnetic fields in a cylindrical region extending between the centers of the two coils. The rotor of the rotational viscometer was parallel to the applied field. The mixed suspension was poured into a rubber mold with a gypsum base for solidification. The molds for casting were Φ10 5 mm cylinders. Different magnetic fields were applied on the castings and removed until the suspensions lost liquidity. The castings with molds were then dried at 60 for 48 h in a chest. After being dried, the green compacts were put in a VSF-120/150 vacuum sintering furnace and heated from room temperature to 300 at 5 min -1, then to 500 at 1 min -1. The green compacts were kept at 500 for 2 h to burn out the PVP, followed by sintering at 1350 for 5 h in vacuum to obtain the final samples. The sintered samples were cut and polished for further characterizations. The longitudinal (parallel to the field) and transverse microstructures were observed under a MeF-3 optical microscopy (Reichert, Austria). The composition distribution was identified by using an X-ray energy dispersion spectroscopy (EDS, GENENIS 4000, USA) - 2 -

3 3. Results Fig. 2 Viscosity variation of the suspension with Ni content at different magnetic fields. Fig. 3 Viscosity variation of the suspension composed of 2 vol. % Ni in solid phase as a function of magnetic field. Fig. 2 shows the Ni content dependence of viscosity for the suspensions at different magnetic fields. The solid content of each suspension was fixed at 20 vol. %, and Ni content in the solid phase was 0, 1 %, 2 %, and 5 vol. %, respectively. The rotational speed was 12 rpm. It can be seen that the viscosity remains unchanged at zero field, but increases with increasing Ni content at other fields. Note that the viscosity keeps a constant as the field changes for the suspension without FM Ni particles. It indicates that the viscosity is very sensitive to the FM particles volume fraction in the suspensions as an external field is applied. Fig. 3 shows the field dependence of viscosity for the suspension composed of 2 vol. % Ni with different rotational speeds. As the field increases, the viscosity increases drastically, indicating an increase of the internal resistance to flow in the suspension occurs. In addition, it can also be seen that the viscosity decreases with the rotational speed at a certain field. This reflects the shear thinning property of the pseudoplastic fluid under different rotational speeds at a certain field

4 Fig. 4 Microstructures of solidified suspension under 8 ka/m field for 20 min on (a) transverse section and (b) longitudinal section. Fig. 5 Microstructures of solidified suspension under 80 ka/m field for 20 min on (a) transverse section and (b) longitudinal section. Figs. 4 and 5 show typical optical micrographs of the solidified suspensions fabricated at 8 ka/m and 80 ka/m magnetic fields, respectively. White phases dispersing in the black matrix were identified to be Ni particles by means of EDS. Ni particles distribute homogenously on the transverse section, as shown in Figs. 4a and 5a; whereas chain-like Ni clusters can be discerned along the longitudinal direction, as shown in Figs. 4b and 5b. It indicates that chain-like magnetic clusters have been formed along the field direction, and becomes more obvious in higher field. 4. Discussion From Figs. 2 and 3, the viscosity variation of suspensions under external fields can be attributed to the magnetized Ni particles. Magnetic moments of Ni particles tend to align along the field direction, but deflect from it when the particles rotate following the flow of suspension. The resulting angle between magnetic moments and field gives rise to a magnetic torque, which hinders the free rotation of Ni particles and therefore increases the viscosity of suspension. Considering rotation motion of the particle in ordinary magnetic fluid, Shliomis [10] derived an equation for rotational viscosity under the magnetic field perpendicular to vorticity. According to Shliomis theory, the maximum value of pure relative rotational viscosity in our suspension would be of the order of 0.6 %. Comparing the results shown in Figs. 2 and 3 with the theoretical approach for rotational viscosity, one can find that there is a big discrepancy and this phenomenon observed in our experiment can no longer be described by the simple hindrance of rotation of single magnetic particles. It is instructive to consider the mechanisms responsible for the increase of viscosity under the magnetic field. In the absence of magnetic field, particle states in suspension are controlled by the following energies: thermal energy E T, gravitational energy, Van der Waals interaction energy and - 4 -

5 Brownian motion energy. With the addition of deflocculant PVP, gravitational energy is conquered, so Ni and ZrO 2 particles disperse homogenously in the suspension [6]. As an external magnetic field is applied on the suspension, Ni particles are magnetized along the field direction, and extra energy is induced, which consists of dipole-field energy E d-f and dipole-dipole energy E d-d among Ni particles. E T, E d-f and E d-d can be expressed as [11]: E ET = kt (1) µ MHV d f = 0 (2) ( MV i i)( MjVj) µ 0 Ed d = d 3 3 i d j di r d j r 4π r ( )( ) where k is Boltzmann s constant, T the absolute temperature in degrees Kelvin, µ 0 the permeability of free space, H the magnetic intensity, M the magnetization intensity, r the distance between the magnetic particles, d the unit vector of the direction of the magnetic dipoles, and r the unit vector pointing from dipole i to dipole j. And the volume for a spherical particle of diameter d is expressed as: V = π d 3 /6 (4) Take the typical values of parameters: k = J K -1, T = 298 K, µ 0 = 4π 10-7 H m, M = A m -1 into Eqs. (1), (2) and (3), and for the suspension in our experiment r = d = 1.2 µm, we can get E T = J, E d-f = J and E d-d = J. The results show that interaction energy is tremendous comparing with the thermal energy, so the thermal energy can be neglected in the presence of magnetic field. Similarly, Van der Waals interaction energy and Brownian motion energy can also be ignored because of the large size of particles and therefore a much smaller magnitude compared to the magnetic energy. So the states of magnetic particles in suspension under a magnetic field are mainly controlled by the magnetic energies. Once two particles contact with each other, they will never be separated again. Such suspension is unstable and the FM particles tend to form agglomeration under the applied magnetic field. Even when the external field is removed, the suspension can not switch back to the initial state. However, when an external magnetic field is applied on the suspension, the total energies of nonmagnetic ZrO 2 particles do not change, and hence the particle states are not affected by the applied field. So the viscosity keeps unchanged as the field is applied for the suspension with only ZrO 2 particles, as shown in Fig. 2. The viscosity variation of suspension composed of Ni and ZrO 2 particles under external fields are therefore attributed to Ni particles. With the increasing of Ni content in suspension, the agglomerations of Ni particles increase, and therefore viscosity of the suspension increases. It can be found from Figs. 4 and 5 that chain-like magnetic clusters are formed along the direction of the applied magnetic field. The chain-like cluster exhibits more resistance to rotation, since the viscous force is proportional to the local velocity difference between the particle structure and the surrounding suspension. So the increase of viscosity of this suspension under the magnetic field, as shown in Figs. 2 and 3, can be mainly attributed to the magnetic clusters formed in suspension. Ni particle chain in suspension at 80 ka/m is more obvious than that at 8 ka/m field, so viscosity of suspension at higher field is much larger than that at lower field. In addition, the shear thinning property of the pseudoplastic fluid is partially attributed to deformation or destruction of the magnetic chains at high rotational speed. 5. Conclusions (1) The viscosity of suspension composed of ZrO 2 and Ni particles increases as a function of magnetic field and content of Ni, which can be attributed to the influence of the external magnetic field (3)

6 on Ni particles. (2) The deviation of experimental viscosity from Shliomis theory can be mainly attributed to the interaction between the magnetic particles and resulting formation of chain-like clusters. Acknowledgment This work was supported by the National Natural Science Foundation of China (No ), the Research Fund for the Doctoral Program of Higher Education ( ), Program for New Century Excellent Talents in University and Program for Innovative Research Team in University (IRT0651). References [1] Turner A P F. Science, 2000, 290 (17): [2] Yin J S, Wang Z L. Nanostruct. Mater., 1999, 11: [3] Chapman J N. J. Magn. Magn. Mater., 1997, 175 (1-2): [4] Fujita T, Mamiya M. J. Magn. Magn. Mater., 1987, 65 (2-3): [5] Warren A P, Hobby P C, Coverdale G N, et al. J. Magn. Magn. Mater., 1996, 155 (1-3): [6] Xiaoling Peng, Mi Yan, Weitang Shi, Scripta Mater., 56 (2007) [7] Pouilloux L, Kaminski E, Labrosse S. Geophys. J. Int. 2007, 170 (2): [8] Odenbach S, Störk H. J. Magn. Magn. Mater., 1998, 183 (1-2): [9] Embs J, Műller H W, Wagner C, Knorr K, et al. Phys. Rev. E, 1999, 61 (3): [10] Shliomis M. Phys. JEPT, 1972, 34: [11] Rosenzweig R E. Ferrohydrodynamics. Cambridge, UK: Cambridge University Press, Author Brief Introduction: Mi Yan, 1965, professor, research field focus on magnetic materials and nano-materials