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Shape response of functional fluid drops in alternating magnetic fields
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 289 (2005) 321–324 www.elsevier.com/locate/jmmm
Shape response of functional fluid drops in alternating magnetic fields S. Sudoa,, A. Nakagawaa, K. Shimadab, H. Nishiyamac a
Department of Mechanical Engineering, Iwaki Meisei University, Iino 5-5-1, Chuohdai, Iwaki 970-8551, Japan b Faculty of System Science and Technology, Akita Prefectural University, Honjo 015-0055, Japan c Institute of Fluid Science, Tohoku University, Sendai 980-8577, Japan Available online 30 November 2004
Abstract The shape responses of droplets of some functional fluids in alternating magnetic fields are investigated experimentally. The three kinds of magnetizable fluid drops, that is, magnetic fluid, magneto-rheological fluid, and magnetic compound fluid are investigated. The experimental results of the three kinds of functional fluid drops are compared to each other. It is found that the shape responses reflect cluster structure of particles in liquids. r 2004 Elsevier B.V. All rights reserved. Keywords: Droplet; Magnetic fluid; Magneto-rheological fluid; Magnetic compound fluid
1. Introduction Since various functional fluids have been developed, extensive investigations on the functional fluids have been conducted by a number of researchers. Recently, a magnetic compound fluid (MCF) was developed by Shimada et al. [1] as a new smart fluid, and an experimental application of microscopic polishing using MCF was proposed. In the previous papers, the authors also studied the droplet shape deformations of magnetic fluid, magneto-rheological (MR) suspension, and MCF in a homogeneous magnetic field [2,3]. However, research data on the dynamic behavior of MR suspension drop, MCF drop are insufficient, and there still remains a wide unexplored domain. In this paper, the dynamic shape responses of some functional fluid droplets in the alternating magnetic fields are studied experimentally. Furthermore, the Corresponding author. Tel.: +81 246 29 7185; +81 246 29 0577. E-mail address: [email protected] (S. Sudo).
fax:
particle cluster structures in functional fluids undergoing lower frequency periodic oscillations of magnetic field are discussed based on the experimental data.
2. Experimental apparatus and procedures Fig. 1 shows a schematic diagram of the experimental apparatus to study the shape responses of functional fluid droplets. The experimental apparatus consists of the droplet-container system, magnetic field generation system, and high-speed video camera system. The rectangular container is 235 mm long and 99 mm 59 mm wide. The container is partly filled with non-magnetic immiscible liquid (glycerin). A functional fluid droplet is injected into the glycerin by a medical syringe. An electromagnet is used to apply the alternating magnetic field to the droplets of magnetic functional fluids. The alternating magnetic field is generated by applying AC voltage to the electromagnet. The AC signal is supplied from the frequency synthesizer. The high-speed video camera system with a motion grabber
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.11.091
ARTICLE IN PRESS S. Sudo et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 321–324
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where H0 is the amplitude of oscillating magnetic field, o the excitation angular frequency ðo ¼ 2pf 0 Þ; and t the time. Fig. 2 shows the shape response of magnetic fluid drop with the initial diameter d ¼ 2:21 mm at the frequency f 0 ¼ 5 Hz: In Fig. 2, ll is the length of the major axis, and ls is the length of the minor axis of the droplet ellipse. The shape deformation of the droplet shows the transient response. The droplet is extended through the elongation and contraction shape oscillation. The time variation in droplet shape is given by 1
LðtÞ ¼ 1 þ Lm ð1 eat Þ þ b sin 2ot;
(2)
where L(t) is the dimension length of the major axis (ll / d), Lm the dimensionless mean length after the fixed time progress, and a and b the constants. This phenomenon is similar to the growth characteristics of a single bubble undergoing arbitrarily large-amplitude periodic radial oscillations in liquid by the process of rectified diffusion. The chain formation of magnetic particles in carrier liquid grows with time for the steady state.
Fig. 1. Schematic diagram of experimental apparatus.
3.2. Response of MCF droplet The shape response of MCF droplet in the alternating magnetic field is shown in Fig. 3. The shape response of MCF droplet shows the same tendency as the response Fig. 2. Transient response of a magnetic fluid droplet.
and a personal computer is used to analyze the shape response of functional fluid droplets. Measured sample functional fluids are kerosene-based ferricolloid HC-50 made by Taiho Industries Co. Ltd., MR suspension MRF-132LD made by Lord Corporation, and MCF developed by Shimada and others. The MCF is compounded of kerosene-based ferricolloid HC-50 and carbonyl iron powder with 1.2 mm diameter.
3. Experimental results and discussion
Fig. 3. Transient response of a MCF droplet.
3.1. Magnetic fluid droplet The behavior of a droplet of magnetic fluid in a homogeneous magnetic field has been studied by a number of researchers [2–5]. In general, the magnetic fluid droplet in the homogeneous magnetic field is stretched along the magnetic field. The drop shape can be obtained by a minimization of energy. The relation between the droplet shape and the magnetic field strength has already been obtained by Sudo et al. [2]. In this paragraph, the shape responses of a magnetic fluid droplet in the alternating magnetic field are studied. The alternating magnetic field is given by H ¼ H 0 sin ot;
(1)
Fig. 4. Shape response of a MR fluid droplet.
ARTICLE IN PRESS S. Sudo et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 321–324
323
Fig. 5. Schematic models of cluster formation in three magnetic functional fluids.
of magnetic fluid droplet. However, the effect of the oscillating magnetic field is smaller than the response of the magnetic fluid droplet. The constant b in Eq. (2) becomes smaller compared with that of magnetic fluid droplets. This fact shows that the particle cluster structure of MCF is difficult to collapse compared with the magnetic fluid. The MCF is composed of nanometer size magnetite and micrometer size iron particles in a solvent. Therefore, the carbonyl iron particles take the multidomain structure, and the iron particles show residual magnetization. 3.3. Response of MR fluid droplet The shape response of MR fluid droplet in the alternating magnetic field at f 0 ¼ 5 Hz is shown in Fig. 4. In the shape response of the droplet, the effect of the oscillating magnetic field hardly appears in Fig. 4. The MR suspension forms rigid aggregates in the presence of the field. The particle cluster structure of MR suspension is also difficult to collapse, because the size of magnetic particles is micrometer order. The MR suspension droplet does not show shape oscillation in the alternating magnetic field. The effect of the residual magnetization of magnetic particles has strongly appeared in the shape response of MR suspension droplet in the alternating magnetic field. This phenomenon in the MR suspension response is unique. 3.4. Differences in droplet response As was stated previously, the shape responses of magnetic fluid, MCF and MR fluid droplets in the alternating magnetic field are different. The time required for the formation of magnetic particle clusters in each fluid is different. The details of the formation process of needle-like structures stretched in the direction of the magnetic field were reported for some magnetic fluids [6]. Fig. 5(a) corresponds to the state when the clusters were formed by the magnetic field. Fig. 5(b) shows the schematic model of cluster formation in
MCF. Magnetite and iron particles form rodlike clusters under the applied magnetic field. Such clusters are difficult to collapse due to the residual magnetization of iron particles. The cluster formation of iron particles in MR suspension is shown in Fig. 5(c). MR fluids are suspensions of micro-sized, magnetizable particles in synthetic oil. The MR suspension forms most rigid aggregates in the magnetic field compared with the other two magnetic functional fluids. These phenomena in the shape responses of functional fluid drops are closely related to two magnetic relaxation mechanisms. In larger size particles, the particle rotation mechanism is characterized by a Brownian rotation diffusion time having hydrodynamic origin [7]. In smaller size particles, the particle’s magnetic moment obeys the Neel rotational relaxation mechanism. These magnetic relaxation processes decide the droplet response.
4. Conclusions (1) When the droplets of functional fluids are subjected to an oscillatory magnetic field, shape responses of the droplets show the transient response. After the fixed time progress, the droplets of magnetic fluid and MCF show steady oscillatory responses. (2) The droplet of MR suspension does not show shape oscillation at frequencies over 1 Hz. MR droplet shows fixed elongation after the fixed time progress.
References [1] K. Shimada, Y. Akagami, S. Kamiyama, T. Fujita, T. Miyazaki, A. Shibayama, J. Intell. Mater. Syst. Struct. 13 (2002) 405. [2] S. Sudo, H. Hashimoto, A. Ikeda, JSME Int. J. 32 (1989) 47. [3] S. Sudo, A. Nakagawa, K. Shimada, H. Nishiyama, Magnetohydrodynamics 39 (2003) 359.
ARTICLE IN PRESS 324
S. Sudo et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 321–324
[4] V.I. Arkipenko, Yu.D. Barkov, V.G. Bashtovoi, Magnetohydrodynamics 14 (1979) 131. [5] V.G. Bashtovoi, A.R. Reks, Ye.M. Tayts, HEAT TRANSFER-Soviet Research 17 (1985) 79.
[6] B. Jeyadevan, I. Nakatani, J. Magn. Magn. Mater. 201 (1999) 62. [7] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985.
Journal of Magnetism and Magnetic Materials 289 (2005) 321–324 www.elsevier.com/locate/jmmm
Shape response of functional fluid drops in alternating magnetic fields S. Sudoa,, A. Nakagawaa, K. Shimadab, H. Nishiyamac a
Department of Mechanical Engineering, Iwaki Meisei University, Iino 5-5-1, Chuohdai, Iwaki 970-8551, Japan b Faculty of System Science and Technology, Akita Prefectural University, Honjo 015-0055, Japan c Institute of Fluid Science, Tohoku University, Sendai 980-8577, Japan Available online 30 November 2004
Abstract The shape responses of droplets of some functional fluids in alternating magnetic fields are investigated experimentally. The three kinds of magnetizable fluid drops, that is, magnetic fluid, magneto-rheological fluid, and magnetic compound fluid are investigated. The experimental results of the three kinds of functional fluid drops are compared to each other. It is found that the shape responses reflect cluster structure of particles in liquids. r 2004 Elsevier B.V. All rights reserved. Keywords: Droplet; Magnetic fluid; Magneto-rheological fluid; Magnetic compound fluid
1. Introduction Since various functional fluids have been developed, extensive investigations on the functional fluids have been conducted by a number of researchers. Recently, a magnetic compound fluid (MCF) was developed by Shimada et al. [1] as a new smart fluid, and an experimental application of microscopic polishing using MCF was proposed. In the previous papers, the authors also studied the droplet shape deformations of magnetic fluid, magneto-rheological (MR) suspension, and MCF in a homogeneous magnetic field [2,3]. However, research data on the dynamic behavior of MR suspension drop, MCF drop are insufficient, and there still remains a wide unexplored domain. In this paper, the dynamic shape responses of some functional fluid droplets in the alternating magnetic fields are studied experimentally. Furthermore, the Corresponding author. Tel.: +81 246 29 7185; +81 246 29 0577. E-mail address: [email protected] (S. Sudo).
fax:
particle cluster structures in functional fluids undergoing lower frequency periodic oscillations of magnetic field are discussed based on the experimental data.
2. Experimental apparatus and procedures Fig. 1 shows a schematic diagram of the experimental apparatus to study the shape responses of functional fluid droplets. The experimental apparatus consists of the droplet-container system, magnetic field generation system, and high-speed video camera system. The rectangular container is 235 mm long and 99 mm 59 mm wide. The container is partly filled with non-magnetic immiscible liquid (glycerin). A functional fluid droplet is injected into the glycerin by a medical syringe. An electromagnet is used to apply the alternating magnetic field to the droplets of magnetic functional fluids. The alternating magnetic field is generated by applying AC voltage to the electromagnet. The AC signal is supplied from the frequency synthesizer. The high-speed video camera system with a motion grabber
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.11.091
ARTICLE IN PRESS S. Sudo et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 321–324
322
where H0 is the amplitude of oscillating magnetic field, o the excitation angular frequency ðo ¼ 2pf 0 Þ; and t the time. Fig. 2 shows the shape response of magnetic fluid drop with the initial diameter d ¼ 2:21 mm at the frequency f 0 ¼ 5 Hz: In Fig. 2, ll is the length of the major axis, and ls is the length of the minor axis of the droplet ellipse. The shape deformation of the droplet shows the transient response. The droplet is extended through the elongation and contraction shape oscillation. The time variation in droplet shape is given by 1
LðtÞ ¼ 1 þ Lm ð1 eat Þ þ b sin 2ot;
(2)
where L(t) is the dimension length of the major axis (ll / d), Lm the dimensionless mean length after the fixed time progress, and a and b the constants. This phenomenon is similar to the growth characteristics of a single bubble undergoing arbitrarily large-amplitude periodic radial oscillations in liquid by the process of rectified diffusion. The chain formation of magnetic particles in carrier liquid grows with time for the steady state.
Fig. 1. Schematic diagram of experimental apparatus.
3.2. Response of MCF droplet The shape response of MCF droplet in the alternating magnetic field is shown in Fig. 3. The shape response of MCF droplet shows the same tendency as the response Fig. 2. Transient response of a magnetic fluid droplet.
and a personal computer is used to analyze the shape response of functional fluid droplets. Measured sample functional fluids are kerosene-based ferricolloid HC-50 made by Taiho Industries Co. Ltd., MR suspension MRF-132LD made by Lord Corporation, and MCF developed by Shimada and others. The MCF is compounded of kerosene-based ferricolloid HC-50 and carbonyl iron powder with 1.2 mm diameter.
3. Experimental results and discussion
Fig. 3. Transient response of a MCF droplet.
3.1. Magnetic fluid droplet The behavior of a droplet of magnetic fluid in a homogeneous magnetic field has been studied by a number of researchers [2–5]. In general, the magnetic fluid droplet in the homogeneous magnetic field is stretched along the magnetic field. The drop shape can be obtained by a minimization of energy. The relation between the droplet shape and the magnetic field strength has already been obtained by Sudo et al. [2]. In this paragraph, the shape responses of a magnetic fluid droplet in the alternating magnetic field are studied. The alternating magnetic field is given by H ¼ H 0 sin ot;
(1)
Fig. 4. Shape response of a MR fluid droplet.
ARTICLE IN PRESS S. Sudo et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 321–324
323
Fig. 5. Schematic models of cluster formation in three magnetic functional fluids.
of magnetic fluid droplet. However, the effect of the oscillating magnetic field is smaller than the response of the magnetic fluid droplet. The constant b in Eq. (2) becomes smaller compared with that of magnetic fluid droplets. This fact shows that the particle cluster structure of MCF is difficult to collapse compared with the magnetic fluid. The MCF is composed of nanometer size magnetite and micrometer size iron particles in a solvent. Therefore, the carbonyl iron particles take the multidomain structure, and the iron particles show residual magnetization. 3.3. Response of MR fluid droplet The shape response of MR fluid droplet in the alternating magnetic field at f 0 ¼ 5 Hz is shown in Fig. 4. In the shape response of the droplet, the effect of the oscillating magnetic field hardly appears in Fig. 4. The MR suspension forms rigid aggregates in the presence of the field. The particle cluster structure of MR suspension is also difficult to collapse, because the size of magnetic particles is micrometer order. The MR suspension droplet does not show shape oscillation in the alternating magnetic field. The effect of the residual magnetization of magnetic particles has strongly appeared in the shape response of MR suspension droplet in the alternating magnetic field. This phenomenon in the MR suspension response is unique. 3.4. Differences in droplet response As was stated previously, the shape responses of magnetic fluid, MCF and MR fluid droplets in the alternating magnetic field are different. The time required for the formation of magnetic particle clusters in each fluid is different. The details of the formation process of needle-like structures stretched in the direction of the magnetic field were reported for some magnetic fluids [6]. Fig. 5(a) corresponds to the state when the clusters were formed by the magnetic field. Fig. 5(b) shows the schematic model of cluster formation in
MCF. Magnetite and iron particles form rodlike clusters under the applied magnetic field. Such clusters are difficult to collapse due to the residual magnetization of iron particles. The cluster formation of iron particles in MR suspension is shown in Fig. 5(c). MR fluids are suspensions of micro-sized, magnetizable particles in synthetic oil. The MR suspension forms most rigid aggregates in the magnetic field compared with the other two magnetic functional fluids. These phenomena in the shape responses of functional fluid drops are closely related to two magnetic relaxation mechanisms. In larger size particles, the particle rotation mechanism is characterized by a Brownian rotation diffusion time having hydrodynamic origin [7]. In smaller size particles, the particle’s magnetic moment obeys the Neel rotational relaxation mechanism. These magnetic relaxation processes decide the droplet response.
4. Conclusions (1) When the droplets of functional fluids are subjected to an oscillatory magnetic field, shape responses of the droplets show the transient response. After the fixed time progress, the droplets of magnetic fluid and MCF show steady oscillatory responses. (2) The droplet of MR suspension does not show shape oscillation at frequencies over 1 Hz. MR droplet shows fixed elongation after the fixed time progress.
References [1] K. Shimada, Y. Akagami, S. Kamiyama, T. Fujita, T. Miyazaki, A. Shibayama, J. Intell. Mater. Syst. Struct. 13 (2002) 405. [2] S. Sudo, H. Hashimoto, A. Ikeda, JSME Int. J. 32 (1989) 47. [3] S. Sudo, A. Nakagawa, K. Shimada, H. Nishiyama, Magnetohydrodynamics 39 (2003) 359.
ARTICLE IN PRESS 324
S. Sudo et al. / Journal of Magnetism and Magnetic Materials 289 (2005) 321–324
[4] V.I. Arkipenko, Yu.D. Barkov, V.G. Bashtovoi, Magnetohydrodynamics 14 (1979) 131. [5] V.G. Bashtovoi, A.R. Reks, Ye.M. Tayts, HEAT TRANSFER-Soviet Research 17 (1985) 79.
[6] B. Jeyadevan, I. Nakatani, J. Magn. Magn. Mater. 201 (1999) 62. [7] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, Cambridge, 1985.